عرض مصدر جدول تفكيك الأعداد الصحيحة الغاوسية

{{يتيمة|تاريخ=ديسمبر 2015}}

في [[نظرية الأعداد]]، '''عدد طبيعي غاوسي''' هو [[عدد مركب|عدد عقدي]] جزءه الحقيقي وجزءه التخيلي هما عددان [[عدد صحيح|صحيحان]].<ref>{{استشهاد ويب| مسار = http://mathworld.wolfram.com/GaussianPrime.html | عنوان = معلومات عن جدول تفكيك الأعداد الصحيحة الغاوسية على موقع mathworld.wolfram.com | ناشر = mathworld.wolfram.com| مسار أرشيف = https://web.archive.org/web/20181217052109/http://mathworld.wolfram.com/GaussianPrime.html | تاريخ أرشيف = 17 ديسمبر 2018 }}</ref>

:<math>\mathbb{Z}[i]=\{a+bi \mid a,b\in \mathbb{Z} \}</math> حيث <math> i = \sqrt{-1}</math>.

[[ملف:Gaussian integer lattice.svg|thumb|217px|أعداد صحيحة غاوسية as [[مشبك (زمرة)|مشبك النقط]] في [[مستوى عقدي|المستوى العقدي]]]]
== معضلات لم تحلحل بعد ==
[[ملف:gauss-primes-768x768.png|170px|thumb|التوزيع في المستوى للأعداد الأولية الغاوسية الصغيرة]]
تسأل [[معضلة الدائرة لغاوس]] عن عدد النقط في [[مشبك (زمرة)|مشبك النقط]] الموجودات داخل دائرة ما مركزها هو مركز المعلم. يكافئ هذا السؤال ما يلي: كم عدد الأعداد الصحيحة الغاوسية الذين [[معيار (رياضيات)|معيارهم]] لا يتجاوز قيمة معينة ؟

==التفكيك==
{| class="wikitable sortable" style="float:left; margin-right:1em"
! المعيار || العدد الصحيح || العامل
|-
| 2 || {{math| 1+''i''}} || (p)
|-
| 4 || {{math| 2}} || {{math| −''i''&middot;(1+''i'')<sup>2</sup>}}
|-
| 5 || {{math| 1+2''i''}} <br />{{math| 2+''i''}} || (p) <br />(p)
|-
| 8 || {{math| 2+2''i''}} || {{math| −''i''&middot;(1+''i'')<sup>3</sup>}}
|-
| 9 || {{math| 3}} || (p)
|-
| 10 || {{math| 1+3''i''}} <br />{{math| 3+''i''}} || {{math| (1+''i'')&middot;(2+''i'')}} <br />{{math| (1+''i'')&middot;(2−''i'')}}
|-
| 13 || {{math| 2+3''i''}} <br />{{math| 3+2''i''}} || (p) <br />(p)
|-
| 16 || {{math| 4}} || {{math| −(1+''i'')<sup>4</sup>}}
|-
| 17 || {{math| 1+4''i''}} <br />{{math| 4+''i''}} || (p) <br />(p)
|-
| 18 || {{math| 3+3''i''}} || {{math| (1+''i'')&middot;3}}
|-
| 20 || {{math| 2+4''i''}} <br />{{math| 4+2''i''}} || {{math| (1+''i'')<sup>2</sup>&middot;(2−''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2+''i'')}}
|-
| 25 || {{math| 3+4''i''}} <br />{{math| 4+3''i''}} <br />{{math| 5}} || {{math| (2+''i'')<sup>2</sup>}} <br />{{math| ''i''&middot;(2−''i'')<sup>2</sup>}} <br />{{math| (2+''i'')&middot;(2−''i'')}}
|-
| 26 || {{math| 1+5''i''}} <br />{{math| 5+''i''}} || {{math| (1+''i'')&middot;(3+2''i'')}} <br />{{math| (1+''i'')&middot;(3−2''i'')}}
|-
| 29 || {{math| 2+5''i''}} <br />{{math| 5+2''i''}} || (p) <br />(p)
|-
| 32 || {{math| 4+4''i''}} || {{math| −(1+''i'')<sup>5</sup>}}
|-
| 34 || {{math| 3+5''i''}} <br />{{math| 5+3''i''}} || {{math| (1+''i'')&middot;(4+''i'')}} <br />{{math| (1+''i'')&middot;(4−''i'')}}
|-
| 36 || {{math| 6}} || {{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;3}}
|-
| 37 || {{math| 1+6''i''}} <br />{{math| 6+''i''}} || (p) <br />(p)
|-
| 40 || {{math| 2+6''i''}} <br />{{math| 6+2''i''}} || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(2+''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(2−''i'')}}
|-
| 41 || {{math| 4+5''i''}} <br />{{math| 5+4''i''}} || (p) <br />(p)
|-
| 45 || {{math| 3+6''i''}} <br />{{math| 6+3''i''}} || {{math| ''i''&middot;(2−''i'')&middot;3}} <br />{{math| (2+''i'')&middot;3}}
|-
| 49 || {{math| 7}} || (p)
|-
| 50 || {{math| 1+7''i''}} <br />{{math| 5+5''i''}} <br />{{math| 7+''i''}} || {{math| ''i''&middot;(1+''i'')&middot;(2−''i'')<sup>2</sup>}} <br />{{math| (1+''i'')&middot;(2+''i'')&middot;(2−''i'')}} <br />{{math| −''i''&middot;(1+''i'')&middot;(2+''i'')<sup>2</sup>}}
|-
| 52 || {{math| 4+6''i''}} <br />{{math| 6+4''i''}} || {{math| (1+''i'')<sup>2</sup>&middot;(3−2''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(3+2''i'')}}
|-
| 53 || {{math| 2+7''i''}} <br />{{math| 7+2''i''}} || (p) <br />(p)
|-
| 58 || {{math| 3+7''i''}} <br />{{math| 7+3''i''}} || {{math| (1+''i'')&middot;(5+2''i'')}} <br />{{math| (1+''i'')&middot;(5−2''i'')}}
|-
| 61 || {{math| 5+6''i''}} <br />{{math| 6+5''i''}} || (p) <br />(p)
|-
| 64 || {{math| 8}} || {{math| ''i''&middot;(1+''i'')<sup>6</sup>}}
|-
| 65 || {{math| 1+8''i''}} <br />{{math| 4+7''i''}} <br />{{math| 7+4''i''}} <br />{{math| 8+''i''}} || {{math| ''i''&middot;(2+''i'')&middot;(3−2''i'')}} <br />{{math| (2+''i'')&middot;(3+2''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(3−2''i'')}} <br />{{math| (2−''i'')&middot;(3+2''i'')}}
|-
| 68 || {{math| 2+8''i''}} <br />{{math| 8+2''i''}} || {{math| (1+''i'')<sup>2</sup>&middot;(4−''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(4+''i'')}}
|-
| 72 || {{math| 6+6''i''}} || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;3}}
|-
| 73 || {{math| 3+8''i''}} <br />{{math| 8+3''i''}} || (p) <br />(p)
|-
| 74 || {{math| 5+7''i''}} <br />{{math| 7+5''i''}} || {{math| (1+''i'')&middot;(6+''i'')}} <br />{{math| (1+''i'')&middot;(6−''i'')}}
|-
| 80 || {{math| 4+8''i''}} <br />{{math| 8+4''i''}} || {{math| −''i''&middot;(1+''i'')<sup>4</sup>&middot;(2−''i'')}} <br />{{math| −(1+''i'')<sup>4</sup>&middot;(2+''i'')}}
|-
| 81 || {{math| 9}} || {{math| 3<sup>2</sup>}}
|-
| 82 || {{math| 1+9''i''}} <br />{{math| 9+''i''}} || {{math| (1+''i'')&middot;(5+4''i'')}} <br />{{math| (1+''i'')&middot;(5−4''i'')}}
|-
| 85 || {{math| 2+9''i''}} <br />{{math| 6+7''i''}} <br />{{math| 7+6''i''}} <br />{{math| 9+2''i''}} || {{math| ''i''&middot;(2−''i'')&middot;(4+''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(4−''i'')}} <br />{{math| (2+''i'')&middot;(4+''i'')}} <br />{{math| (2+''i'')&middot;(4−''i'')}}
|-
| 89 || {{math| 5+8''i''}} <br />{{math| 8+5''i''}} || (p) <br />(p)
|-
| 90 || {{math| 3+9''i''}} <br />{{math| 9+3''i''}} || {{math| (1+''i'')&middot;(2+''i'')&middot;3}} <br />{{math| (1+''i'')&middot;(2−''i'')&middot;3}}
|-
| 97 || {{math| 4+9''i''}} <br />{{math| 9+4''i''}} || (p) <br />(p)
|-
| 98 || {{math| 7+7''i''}} || {{math| (1+''i'')&middot;7}}
|-
| 100 || {{math| 6+8''i''}} <br />{{math| 8+6''i''}} <br />{{math| 10}} || {{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2+''i'')<sup>2</sup>}} <br />{{math| (1+''i'')<sup>2</sup>&middot;(2−''i'')<sup>2</sup>}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2+''i'')&middot;(2−''i'')}}
|-
| 101 || {{math| 1+10''i''}} <br />{{math| 10+''i''}} || (p) <br />(p)
|-
| 104 || {{math| 2+10''i''}} <br />{{math| 10+2''i''}} || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(3+2''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(3−2''i'')}}
|-
| 106 || {{math| 5+9''i''}} <br />{{math| 9+5''i''}} || {{math| (1+''i'')&middot;(7+2''i'')}} <br />{{math| (1+''i'')&middot;(7−2''i'')}}
|-
| 109 || {{math| 3+10''i''}} <br />{{math| 10+3''i''}} || (p) <br />(p)
|-
| 113 || {{math| 7+8''i''}} <br />{{math| 8+7''i''}} || (p) <br />(p)
|-
| 116 || {{math| 4+10''i''}} <br />{{math| 10+4''i''}} || {{math| (1+''i'')<sup>2</sup>&middot;(5−2''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(5+2''i'')}}
|-
| 117 || {{math| 6+9''i''}} <br />{{math| 9+6''i''}} || {{math| ''i''&middot;3&middot;(3−2''i'')}} <br />{{math| 3&middot;(3+2''i'')}}
|-
| 121 || {{math| 11}} || (p)
|-
| 122  || {{math| 1+11''i''}} <br />{{math| 11+''i''}}  || {{math| (1+''i'')&middot;(6+5''i'')}} <br />{{math| (1+''i'')&middot;(6−5''i'')}}
|-
| 125  || {{math| 2+11''i''}} <br />{{math| 5+10''i''}} <br />{{math| 10+5''i''}} <br />{{math| 11+2''i''}}  || {{math| (2+''i'')<sup>3</sup>}} <br />{{math| ''i''&middot;(2+''i'')&middot;(2−''i'')<sup>2</sup>}} <br />{{math| (2+''i'')<sup>2</sup>&middot;(2−''i'')}} <br />{{math| ''i''&middot;(2−''i'')<sup>3</sup>}}
|-
| 128  || {{math| 8+8''i''}}  || {{math| ''i''&middot;(1+''i'')<sup>7</sup>}}
|-
| 130  || {{math| 3+11''i''}} <br />{{math| 7+9''i''}} <br />{{math| 9+7''i''}} <br />{{math| 11+3''i''}}  || {{math| ''i''&middot;(1+''i'')&middot;(2−''i'')&middot;(3−2''i'')}} <br />{{math| (1+''i'')&middot;(2−''i'')&middot;(3+2''i'')}} <br />{{math| (1+''i'')&middot;(2+''i'')&middot;(3−2''i'')}} <br />{{math| −''i''&middot;(1+''i'')&middot;(2+''i'')&middot;(3+2''i'')}}
|-
| 136  || {{math| 6+10''i''}} <br />{{math| 10+6''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(4+''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(4−''i'')}}
|-
| 137  || {{math| 4+11''i''}} <br />{{math| 11+4''i''}}  || (p) <br />(p)
|-
| 144  || {{math| 12}}  || {{math| −(1+''i'')<sup>4</sup>&middot;3}}
|-
| 145  || {{math| 1+12''i''}} <br />{{math| 8+9''i''}} <br />{{math| 9+8''i''}} <br />{{math| 12+''i''}}  || {{math| ''i''&middot;(2−''i'')&middot;(5+2''i'')}} <br />{{math| (2+''i'')&middot;(5+2''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(5−2''i'')}} <br />{{math| (2+''i'')&middot;(5−2''i'')}}
|-
| 146  || {{math| 5+11''i''}} <br />{{math| 11+5''i''}}  || {{math| (1+''i'')&middot;(8+3''i'')}} <br />{{math| (1+''i'')&middot;(8−3''i'')}}
|-
| 148  || {{math| 2+12''i''}} <br />{{math| 12+2''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(6−''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(6+''i'')}}
|-
| 149  || {{math| 7+10''i''}} <br />{{math| 10+7''i''}}  || (p) <br />(p)
|-
| 153  || {{math| 3+12''i''}} <br />{{math| 12+3''i''}}  || {{math| ''i''&middot;3&middot;(4−''i'')}} <br />{{math| 3&middot;(4+''i'')}}
|-
| 157  || {{math| 6+11''i''}} <br />{{math| 11+6''i''}}  || (p) <br />(p)
|-
| 160  || {{math| 4+12''i''}} <br />{{math| 12+4''i''}}  || {{math| −(1+''i'')<sup>5</sup>&middot;(2+''i'')}} <br />{{math| −(1+''i'')<sup>5</sup>&middot;(2−''i'')}}
|-
| 162  || {{math| 9+9''i''}}  || {{math| (1+''i'')&middot;3<sup>2</sup>}}
|-
| 164  || {{math| 8+10''i''}} <br />{{math| 10+8''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(5−4''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(5+4''i'')}}
|-
| 169  || {{math| 5+12''i''}} <br />{{math| 12+5''i''}} <br />{{math| 13}}  || {{math| (3+2''i'')<sup>2</sup>}} <br />{{math| ''i''&middot;(3−2''i'')<sup>2</sup>}} <br />{{math| (3+2''i'')&middot;(3−2''i'')}}
|-
| 170  || {{math| 1+13''i''}} <br />{{math| 7+11''i''}} <br />{{math| 11+7''i''}} <br />{{math| 13+''i''}}  || {{math| (1+''i'')&middot;(2+''i'')&middot;(4+''i'')}} <br />{{math| (1+''i'')&middot;(2+''i'')&middot;(4−''i'')}} <br />{{math| (1+''i'')&middot;(2−''i'')&middot;(4+''i'')}} <br />{{math| (1+''i'')&middot;(2−''i'')&middot;(4−''i'')}}
|-
| 173  || {{math| 2+13''i''}} <br />{{math| 13+2''i''}}  || (p) <br />(p)
|-
| 178  || {{math| 3+13''i''}} <br />{{math| 13+3''i''}}  || {{math| (1+''i'')&middot;(8+5''i'')}} <br />{{math| (1+''i'')&middot;(8−5''i'')}}
|-
| 180  || {{math| 6+12''i''}} <br />{{math| 12+6''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(2−''i'')&middot;3}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2+''i'')&middot;3}}
|-
| 181  || {{math| 9+10''i''}} <br />{{math| 10+9''i''}}  || (p) <br />(p)
|-
| 185  || {{math| 4+13''i''}} <br />{{math| 8+11''i''}} <br />{{math| 11+8''i''}} <br />{{math| 13+4''i''}}  || {{math| ''i''&middot;(2−''i'')&middot;(6+''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(6−''i'')}} <br />{{math| (2+''i'')&middot;(6+''i'')}} <br />{{math| (2+''i'')&middot;(6−''i'')}}
|-
| 193  || {{math| 7+12''i''}} <br />{{math| 12+7''i''}}  || (p) <br />(p)
|-
| 194  || {{math| 5+13''i''}} <br />{{math| 13+5''i''}}  || {{math| (1+''i'')&middot;(9+4''i'')}} <br />{{math| (1+''i'')&middot;(9−4''i'')}}
|-
| 196  || {{math| 14}}  || {{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;7}}
|-
| 197  || {{math| 1+14''i''}} <br />{{math| 14+''i''}}  || (p) <br />(p)
|-
| 200  || {{math| 2+14''i''}} <br />{{math| 10+10''i''}} <br />{{math| 14+2''i''}}  || {{math| (1+''i'')<sup>3</sup>&middot;(2−''i'')<sup>2</sup>}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(2+''i'')&middot;(2−''i'')}} <br />{{math| −(1+''i'')<sup>3</sup>&middot;(2+''i'')<sup>2</sup>}}
|-
| 202  || {{math| 9+11''i''}} <br />{{math| 11+9''i''}}  || {{math| (1+''i'')&middot;(10+''i'')}} <br />{{math| (1+''i'')&middot;(10−''i'')}}
|-
| 205  || {{math| 3+14''i''}} <br />{{math| 6+13''i''}} <br />{{math| 13+6''i''}} <br />{{math| 14+3''i''}}  || {{math| ''i''&middot;(2+''i'')&middot;(5−4''i'')}} <br />{{math| (2+''i'')&middot;(5+4''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(5−4''i'')}} <br />{{math| (2−''i'')&middot;(5+4''i'')}}
|-
| 208  || {{math| 8+12''i''}} <br />{{math| 12+8''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>4</sup>&middot;(3−2''i'')}} <br />{{math| −(1+''i'')<sup>4</sup>&middot;(3+2''i'')}}
|-
| 212  || {{math| 4+14''i''}} <br />{{math| 14+4''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(7−2''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(7+2''i'')}}
|-
| 218  || {{math| 7+13''i''}} <br />{{math| 13+7''i''}}  || {{math| (1+''i'')&middot;(10+3''i'')}} <br />{{math| (1+''i'')&middot;(10−3''i'')}}
|-
| 221  || {{math| 5+14''i''}} <br />{{math| 10+11''i''}} <br />{{math| 11+10''i''}} <br />{{math| 14+5''i''}}  || {{math| ''i''&middot;(3−2''i'')&middot;(4+''i'')}} <br />{{math| (3+2''i'')&middot;(4+''i'')}} <br />{{math| ''i''&middot;(3−2''i'')&middot;(4−''i'')}} <br />{{math| (3+2''i'')&middot;(4−''i'')}}
|-
| 225  || {{math| 9+12''i''}} <br />{{math| 12+9''i''}} <br />{{math| 15}}  || {{math| (2+''i'')<sup>2</sup>&middot;3}} <br />{{math| ''i''&middot;(2−''i'')<sup>2</sup>&middot;3}} <br />{{math| (2+''i'')&middot;(2−''i'')&middot;3}}
|-
| 226  || {{math| 1+15''i''}} <br />{{math| 15+''i''}}  || {{math| (1+''i'')&middot;(8+7''i'')}} <br />{{math| (1+''i'')&middot;(8−7''i'')}}
|-
| 229  || {{math| 2+15''i''}} <br />{{math| 15+2''i''}}  || (p) <br />(p)
|-
| 232  || {{math| 6+14''i''}} <br />{{math| 14+6''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(5+2''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(5−2''i'')}}
|-
| 233  || {{math| 8+13''i''}} <br />{{math| 13+8''i''}}  || (p) <br />(p)
|-
| 234  || {{math| 3+15''i''}} <br />{{math| 15+3''i''}}  || {{math| (1+''i'')&middot;3&middot;(3+2''i'')}} <br />{{math| (1+''i'')&middot;3&middot;(3−2''i'')}}
|-
| 241  || {{math| 4+15''i''}} <br />{{math| 15+4''i''}}  || (p) <br />(p)
|-
| 242  || {{math| 11+11''i''}}  || {{math| (1+''i'')&middot;11}}
|-
| 244  || {{math| 10+12''i''}} <br />{{math| 12+10''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(6−5''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(6+5''i'')}}
|-
| 245  || {{math| 7+14''i''}} <br />{{math| 14+7''i''}}  || {{math| ''i''&middot;(2−''i'')&middot;7}} <br />{{math| (2+''i'')&middot;7}}
|-
| 250  || {{math| 5+15''i''}} <br />{{math| 9+13''i''}} <br />{{math| 13+9''i''}} <br />{{math| 15+5''i''}}  || {{math| (1+''i'')&middot;(2+''i'')<sup>2</sup>&middot;(2−''i'')}} <br />{{math| ''i''&middot;(1+''i'')&middot;(2−''i'')<sup>3</sup>}} <br />{{math| −''i''&middot;(1+''i'')&middot;(2+''i'')<sup>3</sup>}} <br />{{math| (1+''i'')&middot;(2+''i'')&middot;(2−''i'')<sup>2</sup>}}
|}
{| class="wikitable sortable" style="float:left; margin-right:1em"
! المعيار || العدد الصحيح|| العوامل
|-
| 256  || {{math| 16}}  || {{math| (1+''i'')<sup>8</sup>}}
|-
| 257  || {{math| 1+16''i''}} <br />{{math| 16+''i''}}  || (p) <br />(p)
|-
| 260  || {{math| 2+16''i''}} <br />{{math| 8+14''i''}} <br />{{math| 14+8''i''}} <br />{{math| 16+2''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(2+''i'')&middot;(3−2''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2+''i'')&middot;(3+2''i'')}} <br />{{math| (1+''i'')<sup>2</sup>&middot;(2−''i'')&middot;(3−2''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2−''i'')&middot;(3+2''i'')}}
|-
| 261  || {{math| 6+15''i''}} <br />{{math| 15+6''i''}}  || {{math| ''i''&middot;3&middot;(5−2''i'')}} <br />{{math| 3&middot;(5+2''i'')}}
|-
| 265  || {{math| 3+16''i''}} <br />{{math| 11+12''i''}} <br />{{math| 12+11''i''}} <br />{{math| 16+3''i''}}  || {{math| ''i''&middot;(2−''i'')&middot;(7+2''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(7−2''i'')}} <br />{{math| (2+''i'')&middot;(7+2''i'')}} <br />{{math| (2+''i'')&middot;(7−2''i'')}}
|-
| 269  || {{math| 10+13''i''}} <br />{{math| 13+10''i''}}  || (p) <br />(p)
|-
| 272  || {{math| 4+16''i''}} <br />{{math| 16+4''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>4</sup>&middot;(4−''i'')}} <br />{{math| −(1+''i'')<sup>4</sup>&middot;(4+''i'')}}
|-
| 274  || {{math| 7+15''i''}} <br />{{math| 15+7''i''}}  || {{math| (1+''i'')&middot;(11+4''i'')}} <br />{{math| (1+''i'')&middot;(11−4''i'')}}
|-
| 277  || {{math| 9+14''i''}} <br />{{math| 14+9''i''}}  || (p) <br />(p)
|-
| 281  || {{math| 5+16''i''}} <br />{{math| 16+5''i''}}  || (p) <br />(p)
|-
| 288  || {{math| 12+12''i''}}  || {{math| −(1+''i'')<sup>5</sup>&middot;3}}
|-
| 289  || {{math| 8+15''i''}} <br />{{math| 15+8''i''}} <br />{{math| 17}}  || {{math| ''i''&middot;(4−''i'')<sup>2</sup>}} <br />{{math| (4+''i'')<sup>2</sup>}} <br />{{math| (4+''i'')&middot;(4−''i'')}}
|-
| 290  || {{math| 1+17''i''}} <br />{{math| 11+13''i''}} <br />{{math| 13+11''i''}} <br />{{math| 17+''i''}}  || {{math| ''i''&middot;(1+''i'')&middot;(2−''i'')&middot;(5−2''i'')}} <br />{{math| (1+''i'')&middot;(2+''i'')&middot;(5−2''i'')}} <br />{{math| (1+''i'')&middot;(2−''i'')&middot;(5+2''i'')}} <br />{{math| −''i''&middot;(1+''i'')&middot;(2+''i'')&middot;(5+2''i'')}}
|-
| 292  || {{math| 6+16''i''}} <br />{{math| 16+6''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(8−3''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(8+3''i'')}}
|-
| 293  || {{math| 2+17''i''}} <br />{{math| 17+2''i''}}  || (p) <br />(p)
|-
| 296  || {{math| 10+14''i''}} <br />{{math| 14+10''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(6+''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(6−''i'')}}
|-
| 298  || {{math| 3+17''i''}} <br />{{math| 17+3''i''}}  || {{math| (1+''i'')&middot;(10+7''i'')}} <br />{{math| (1+''i'')&middot;(10−7''i'')}}
|-
| 305  || {{math| 4+17''i''}} <br />{{math| 7+16''i''}} <br />{{math| 16+7''i''}} <br />{{math| 17+4''i''}}  || {{math| ''i''&middot;(2+''i'')&middot;(6−5''i'')}} <br />{{math| (2+''i'')&middot;(6+5''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(6−5''i'')}} <br />{{math| (2−''i'')&middot;(6+5''i'')}}
|-
| 306  || {{math| 9+15''i''}} <br />{{math| 15+9''i''}}  || {{math| (1+''i'')&middot;3&middot;(4+''i'')}} <br />{{math| (1+''i'')&middot;3&middot;(4−''i'')}}
|-
| 313  || {{math| 12+13''i''}} <br />{{math| 13+12''i''}}  || (p) <br />(p)
|-
| 314  || {{math| 5+17''i''}} <br />{{math| 17+5''i''}}  || {{math| (1+''i'')&middot;(11+6''i'')}} <br />{{math| (1+''i'')&middot;(11−6''i'')}}
|-
| 317  || {{math| 11+14''i''}} <br />{{math| 14+11''i''}}  || (p) <br />(p)
|-
| 320  || {{math| 8+16''i''}} <br />{{math| 16+8''i''}}  || {{math| −(1+''i'')<sup>6</sup>&middot;(2−''i'')}} <br />{{math| ''i''&middot;(1+''i'')<sup>6</sup>&middot;(2+''i'')}}
|-
| 324  || {{math| 18}}  || {{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;3<sup>2</sup>}}
|-
| 325  || {{math| 1+18''i''}} <br />{{math| 6+17''i''}} <br />{{math| 10+15''i''}} <br />{{math| 15+10''i''}} <br />{{math| 17+6''i''}} <br />{{math| 18+''i''}}  || {{math| (2+''i'')<sup>2</sup>&middot;(3+2''i'')}} <br />{{math| ''i''&middot;(2−''i'')<sup>2</sup>&middot;(3+2''i'')}} <br />{{math| ''i''&middot;(2+''i'')&middot;(2−''i'')&middot;(3−2''i'')}} <br />{{math| (2+''i'')&middot;(2−''i'')&middot;(3+2''i'')}} <br />{{math| (2+''i'')<sup>2</sup>&middot;(3−2''i'')}} <br />{{math| ''i''&middot;(2−''i'')<sup>2</sup>&middot;(3−2''i'')}}
|-
| 328  || {{math| 2+18''i''}} <br />{{math| 18+2''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(5+4''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(5−4''i'')}}
|-
| 333  || {{math| 3+18''i''}} <br />{{math| 18+3''i''}}  || {{math| ''i''&middot;3&middot;(6−''i'')}} <br />{{math| 3&middot;(6+''i'')}}
|-
| 337  || {{math| 9+16''i''}} <br />{{math| 16+9''i''}}  || (p) <br />(p)
|-
| 338  || {{math| 7+17''i''}} <br />{{math| 13+13''i''}} <br />{{math| 17+7''i''}}  || {{math| ''i''&middot;(1+''i'')&middot;(3−2''i'')<sup>2</sup>}} <br />{{math| (1+''i'')&middot;(3+2''i'')&middot;(3−2''i'')}} <br />{{math| −''i''&middot;(1+''i'')&middot;(3+2''i'')<sup>2</sup>}}
|-
| 340  || {{math| 4+18''i''}} <br />{{math| 12+14''i''}} <br />{{math| 14+12''i''}} <br />{{math| 18+4''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(2−''i'')&middot;(4+''i'')}} <br />{{math| (1+''i'')<sup>2</sup>&middot;(2−''i'')&middot;(4−''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2+''i'')&middot;(4+''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2+''i'')&middot;(4−''i'')}}
|-
| 346  || {{math| 11+15''i''}} <br />{{math| 15+11''i''}}  || {{math| (1+''i'')&middot;(13+2''i'')}} <br />{{math| (1+''i'')&middot;(13−2''i'')}}
|-
| 349  || {{math| 5+18''i''}} <br />{{math| 18+5''i''}}  || (p) <br />(p)
|-
| 353  || {{math| 8+17''i''}} <br />{{math| 17+8''i''}}  || (p) <br />(p)
|-
| 356  || {{math| 10+16''i''}} <br />{{math| 16+10''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(8−5''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(8+5''i'')}}
|-
| 360  || {{math| 6+18''i''}} <br />{{math| 18+6''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(2+''i'')&middot;3}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(2−''i'')&middot;3}}
|-
| 361  || {{math| 19}}  || (p)
|-
| 362  || {{math| 1+19''i''}} <br />{{math| 19+''i''}}  || {{math| (1+''i'')&middot;(10+9''i'')}} <br />{{math| (1+''i'')&middot;(10−9''i'')}}
|-
| 365  || {{math| 2+19''i''}} <br />{{math| 13+14''i''}} <br />{{math| 14+13''i''}} <br />{{math| 19+2''i''}}  || {{math| ''i''&middot;(2−''i'')&middot;(8+3''i'')}} <br />{{math| (2+''i'')&middot;(8+3''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(8−3''i'')}} <br />{{math| (2+''i'')&middot;(8−3''i'')}}
|-
| 369  || {{math| 12+15''i''}} <br />{{math| 15+12''i''}}  || {{math| ''i''&middot;3&middot;(5−4''i'')}} <br />{{math| 3&middot;(5+4''i'')}}
|-
| 370  || {{math| 3+19''i''}} <br />{{math| 9+17''i''}} <br />{{math| 17+9''i''}} <br />{{math| 19+3''i''}}  || {{math| (1+''i'')&middot;(2+''i'')&middot;(6+''i'')}} <br />{{math| (1+''i'')&middot;(2+''i'')&middot;(6−''i'')}} <br />{{math| (1+''i'')&middot;(2−''i'')&middot;(6+''i'')}} <br />{{math| (1+''i'')&middot;(2−''i'')&middot;(6−''i'')}}
|-
| 373  || {{math| 7+18''i''}} <br />{{math| 18+7''i''}}  || (p) <br />(p)
|-
| 377  || {{math| 4+19''i''}} <br />{{math| 11+16''i''}} <br />{{math| 16+11''i''}} <br />{{math| 19+4''i''}}  || {{math| ''i''&middot;(3−2''i'')&middot;(5+2''i'')}} <br />{{math| (3+2''i'')&middot;(5+2''i'')}} <br />{{math| ''i''&middot;(3−2''i'')&middot;(5−2''i'')}} <br />{{math| (3+2''i'')&middot;(5−2''i'')}}
|-
| 386  || {{math| 5+19''i''}} <br />{{math| 19+5''i''}}  || {{math| (1+''i'')&middot;(12+7''i'')}} <br />{{math| (1+''i'')&middot;(12−7''i'')}}
|-
| 388  || {{math| 8+18''i''}} <br />{{math| 18+8''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(9−4''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(9+4''i'')}}
|-
| 389  || {{math| 10+17''i''}} <br />{{math| 17+10''i''}}  || (p) <br />(p)
|-
| 392  || {{math| 14+14''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;7}}
|-
| 394  || {{math| 13+15''i''}} <br />{{math| 15+13''i''}}  || {{math| (1+''i'')&middot;(14+''i'')}} <br />{{math| (1+''i'')&middot;(14−''i'')}}
|-
| 397  || {{math| 6+19''i''}} <br />{{math| 19+6''i''}}  || (p) <br />(p)
|-
| 400  || {{math| 12+16''i''}} <br />{{math| 16+12''i''}} <br />{{math| 20}}  || {{math| −(1+''i'')<sup>4</sup>&middot;(2+''i'')<sup>2</sup>}} <br />{{math| −''i''&middot;(1+''i'')<sup>4</sup>&middot;(2−''i'')<sup>2</sup>}} <br />{{math| −(1+''i'')<sup>4</sup>&middot;(2+''i'')&middot;(2−''i'')}}
|-
| 401  || {{math| 1+20''i''}} <br />{{math| 20+''i''}}  || (p) <br />(p)
|-
| 404  || {{math| 2+20''i''}} <br />{{math| 20+2''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(10−''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(10+''i'')}}
|-
| 405  || {{math| 9+18''i''}} <br />{{math| 18+9''i''}}  || {{math| ''i''&middot;(2−''i'')&middot;3<sup>2</sup>}} <br />{{math| (2+''i'')&middot;3<sup>2</sup>}}
|-
| 409  || {{math| 3+20''i''}} <br />{{math| 20+3''i''}}  || (p) <br />(p)
|-
| 410  || {{math| 7+19''i''}} <br />{{math| 11+17''i''}} <br />{{math| 17+11''i''}} <br />{{math| 19+7''i''}}  || {{math| ''i''&middot;(1+''i'')&middot;(2−''i'')&middot;(5−4''i'')}} <br />{{math| (1+''i'')&middot;(2−''i'')&middot;(5+4''i'')}} <br />{{math| (1+''i'')&middot;(2+''i'')&middot;(5−4''i'')}} <br />{{math| −''i''&middot;(1+''i'')&middot;(2+''i'')&middot;(5+4''i'')}}
|-
| 416  || {{math| 4+20''i''}} <br />{{math| 20+4''i''}}  || {{math| −(1+''i'')<sup>5</sup>&middot;(3+2''i'')}} <br />{{math| −(1+''i'')<sup>5</sup>&middot;(3−2''i'')}}
|-
| 421  || {{math| 14+15''i''}} <br />{{math| 15+14''i''}}  || (p) <br />(p)
|-
| 424  || {{math| 10+18''i''}} <br />{{math| 18+10''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(7+2''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(7−2''i'')}}
|-
| 425  || {{math| 5+20''i''}} <br />{{math| 8+19''i''}} <br />{{math| 13+16''i''}} <br />{{math| 16+13''i''}} <br />{{math| 19+8''i''}} <br />{{math| 20+5''i''}}  || {{math| ''i''&middot;(2+''i'')&middot;(2−''i'')&middot;(4−''i'')}} <br />{{math| (2+''i'')<sup>2</sup>&middot;(4+''i'')}} <br />{{math| ''i''&middot;(2−''i'')<sup>2</sup>&middot;(4+''i'')}} <br />{{math| (2+''i'')<sup>2</sup>&middot;(4−''i'')}} <br />{{math| ''i''&middot;(2−''i'')<sup>2</sup>&middot;(4−''i'')}} <br />{{math| (2+''i'')&middot;(2−''i'')&middot;(4+''i'')}}
|-
| 433  || {{math| 12+17''i''}} <br />{{math| 17+12''i''}}  || (p) <br />(p)
|-
| 436  || {{math| 6+20''i''}} <br />{{math| 20+6''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(10−3''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(10+3''i'')}}
|-
| 441  || {{math| 21}}  || {{math| 3&middot;7}}
|-
| 442  || {{math| 1+21''i''}} <br />{{math| 9+19''i''}} <br />{{math| 19+9''i''}} <br />{{math| 21+''i''}}  || {{math| ''i''&middot;(1+''i'')&middot;(3−2''i'')&middot;(4−''i'')}} <br />{{math| (1+''i'')&middot;(3+2''i'')&middot;(4−''i'')}} <br />{{math| (1+''i'')&middot;(3−2''i'')&middot;(4+''i'')}} <br />{{math| −''i''&middot;(1+''i'')&middot;(3+2''i'')&middot;(4+''i'')}}
|-
| 445  || {{math| 2+21''i''}} <br />{{math| 11+18''i''}} <br />{{math| 18+11''i''}} <br />{{math| 21+2''i''}}  || {{math| ''i''&middot;(2+''i'')&middot;(8−5''i'')}} <br />{{math| (2+''i'')&middot;(8+5''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(8−5''i'')}} <br />{{math| (2−''i'')&middot;(8+5''i'')}}
|-
| 449  || {{math| 7+20''i''}} <br />{{math| 20+7''i''}}  || (p) <br />(p)
|-
| 450  || {{math| 3+21''i''}} <br />{{math| 15+15''i''}} <br />{{math| 21+3''i''}}  || {{math| ''i''&middot;(1+''i'')&middot;(2−''i'')<sup>2</sup>&middot;3}} <br />{{math| (1+''i'')&middot;(2+''i'')&middot;(2−''i'')&middot;3}} <br />{{math| −''i''&middot;(1+''i'')&middot;(2+''i'')<sup>2</sup>&middot;3}}
|-
| 452  || {{math| 14+16''i''}} <br />{{math| 16+14''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(8−7''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(8+7''i'')}}
|-
| 457  || {{math| 4+21''i''}} <br />{{math| 21+4''i''}}  || (p) <br />(p)
|-
| 458  || {{math| 13+17''i''}} <br />{{math| 17+13''i''}}  || {{math| (1+''i'')&middot;(15+2''i'')}} <br />{{math| (1+''i'')&middot;(15−2''i'')}}
|-
| 461  || {{math| 10+19''i''}} <br />{{math| 19+10''i''}}  || (p) <br />(p)
|-
| 464  || {{math| 8+20''i''}} <br />{{math| 20+8''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>4</sup>&middot;(5−2''i'')}} <br />{{math| −(1+''i'')<sup>4</sup>&middot;(5+2''i'')}}
|-
| 466  || {{math| 5+21''i''}} <br />{{math| 21+5''i''}}  || {{math| (1+''i'')&middot;(13+8''i'')}} <br />{{math| (1+''i'')&middot;(13−8''i'')}}
|-
| 468  || {{math| 12+18''i''}} <br />{{math| 18+12''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;3&middot;(3−2''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;3&middot;(3+2''i'')}}
|-
| 477  || {{math| 6+21''i''}} <br />{{math| 21+6''i''}}  || {{math| ''i''&middot;3&middot;(7−2''i'')}} <br />{{math| 3&middot;(7+2''i'')}}
|-
| 481  || {{math| 9+20''i''}} <br />{{math| 15+16''i''}} <br />{{math| 16+15''i''}} <br />{{math| 20+9''i''}}  || {{math| ''i''&middot;(3−2''i'')&middot;(6+''i'')}} <br />{{math| ''i''&middot;(3−2''i'')&middot;(6−''i'')}} <br />{{math| (3+2''i'')&middot;(6+''i'')}} <br />{{math| (3+2''i'')&middot;(6−''i'')}}
|-
| 482  || {{math| 11+19''i''}} <br />{{math| 19+11''i''}}  || {{math| (1+''i'')&middot;(15+4''i'')}} <br />{{math| (1+''i'')&middot;(15−4''i'')}}
|-
| 484  || {{math| 22}}  || {{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;11}}
|-
| 485  || {{math| 1+22''i''}} <br />{{math| 14+17''i''}} <br />{{math| 17+14''i''}} <br />{{math| 22+''i''}}  || {{math| ''i''&middot;(2−''i'')&middot;(9+4''i'')}} <br />{{math| (2+''i'')&middot;(9+4''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(9−4''i'')}} <br />{{math| (2+''i'')&middot;(9−4''i'')}}
|-
| 488  || {{math| 2+22''i''}} <br />{{math| 22+2''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(6+5''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(6−5''i'')}}
|-
| 490  || {{math| 7+21''i''}} <br />{{math| 21+7''i''}}  || {{math| (1+''i'')&middot;(2+''i'')&middot;7}} <br />{{math| (1+''i'')&middot;(2−''i'')&middot;7}}
|-
| 493  || {{math| 3+22''i''}} <br />{{math| 13+18''i''}} <br />{{math| 18+13''i''}} <br />{{math| 22+3''i''}}  || {{math| ''i''&middot;(4+''i'')&middot;(5−2''i'')}} <br />{{math| ''i''&middot;(4−''i'')&middot;(5−2''i'')}} <br />{{math| (4+''i'')&middot;(5+2''i'')}} <br />{{math| (4−''i'')&middot;(5+2''i'')}}
|-
| 500  || {{math| 4+22''i''}} <br />{{math| 10+20''i''}} <br />{{math| 20+10''i''}} <br />{{math| 22+4''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2+''i'')<sup>3</sup>}} <br />{{math| (1+''i'')<sup>2</sup>&middot;(2+''i'')&middot;(2−''i'')<sup>2</sup>}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2+''i'')<sup>2</sup>&middot;(2−''i'')}} <br />{{math| (1+''i'')<sup>2</sup>&middot;(2−''i'')<sup>3</sup>}}
|}
{| class="wikitable sortable" style="float:left; margin-right:1em"
! المعيار || العدد الصحيح|| العوامل
|-
| 505  || {{math| 8+21''i''}} <br />{{math| 12+19''i''}} <br />{{math| 19+12''i''}} <br />{{math| 21+8''i''}}  || {{math| ''i''&middot;(2−''i'')&middot;(10+''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(10−''i'')}} <br />{{math| (2+''i'')&middot;(10+''i'')}} <br />{{math| (2+''i'')&middot;(10−''i'')}}
|-
| 509  || {{math| 5+22''i''}} <br />{{math| 22+5''i''}}  || (p) <br />(p)
|-
| 512  || {{math| 16+16''i''}}  || {{math| (1+''i'')<sup>9</sup>}}
|-
| 514  || {{math| 15+17''i''}} <br />{{math| 17+15''i''}}  || {{math| (1+''i'')&middot;(16+''i'')}} <br />{{math| (1+''i'')&middot;(16−''i'')}}
|-
| 520  || {{math| 6+22''i''}} <br />{{math| 14+18''i''}} <br />{{math| 18+14''i''}} <br />{{math| 22+6''i''}}  || {{math| (1+''i'')<sup>3</sup>&middot;(2−''i'')&middot;(3−2''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(2−''i'')&middot;(3+2''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(2+''i'')&middot;(3−2''i'')}} <br />{{math| −(1+''i'')<sup>3</sup>&middot;(2+''i'')&middot;(3+2''i'')}}
|-
| 521  || {{math| 11+20''i''}} <br />{{math| 20+11''i''}}  || (p) <br />(p)
|-
| 522  || {{math| 9+21''i''}} <br />{{math| 21+9''i''}}  || {{math| (1+''i'')&middot;3&middot;(5+2''i'')}} <br />{{math| (1+''i'')&middot;3&middot;(5−2''i'')}}
|-
| 529  || {{math| 23}}  || (p)
|-
| 530  || {{math| 1+23''i''}} <br />{{math| 13+19''i''}} <br />{{math| 19+13''i''}} <br />{{math| 23+''i''}}  || {{math| (1+''i'')&middot;(2+''i'')&middot;(7+2''i'')}} <br />{{math| (1+''i'')&middot;(2+''i'')&middot;(7−2''i'')}} <br />{{math| (1+''i'')&middot;(2−''i'')&middot;(7+2''i'')}} <br />{{math| (1+''i'')&middot;(2−''i'')&middot;(7−2''i'')}}
|-
| 533  || {{math| 2+23''i''}} <br />{{math| 7+22''i''}} <br />{{math| 22+7''i''}} <br />{{math| 23+2''i''}}  || {{math| ''i''&middot;(3+2''i'')&middot;(5−4''i'')}} <br />{{math| (3+2''i'')&middot;(5+4''i'')}} <br />{{math| ''i''&middot;(3−2''i'')&middot;(5−4''i'')}} <br />{{math| (3−2''i'')&middot;(5+4''i'')}}
|-
| 538  || {{math| 3+23''i''}} <br />{{math| 23+3''i''}}  || {{math| (1+''i'')&middot;(13+10''i'')}} <br />{{math| (1+''i'')&middot;(13−10''i'')}}
|-
| 541  || {{math| 10+21''i''}} <br />{{math| 21+10''i''}}  || (p) <br />(p)
|-
| 544  || {{math| 12+20''i''}} <br />{{math| 20+12''i''}}  || {{math| −(1+''i'')<sup>5</sup>&middot;(4+''i'')}} <br />{{math| −(1+''i'')<sup>5</sup>&middot;(4−''i'')}}
|-
| 545  || {{math| 4+23''i''}} <br />{{math| 16+17''i''}} <br />{{math| 17+16''i''}} <br />{{math| 23+4''i''}}  || {{math| ''i''&middot;(2−''i'')&middot;(10+3''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(10−3''i'')}} <br />{{math| (2+''i'')&middot;(10+3''i'')}} <br />{{math| (2+''i'')&middot;(10−3''i'')}}
|-
| 548  || {{math| 8+22''i''}} <br />{{math| 22+8''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(11−4''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(11+4''i'')}}
|-
| 549  || {{math| 15+18''i''}} <br />{{math| 18+15''i''}}  || {{math| ''i''&middot;3&middot;(6−5''i'')}} <br />{{math| 3&middot;(6+5''i'')}}
|-
| 554  || {{math| 5+23''i''}} <br />{{math| 23+5''i''}}  || {{math| (1+''i'')&middot;(14+9''i'')}} <br />{{math| (1+''i'')&middot;(14−9''i'')}}
|-
| 557  || {{math| 14+19''i''}} <br />{{math| 19+14''i''}}  || (p) <br />(p)
|-
| 562  || {{math| 11+21''i''}} <br />{{math| 21+11''i''}}  || {{math| (1+''i'')&middot;(16+5''i'')}} <br />{{math| (1+''i'')&middot;(16−5''i'')}}
|-
| 565  || {{math| 6+23''i''}} <br />{{math| 9+22''i''}} <br />{{math| 22+9''i''}} <br />{{math| 23+6''i''}}  || {{math| ''i''&middot;(2+''i'')&middot;(8−7''i'')}} <br />{{math| (2+''i'')&middot;(8+7''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(8−7''i'')}} <br />{{math| (2−''i'')&middot;(8+7''i'')}}
|-
| 569  || {{math| 13+20''i''}} <br />{{math| 20+13''i''}}  || (p) <br />(p)
|-
| 576  || {{math| 24}}  || {{math| ''i''&middot;(1+''i'')<sup>6</sup>&middot;3}}
|-
| 577  || {{math| 1+24''i''}} <br />{{math| 24+''i''}}  || (p) <br />(p)
|-
| 578  || {{math| 7+23''i''}} <br />{{math| 17+17''i''}} <br />{{math| 23+7''i''}}  || {{math| (1+''i'')&middot;(4+''i'')<sup>2</sup>}} <br />{{math| (1+''i'')&middot;(4+''i'')&middot;(4−''i'')}} <br />{{math| (1+''i'')&middot;(4−''i'')<sup>2</sup>}}
|-
| 580  || {{math| 2+24''i''}} <br />{{math| 16+18''i''}} <br />{{math| 18+16''i''}} <br />{{math| 24+2''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(2−''i'')&middot;(5+2''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2+''i'')&middot;(5+2''i'')}} <br />{{math| (1+''i'')<sup>2</sup>&middot;(2−''i'')&middot;(5−2''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2+''i'')&middot;(5−2''i'')}}
|-
| 584  || {{math| 10+22''i''}} <br />{{math| 22+10''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(8+3''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(8−3''i'')}}
|-
| 585  || {{math| 3+24''i''}} <br />{{math| 12+21''i''}} <br />{{math| 21+12''i''}} <br />{{math| 24+3''i''}}  || {{math| ''i''&middot;(2+''i'')&middot;3&middot;(3−2''i'')}} <br />{{math| (2+''i'')&middot;3&middot;(3+2''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;3&middot;(3−2''i'')}} <br />{{math| (2−''i'')&middot;3&middot;(3+2''i'')}}
|-
| 586  || {{math| 15+19''i''}} <br />{{math| 19+15''i''}}  || {{math| (1+''i'')&middot;(17+2''i'')}} <br />{{math| (1+''i'')&middot;(17−2''i'')}}
|-
| 592  || {{math| 4+24''i''}} <br />{{math| 24+4''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>4</sup>&middot;(6−''i'')}} <br />{{math| −(1+''i'')<sup>4</sup>&middot;(6+''i'')}}
|-
| 593  || {{math| 8+23''i''}} <br />{{math| 23+8''i''}}  || (p) <br />(p)
|-
| 596  || {{math| 14+20''i''}} <br />{{math| 20+14''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(10−7''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(10+7''i'')}}
|-
| 601  || {{math| 5+24''i''}} <br />{{math| 24+5''i''}}  || (p) <br />(p)
|-
| 605  || {{math| 11+22''i''}} <br />{{math| 22+11''i''}}  || {{math| ''i''&middot;(2−''i'')&middot;11}} <br />{{math| (2+''i'')&middot;11}}
|-
| 610  || {{math| 9+23''i''}} <br />{{math| 13+21''i''}} <br />{{math| 21+13''i''}} <br />{{math| 23+9''i''}}  || {{math| ''i''&middot;(1+''i'')&middot;(2−''i'')&middot;(6−5''i'')}} <br />{{math| (1+''i'')&middot;(2−''i'')&middot;(6+5''i'')}} <br />{{math| (1+''i'')&middot;(2+''i'')&middot;(6−5''i'')}} <br />{{math| −''i''&middot;(1+''i'')&middot;(2+''i'')&middot;(6+5''i'')}}
|-
| 612  || {{math| 6+24''i''}} <br />{{math| 24+6''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;3&middot;(4−''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;3&middot;(4+''i'')}}
|-
| 613  || {{math| 17+18''i''}} <br />{{math| 18+17''i''}}  || (p) <br />(p)
|-
| 617  || {{math| 16+19''i''}} <br />{{math| 19+16''i''}}  || (p) <br />(p)
|-
| 625  || {{math| 7+24''i''}} <br />{{math| 15+20''i''}} <br />{{math| 20+15''i''}} <br />{{math| 24+7''i''}} <br />{{math| 25}}  || {{math| −(2−''i'')<sup>4</sup>}} <br />{{math| (2+''i'')<sup>3</sup>&middot;(2−''i'')}} <br />{{math| ''i''&middot;(2+''i'')&middot;(2−''i'')<sup>3</sup>}} <br />{{math| −''i''&middot;(2+''i'')<sup>4</sup>}} <br />{{math| (2+''i'')<sup>2</sup>&middot;(2−''i'')<sup>2</sup>}}
|-
| 626  || {{math| 1+25''i''}} <br />{{math| 25+''i''}}  || {{math| (1+''i'')&middot;(13+12''i'')}} <br />{{math| (1+''i'')&middot;(13−12''i'')}}
|-
| 628  || {{math| 12+22''i''}} <br />{{math| 22+12''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(11−6''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(11+6''i'')}}
|-
| 629  || {{math| 2+25''i''}} <br />{{math| 10+23''i''}} <br />{{math| 23+10''i''}} <br />{{math| 25+2''i''}}  || {{math| ''i''&middot;(4−''i'')&middot;(6+''i'')}} <br />{{math| ''i''&middot;(4−''i'')&middot;(6−''i'')}} <br />{{math| (4+''i'')&middot;(6+''i'')}} <br />{{math| (4+''i'')&middot;(6−''i'')}}
|-
| 634  || {{math| 3+25''i''}} <br />{{math| 25+3''i''}}  || {{math| (1+''i'')&middot;(14+11''i'')}} <br />{{math| (1+''i'')&middot;(14−11''i'')}}
|-
| 637  || {{math| 14+21''i''}} <br />{{math| 21+14''i''}}  || {{math| ''i''&middot;(3−2''i'')&middot;7}} <br />{{math| (3+2''i'')&middot;7}}
|-
| 640  || {{math| 8+24''i''}} <br />{{math| 24+8''i''}}  || {{math| ''i''&middot;(1+''i'')<sup>7</sup>&middot;(2+''i'')}} <br />{{math| ''i''&middot;(1+''i'')<sup>7</sup>&middot;(2−''i'')}}
|-
| 641  || {{math| 4+25''i''}} <br />{{math| 25+4''i''}}  || (p) <br />(p)
|-
| 648  || {{math| 18+18''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;3<sup>2</sup>}}
|-
| 650  || {{math| 5+25''i''}} <br />{{math| 11+23''i''}} <br />{{math| 17+19''i''}} <br />{{math| 19+17''i''}} <br />{{math| 23+11''i''}} <br />{{math| 25+5''i''}}  || {{math| (1+''i'')&middot;(2+''i'')&middot;(2−''i'')&middot;(3+2''i'')}} <br />{{math| (1+''i'')&middot;(2+''i'')<sup>2</sup>&middot;(3−2''i'')}} <br />{{math| ''i''&middot;(1+''i'')&middot;(2−''i'')<sup>2</sup>&middot;(3−2''i'')}} <br />{{math| −''i''&middot;(1+''i'')&middot;(2+''i'')<sup>2</sup>&middot;(3+2''i'')}} <br />{{math| (1+''i'')&middot;(2−''i'')<sup>2</sup>&middot;(3+2''i'')}} <br />{{math| (1+''i'')&middot;(2+''i'')&middot;(2−''i'')&middot;(3−2''i'')}}
|-
| 653  || {{math| 13+22''i''}} <br />{{math| 22+13''i''}}  || (p) <br />(p)
|-
| 656  || {{math| 16+20''i''}} <br />{{math| 20+16''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>4</sup>&middot;(5−4''i'')}} <br />{{math| −(1+''i'')<sup>4</sup>&middot;(5+4''i'')}}
|-
| 657  || {{math| 9+24''i''}} <br />{{math| 24+9''i''}}  || {{math| ''i''&middot;3&middot;(8−3''i'')}} <br />{{math| 3&middot;(8+3''i'')}}
|-
| 661  || {{math| 6+25''i''}} <br />{{math| 25+6''i''}}  || (p) <br />(p)
|-
| 666  || {{math| 15+21''i''}} <br />{{math| 21+15''i''}}  || {{math| (1+''i'')&middot;3&middot;(6+''i'')}} <br />{{math| (1+''i'')&middot;3&middot;(6−''i'')}}
|-
| 673  || {{math| 12+23''i''}} <br />{{math| 23+12''i''}}  || (p) <br />(p)
|-
| 674  || {{math| 7+25''i''}} <br />{{math| 25+7''i''}}  || {{math| (1+''i'')&middot;(16+9''i'')}} <br />{{math| (1+''i'')&middot;(16−9''i'')}}
|-
| 676  || {{math| 10+24''i''}} <br />{{math| 24+10''i''}} <br />{{math| 26}}  || {{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(3+2''i'')<sup>2</sup>}} <br />{{math| (1+''i'')<sup>2</sup>&middot;(3−2''i'')<sup>2</sup>}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(3+2''i'')&middot;(3−2''i'')}}
|-
| 677  || {{math| 1+26''i''}} <br />{{math| 26+''i''}}  || (p) <br />(p)
|-
| 680  || {{math| 2+26''i''}} <br />{{math| 14+22''i''}} <br />{{math| 22+14''i''}} <br />{{math| 26+2''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(2+''i'')&middot;(4+''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(2+''i'')&middot;(4−''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(2−''i'')&middot;(4+''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(2−''i'')&middot;(4−''i'')}}
|-
| 685  || {{math| 3+26''i''}} <br />{{math| 18+19''i''}} <br />{{math| 19+18''i''}} <br />{{math| 26+3''i''}}  || {{math| ''i''&middot;(2−''i'')&middot;(11+4''i'')}} <br />{{math| (2+''i'')&middot;(11+4''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(11−4''i'')}} <br />{{math| (2+''i'')&middot;(11−4''i'')}}
|-
| 689  || {{math| 8+25''i''}} <br />{{math| 17+20''i''}} <br />{{math| 20+17''i''}} <br />{{math| 25+8''i''}}  || {{math| ''i''&middot;(3−2''i'')&middot;(7+2''i'')}} <br />{{math| (3+2''i'')&middot;(7+2''i'')}} <br />{{math| ''i''&middot;(3−2''i'')&middot;(7−2''i'')}} <br />{{math| (3+2''i'')&middot;(7−2''i'')}}
|-
| 692  || {{math| 4+26''i''}} <br />{{math| 26+4''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(13−2''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(13+2''i'')}}
|-
| 697  || {{math| 11+24''i''}} <br />{{math| 16+21''i''}} <br />{{math| 21+16''i''}} <br />{{math| 24+11''i''}}  || {{math| ''i''&middot;(4+''i'')&middot;(5−4''i'')}} <br />{{math| (4+''i'')&middot;(5+4''i'')}} <br />{{math| ''i''&middot;(4−''i'')&middot;(5−4''i'')}} <br />{{math| (4−''i'')&middot;(5+4''i'')}}
|-
| 698  || {{math| 13+23''i''}} <br />{{math| 23+13''i''}}  || {{math| (1+''i'')&middot;(18+5''i'')}} <br />{{math| (1+''i'')&middot;(18−5''i'')}}
|-
| 701  || {{math| 5+26''i''}} <br />{{math| 26+5''i''}}  || (p) <br />(p)
|-
| 706  || {{math| 9+25''i''}} <br />{{math| 25+9''i''}}  || {{math| (1+''i'')&middot;(17+8''i'')}} <br />{{math| (1+''i'')&middot;(17−8''i'')}}
|-
| 709  || {{math| 15+22''i''}} <br />{{math| 22+15''i''}}  || (p) <br />(p)
|-
| 712  || {{math| 6+26''i''}} <br />{{math| 26+6''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(8+5''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(8−5''i'')}}
|-
| 720  || {{math| 12+24''i''}} <br />{{math| 24+12''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>4</sup>&middot;(2−''i'')&middot;3}} <br />{{math| −(1+''i'')<sup>4</sup>&middot;(2+''i'')&middot;3}}
|-
| 722  || {{math| 19+19''i''}}  || {{math| (1+''i'')&middot;19}}
|-
| 724  || {{math| 18+20''i''}} <br />{{math| 20+18''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(10−9''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(10+9''i'')}}
|-
| 725  || {{math| 7+26''i''}} <br />{{math| 10+25''i''}} <br />{{math| 14+23''i''}} <br />{{math| 23+14''i''}} <br />{{math| 25+10''i''}} <br />{{math| 26+7''i''}}  || {{math| (2+''i'')<sup>2</sup>&middot;(5+2''i'')}} <br />{{math| ''i''&middot;(2+''i'')&middot;(2−''i'')&middot;(5−2''i'')}} <br />{{math| ''i''&middot;(2−''i'')<sup>2</sup>&middot;(5+2''i'')}} <br />{{math| (2+''i'')<sup>2</sup>&middot;(5−2''i'')}} <br />{{math| (2+''i'')&middot;(2−''i'')&middot;(5+2''i'')}} <br />{{math| ''i''&middot;(2−''i'')<sup>2</sup>&middot;(5−2''i'')}}
|-
| 729  || {{math| 27}}  || {{math| 3<sup>3</sup>}}
|-
| 730  || {{math| 1+27''i''}} <br />{{math| 17+21''i''}} <br />{{math| 21+17''i''}} <br />{{math| 27+''i''}}  || {{math| ''i''&middot;(1+''i'')&middot;(2−''i'')&middot;(8−3''i'')}} <br />{{math| (1+''i'')&middot;(2+''i'')&middot;(8−3''i'')}} <br />{{math| (1+''i'')&middot;(2−''i'')&middot;(8+3''i'')}} <br />{{math| −''i''&middot;(1+''i'')&middot;(2+''i'')&middot;(8+3''i'')}}
|-
| 733  || {{math| 2+27''i''}} <br />{{math| 27+2''i''}}  || (p) <br />(p)
|-
| 738  || {{math| 3+27''i''}} <br />{{math| 27+3''i''}}  || {{math| (1+''i'')&middot;3&middot;(5+4''i'')}} <br />{{math| (1+''i'')&middot;3&middot;(5−4''i'')}}
|-
| 740  || {{math| 8+26''i''}} <br />{{math| 16+22''i''}} <br />{{math| 22+16''i''}} <br />{{math| 26+8''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(2−''i'')&middot;(6+''i'')}} <br />{{math| (1+''i'')<sup>2</sup>&middot;(2−''i'')&middot;(6−''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2+''i'')&middot;(6+''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2+''i'')&middot;(6−''i'')}}
|-
| 745  || {{math| 4+27''i''}} <br />{{math| 13+24''i''}} <br />{{math| 24+13''i''}} <br />{{math| 27+4''i''}}  || {{math| ''i''&middot;(2+''i'')&middot;(10−7''i'')}} <br />{{math| (2+''i'')&middot;(10+7''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(10−7''i'')}} <br />{{math| (2−''i'')&middot;(10+7''i'')}}
|-
| 746  || {{math| 11+25''i''}} <br />{{math| 25+11''i''}}  || {{math| (1+''i'')&middot;(18+7''i'')}} <br />{{math| (1+''i'')&middot;(18−7''i'')}}
|}
{| class="wikitable sortable" style="float:left; margin-right:1em"
! المعيار || العدد الصحيح|| العوامل
|-
| 754  || {{math| 5+27''i''}} <br />{{math| 15+23''i''}} <br />{{math| 23+15''i''}} <br />{{math| 27+5''i''}}  || {{math| ''i''&middot;(1+''i'')&middot;(3−2''i'')&middot;(5−2''i'')}} <br />{{math| (1+''i'')&middot;(3+2''i'')&middot;(5−2''i'')}} <br />{{math| (1+''i'')&middot;(3−2''i'')&middot;(5+2''i'')}} <br />{{math| −''i''&middot;(1+''i'')&middot;(3+2''i'')&middot;(5+2''i'')}}
|-
| 757  || {{math| 9+26''i''}} <br />{{math| 26+9''i''}}  || (p) <br />(p)
|-
| 761  || {{math| 19+20''i''}} <br />{{math| 20+19''i''}}  || (p) <br />(p)
|-
| 765  || {{math| 6+27''i''}} <br />{{math| 18+21''i''}} <br />{{math| 21+18''i''}} <br />{{math| 27+6''i''}}  || {{math| ''i''&middot;(2−''i'')&middot;3&middot;(4+''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;3&middot;(4−''i'')}} <br />{{math| (2+''i'')&middot;3&middot;(4+''i'')}} <br />{{math| (2+''i'')&middot;3&middot;(4−''i'')}}
|-
| 769  || {{math| 12+25''i''}} <br />{{math| 25+12''i''}}  || (p) <br />(p)
|-
| 772  || {{math| 14+24''i''}} <br />{{math| 24+14''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(12−7''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(12+7''i'')}}
|-
| 773  || {{math| 17+22''i''}} <br />{{math| 22+17''i''}}  || (p) <br />(p)
|-
| 776  || {{math| 10+26''i''}} <br />{{math| 26+10''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(9+4''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(9−4''i'')}}
|-
| 778  || {{math| 7+27''i''}} <br />{{math| 27+7''i''}}  || {{math| (1+''i'')&middot;(17+10''i'')}} <br />{{math| (1+''i'')&middot;(17−10''i'')}}
|-
| 784  || {{math| 28}}  || {{math| −(1+''i'')<sup>4</sup>&middot;7}}
|-
| 785  || {{math| 1+28''i''}} <br />{{math| 16+23''i''}} <br />{{math| 23+16''i''}} <br />{{math| 28+''i''}}  || {{math| ''i''&middot;(2+''i'')&middot;(11−6''i'')}} <br />{{math| (2+''i'')&middot;(11+6''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(11−6''i'')}} <br />{{math| (2−''i'')&middot;(11+6''i'')}}
|-
| 788  || {{math| 2+28''i''}} <br />{{math| 28+2''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(14−''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(14+''i'')}}
|-
| 793  || {{math| 3+28''i''}} <br />{{math| 8+27''i''}} <br />{{math| 27+8''i''}} <br />{{math| 28+3''i''}}  || {{math| ''i''&middot;(3+2''i'')&middot;(6−5''i'')}} <br />{{math| (3+2''i'')&middot;(6+5''i'')}} <br />{{math| ''i''&middot;(3−2''i'')&middot;(6−5''i'')}} <br />{{math| (3−2''i'')&middot;(6+5''i'')}}
|-
| 794  || {{math| 13+25''i''}} <br />{{math| 25+13''i''}}  || {{math| (1+''i'')&middot;(19+6''i'')}} <br />{{math| (1+''i'')&middot;(19−6''i'')}}
|-
| 797  || {{math| 11+26''i''}} <br />{{math| 26+11''i''}}  || (p) <br />(p)
|-
| 800  || {{math| 4+28''i''}} <br />{{math| 20+20''i''}} <br />{{math| 28+4''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>5</sup>&middot;(2−''i'')<sup>2</sup>}} <br />{{math| −(1+''i'')<sup>5</sup>&middot;(2+''i'')&middot;(2−''i'')}} <br />{{math| ''i''&middot;(1+''i'')<sup>5</sup>&middot;(2+''i'')<sup>2</sup>}}
|-
| 801  || {{math| 15+24''i''}} <br />{{math| 24+15''i''}}  || {{math| ''i''&middot;3&middot;(8−5''i'')}} <br />{{math| 3&middot;(8+5''i'')}}
|-
| 802  || {{math| 19+21''i''}} <br />{{math| 21+19''i''}}  || {{math| (1+''i'')&middot;(20+''i'')}} <br />{{math| (1+''i'')&middot;(20−''i'')}}
|-
| 808  || {{math| 18+22''i''}} <br />{{math| 22+18''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(10+''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(10−''i'')}}
|-
| 809  || {{math| 5+28''i''}} <br />{{math| 28+5''i''}}  || (p) <br />(p)
|-
| 810  || {{math| 9+27''i''}} <br />{{math| 27+9''i''}}  || {{math| (1+''i'')&middot;(2+''i'')&middot;3<sup>2</sup>}} <br />{{math| (1+''i'')&middot;(2−''i'')&middot;3<sup>2</sup>}}
|-
| 818  || {{math| 17+23''i''}} <br />{{math| 23+17''i''}}  || {{math| (1+''i'')&middot;(20+3''i'')}} <br />{{math| (1+''i'')&middot;(20−3''i'')}}
|-
| 820  || {{math| 6+28''i''}} <br />{{math| 12+26''i''}} <br />{{math| 26+12''i''}} <br />{{math| 28+6''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(2+''i'')&middot;(5−4''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2+''i'')&middot;(5+4''i'')}} <br />{{math| (1+''i'')<sup>2</sup>&middot;(2−''i'')&middot;(5−4''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2−''i'')&middot;(5+4''i'')}}
|-
| 821  || {{math| 14+25''i''}} <br />{{math| 25+14''i''}}  || (p) <br />(p)
|-
| 829  || {{math| 10+27''i''}} <br />{{math| 27+10''i''}}  || (p) <br />(p)
|-
| 832  || {{math| 16+24''i''}} <br />{{math| 24+16''i''}}  || {{math| −(1+''i'')<sup>6</sup>&middot;(3−2''i'')}} <br />{{math| ''i''&middot;(1+''i'')<sup>6</sup>&middot;(3+2''i'')}}
|-
| 833  || {{math| 7+28''i''}} <br />{{math| 28+7''i''}}  || {{math| ''i''&middot;(4−''i'')&middot;7}} <br />{{math| (4+''i'')&middot;7}}
|-
| 841  || {{math| 20+21''i''}} <br />{{math| 21+20''i''}} <br />{{math| 29}}  || {{math| ''i''&middot;(5−2''i'')<sup>2</sup>}} <br />{{math| (5+2''i'')<sup>2</sup>}} <br />{{math| (5+2''i'')&middot;(5−2''i'')}}
|-
| 842  || {{math| 1+29''i''}} <br />{{math| 29+''i''}}  || {{math| (1+''i'')&middot;(15+14''i'')}} <br />{{math| (1+''i'')&middot;(15−14''i'')}}
|-
| 845  || {{math| 2+29''i''}} <br />{{math| 13+26''i''}} <br />{{math| 19+22''i''}} <br />{{math| 22+19''i''}} <br />{{math| 26+13''i''}} <br />{{math| 29+2''i''}}  || {{math| −(2−''i'')&middot;(3−2''i'')<sup>2</sup>}} <br />{{math| ''i''&middot;(2−''i'')&middot;(3+2''i'')&middot;(3−2''i'')}} <br />{{math| ''i''&middot;(2+''i'')&middot;(3−2''i'')<sup>2</sup>}} <br />{{math| (2−''i'')&middot;(3+2''i'')<sup>2</sup>}} <br />{{math| (2+''i'')&middot;(3+2''i'')&middot;(3−2''i'')}} <br />{{math| −''i''&middot;(2+''i'')&middot;(3+2''i'')<sup>2</sup>}}
|-
| 848  || {{math| 8+28''i''}} <br />{{math| 28+8''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>4</sup>&middot;(7−2''i'')}} <br />{{math| −(1+''i'')<sup>4</sup>&middot;(7+2''i'')}}
|-
| 850  || {{math| 3+29''i''}} <br />{{math| 11+27''i''}} <br />{{math| 15+25''i''}} <br />{{math| 25+15''i''}} <br />{{math| 27+11''i''}} <br />{{math| 29+3''i''}}  || {{math| (1+''i'')&middot;(2+''i'')<sup>2</sup>&middot;(4−''i'')}} <br />{{math| ''i''&middot;(1+''i'')&middot;(2−''i'')<sup>2</sup>&middot;(4−''i'')}} <br />{{math| (1+''i'')&middot;(2+''i'')&middot;(2−''i'')&middot;(4+''i'')}} <br />{{math| (1+''i'')&middot;(2+''i'')&middot;(2−''i'')&middot;(4−''i'')}} <br />{{math| −''i''&middot;(1+''i'')&middot;(2+''i'')<sup>2</sup>&middot;(4+''i'')}} <br />{{math| (1+''i'')&middot;(2−''i'')<sup>2</sup>&middot;(4+''i'')}}
|-
| 853  || {{math| 18+23''i''}} <br />{{math| 23+18''i''}}  || (p) <br />(p)
|-
| 857  || {{math| 4+29''i''}} <br />{{math| 29+4''i''}}  || (p) <br />(p)
|-
| 865  || {{math| 9+28''i''}} <br />{{math| 17+24''i''}} <br />{{math| 24+17''i''}} <br />{{math| 28+9''i''}}  || {{math| ''i''&middot;(2−''i'')&middot;(13+2''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(13−2''i'')}} <br />{{math| (2+''i'')&middot;(13+2''i'')}} <br />{{math| (2+''i'')&middot;(13−2''i'')}}
|-
| 866  || {{math| 5+29''i''}} <br />{{math| 29+5''i''}}  || {{math| (1+''i'')&middot;(17+12''i'')}} <br />{{math| (1+''i'')&middot;(17−12''i'')}}
|-
| 872  || {{math| 14+26''i''}} <br />{{math| 26+14''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(10+3''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(10−3''i'')}}
|-
| 873  || {{math| 12+27''i''}} <br />{{math| 27+12''i''}}  || {{math| ''i''&middot;3&middot;(9−4''i'')}} <br />{{math| 3&middot;(9+4''i'')}}
|-
| 877  || {{math| 6+29''i''}} <br />{{math| 29+6''i''}}  || (p) <br />(p)
|-
| 881  || {{math| 16+25''i''}} <br />{{math| 25+16''i''}}  || (p) <br />(p)
|-
| 882  || {{math| 21+21''i''}}  || {{math| (1+''i'')&middot;3&middot;7}}
|-
| 884  || {{math| 10+28''i''}} <br />{{math| 20+22''i''}} <br />{{math| 22+20''i''}} <br />{{math| 28+10''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(3−2''i'')&middot;(4+''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(3+2''i'')&middot;(4+''i'')}} <br />{{math| (1+''i'')<sup>2</sup>&middot;(3−2''i'')&middot;(4−''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(3+2''i'')&middot;(4−''i'')}}
|-
| 890  || {{math| 7+29''i''}} <br />{{math| 19+23''i''}} <br />{{math| 23+19''i''}} <br />{{math| 29+7''i''}}  || {{math| ''i''&middot;(1+''i'')&middot;(2−''i'')&middot;(8−5''i'')}} <br />{{math| (1+''i'')&middot;(2−''i'')&middot;(8+5''i'')}} <br />{{math| (1+''i'')&middot;(2+''i'')&middot;(8−5''i'')}} <br />{{math| −''i''&middot;(1+''i'')&middot;(2+''i'')&middot;(8+5''i'')}}
|-
| 898  || {{math| 13+27''i''}} <br />{{math| 27+13''i''}}  || {{math| (1+''i'')&middot;(20+7''i'')}} <br />{{math| (1+''i'')&middot;(20−7''i'')}}
|-
| 900  || {{math| 18+24''i''}} <br />{{math| 24+18''i''}} <br />{{math| 30}}  || {{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2+''i'')<sup>2</sup>&middot;3}} <br />{{math| (1+''i'')<sup>2</sup>&middot;(2−''i'')<sup>2</sup>&middot;3}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2+''i'')&middot;(2−''i'')&middot;3}}
|-
| 901  || {{math| 1+30''i''}} <br />{{math| 15+26''i''}} <br />{{math| 26+15''i''}} <br />{{math| 30+''i''}}  || {{math| ''i''&middot;(4+''i'')&middot;(7−2''i'')}} <br />{{math| ''i''&middot;(4−''i'')&middot;(7−2''i'')}} <br />{{math| (4+''i'')&middot;(7+2''i'')}} <br />{{math| (4−''i'')&middot;(7+2''i'')}}
|-
| 904  || {{math| 2+30''i''}} <br />{{math| 30+2''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(8+7''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(8−7''i'')}}
|-
| 905  || {{math| 8+29''i''}} <br />{{math| 11+28''i''}} <br />{{math| 28+11''i''}} <br />{{math| 29+8''i''}}  || {{math| ''i''&middot;(2+''i'')&middot;(10−9''i'')}} <br />{{math| (2+''i'')&middot;(10+9''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(10−9''i'')}} <br />{{math| (2−''i'')&middot;(10+9''i'')}}
|-
| 909  || {{math| 3+30''i''}} <br />{{math| 30+3''i''}}  || {{math| ''i''&middot;3&middot;(10−''i'')}} <br />{{math| 3&middot;(10+''i'')}}
|-
| 914  || {{math| 17+25''i''}} <br />{{math| 25+17''i''}}  || {{math| (1+''i'')&middot;(21+4''i'')}} <br />{{math| (1+''i'')&middot;(21−4''i'')}}
|-
| 916  || {{math| 4+30''i''}} <br />{{math| 30+4''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(15−2''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(15+2''i'')}}
|-
| 922  || {{math| 9+29''i''}} <br />{{math| 29+9''i''}}  || {{math| (1+''i'')&middot;(19+10''i'')}} <br />{{math| (1+''i'')&middot;(19−10''i'')}}
|-
| 925  || {{math| 5+30''i''}} <br />{{math| 14+27''i''}} <br />{{math| 21+22''i''}} <br />{{math| 22+21''i''}} <br />{{math| 27+14''i''}} <br />{{math| 30+5''i''}}  || {{math| ''i''&middot;(2+''i'')&middot;(2−''i'')&middot;(6−''i'')}} <br />{{math| (2+''i'')<sup>2</sup>&middot;(6+''i'')}} <br />{{math| ''i''&middot;(2−''i'')<sup>2</sup>&middot;(6+''i'')}} <br />{{math| (2+''i'')<sup>2</sup>&middot;(6−''i'')}} <br />{{math| ''i''&middot;(2−''i'')<sup>2</sup>&middot;(6−''i'')}} <br />{{math| (2+''i'')&middot;(2−''i'')&middot;(6+''i'')}}
|-
| 928  || {{math| 12+28''i''}} <br />{{math| 28+12''i''}}  || {{math| −(1+''i'')<sup>5</sup>&middot;(5+2''i'')}} <br />{{math| −(1+''i'')<sup>5</sup>&middot;(5−2''i'')}}
|-
| 929  || {{math| 20+23''i''}} <br />{{math| 23+20''i''}}  || (p) <br />(p)
|-
| 932  || {{math| 16+26''i''}} <br />{{math| 26+16''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(13−8''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(13+8''i'')}}
|-
| 936  || {{math| 6+30''i''}} <br />{{math| 30+6''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;3&middot;(3+2''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;3&middot;(3−2''i'')}}
|-
| 937  || {{math| 19+24''i''}} <br />{{math| 24+19''i''}}  || (p) <br />(p)
|-
| 941  || {{math| 10+29''i''}} <br />{{math| 29+10''i''}}  || (p) <br />(p)
|-
| 949  || {{math| 7+30''i''}} <br />{{math| 18+25''i''}} <br />{{math| 25+18''i''}} <br />{{math| 30+7''i''}}  || {{math| ''i''&middot;(3−2''i'')&middot;(8+3''i'')}} <br />{{math| (3+2''i'')&middot;(8+3''i'')}} <br />{{math| ''i''&middot;(3−2''i'')&middot;(8−3''i'')}} <br />{{math| (3+2''i'')&middot;(8−3''i'')}}
|-
| 953  || {{math| 13+28''i''}} <br />{{math| 28+13''i''}}  || (p) <br />(p)
|-
| 954  || {{math| 15+27''i''}} <br />{{math| 27+15''i''}}  || {{math| (1+''i'')&middot;3&middot;(7+2''i'')}} <br />{{math| (1+''i'')&middot;3&middot;(7−2''i'')}}
|-
| 961  || {{math| 31}}  || (p)
|-
| 962  || {{math| 1+31''i''}} <br />{{math| 11+29''i''}} <br />{{math| 29+11''i''}} <br />{{math| 31+''i''}}  || {{math| (1+''i'')&middot;(3+2''i'')&middot;(6+''i'')}} <br />{{math| (1+''i'')&middot;(3+2''i'')&middot;(6−''i'')}} <br />{{math| (1+''i'')&middot;(3−2''i'')&middot;(6+''i'')}} <br />{{math| (1+''i'')&middot;(3−2''i'')&middot;(6−''i'')}}
|-
| 964  || {{math| 8+30''i''}} <br />{{math| 30+8''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(15−4''i'')}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(15+4''i'')}}
|-
| 965  || {{math| 2+31''i''}} <br />{{math| 17+26''i''}} <br />{{math| 26+17''i''}} <br />{{math| 31+2''i''}}  || {{math| ''i''&middot;(2+''i'')&middot;(12−7''i'')}} <br />{{math| (2+''i'')&middot;(12+7''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(12−7''i'')}} <br />{{math| (2−''i'')&middot;(12+7''i'')}}
|-
| 968  || {{math| 22+22''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;11}}
|-
| 970  || {{math| 3+31''i''}} <br />{{math| 21+23''i''}} <br />{{math| 23+21''i''}} <br />{{math| 31+3''i''}}  || {{math| ''i''&middot;(1+''i'')&middot;(2−''i'')&middot;(9−4''i'')}} <br />{{math| (1+''i'')&middot;(2+''i'')&middot;(9−4''i'')}} <br />{{math| (1+''i'')&middot;(2−''i'')&middot;(9+4''i'')}} <br />{{math| −''i''&middot;(1+''i'')&middot;(2+''i'')&middot;(9+4''i'')}}
|-
| 976  || {{math| 20+24''i''}} <br />{{math| 24+20''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>4</sup>&middot;(6−5''i'')}} <br />{{math| −(1+''i'')<sup>4</sup>&middot;(6+5''i'')}}
|-
| 977  || {{math| 4+31''i''}} <br />{{math| 31+4''i''}}  || (p) <br />(p)
|-
| 980  || {{math| 14+28''i''}} <br />{{math| 28+14''i''}}  || {{math| (1+''i'')<sup>2</sup>&middot;(2−''i'')&middot;7}} <br />{{math| −''i''&middot;(1+''i'')<sup>2</sup>&middot;(2+''i'')&middot;7}}
|-
| 981  || {{math| 9+30''i''}} <br />{{math| 30+9''i''}}  || {{math| ''i''&middot;3&middot;(10−3''i'')}} <br />{{math| 3&middot;(10+3''i'')}}
|-
| 985  || {{math| 12+29''i''}} <br />{{math| 16+27''i''}} <br />{{math| 27+16''i''}} <br />{{math| 29+12''i''}}  || {{math| ''i''&middot;(2−''i'')&middot;(14+''i'')}} <br />{{math| ''i''&middot;(2−''i'')&middot;(14−''i'')}} <br />{{math| (2+''i'')&middot;(14+''i'')}} <br />{{math| (2+''i'')&middot;(14−''i'')}}
|-
| 986  || {{math| 5+31''i''}} <br />{{math| 19+25''i''}} <br />{{math| 25+19''i''}} <br />{{math| 31+5''i''}}  || {{math| (1+''i'')&middot;(4+''i'')&middot;(5+2''i'')}} <br />{{math| (1+''i'')&middot;(4−''i'')&middot;(5+2''i'')}} <br />{{math| (1+''i'')&middot;(4+''i'')&middot;(5−2''i'')}} <br />{{math| (1+''i'')&middot;(4−''i'')&middot;(5−2''i'')}}
|-
| 997  || {{math| 6+31''i''}} <br />{{math| 31+6''i''}}  || (p) <br />(p)
|-
| 1000  || {{math| 10+30''i''}} <br />{{math| 18+26''i''}} <br />{{math| 26+18''i''}} <br />{{math| 30+10''i''}}  || {{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(2+''i'')<sup>2</sup>&middot;(2−''i'')}} <br />{{math| (1+''i'')<sup>3</sup>&middot;(2−''i'')<sup>3</sup>}} <br />{{math| −(1+''i'')<sup>3</sup>&middot;(2+''i'')<sup>3</sup>}} <br />{{math| −''i''&middot;(1+''i'')<sup>3</sup>&middot;(2+''i'')&middot;(2−''i'')<sup>2</sup>}}
|}{{تحديد يسار}}

== مراجع ==
{{مراجع}}

==وصلات خارجية==
* {{ماثوورلد|title= Gaussian prime| urlname=GaussianPrime}}
* {{ماثوورلد|title= Prime Factorization |urlname= PrimeFactorization}}
* [http://oeis.org/classic/?q=Gaussian+prime OEIS: Gaussian Primes]

==طالع أيضا==
*[[جدول التفكيك إلى عوامل أولية]]
*[[جدول القواعد]]

{{شريط بوابات|رياضيات}}

{{بذرة رياضيات}}

[[تصنيف:أعداد مركبة]]
[[تصنيف:جداول رياضيات]]
[[تصنيف:قوائم متعلقة بالرياضيات]]
[[تصنيف:نظرية الأعداد الابتدائية]]