Table of Gaussian integer factorizations

A Gaussian integer is either the zero, one of the four units (±1, ±i), a Gaussian prime or composite. The article is a table of Gaussian Integers x + iy followed either by an explicit factorization or followed by the label (p) if the integer is a Gaussian prime. The factorizations take the form of an optional unit multiplied by integer powers of Gaussian primes.

Note that there are rational primes which are not Gaussian primes. A simple example is the rational prime 5, which is factored as 5=(2+i)(2−i) in the table, and therefore not a Gaussian prime.

Conventions

The second column of the table contains only integers in the first quadrant, which means the real part x is positive and the imaginary part y is non-negative. The table might have been further reduced to the integers in the first octant of the complex plane using the symmetry y + ix =i (x − iy).

The factorizations are often not unique in the sense that the unit could be absorbed into any other factor with exponent equal to one. The entry 4+2i = −i(1+i)2(2+i), for example, could also be written as 4+2i= (1+i)2(1−2i). The entries in the table resolve this ambiguity by the following convention: the factors are primes in the right complex half plane with absolute value of the real part larger than or equal to the absolute value of the imaginary part.

The entries are sorted according to increasing norm x2 + y2 (sequence A001481 in the OEIS). The table is complete up to the maximum norm at the end of the table in the sense that each composite or prime in the first quadrant appears in the second column.

Gaussian primes occur only for a subset of norms, detailed in sequence OEIS: A055025. This here is a composition of sequences OEIS: A103431 and OEIS: A103432.

Factorizations

Norm 1–250
Norm Integer Factorization
2 1+i (p)
4 2 −i·(1+i)2
5 2+i
1+2i		 (p)
(p)
8 2+2i −i·(1+i)3
9 3 (p)
10 1+3i
3+i		 (1+i)·(2+i)
(1+i)·(2−i)
13 3+2i
2+3i		 (p)
(p)
16 4 −(1+i)4
17 1+4i
4+i		 (p)
(p)
18 3+3i (1+i)·3
20 2+4i
4+2i		 (1+i)2·(2−i)
−i·(1+i)2·(2+i)
25 3+4i
4+3i
5		 (2+i)2
i·(2−i)2
(2+i)·(2−i)
26 1+5i
5+i		 (1+i)·(3+2i)
(1+i)·(3−2i)
29 2+5i
5+2i		 (p)
(p)
32 4+4i −(1+i)5
34 3+5i
5+3i		 (1+i)·(4+i)
(1+i)·(4−i)
36 6 −i·(1+i)2·3
37 1+6i
6+i		 (p)
(p)
40 2+6i
6+2i		 −i·(1+i)3·(2+i)
−i·(1+i)3·(2−i)
41 4+5i
5+4i		 (p)
(p)
45 3+6i
6+3i		 i·(2−i)·3
(2+i)·3
49 7 (p)
50 1+7i
5+5i
7+i		 i·(1+i)·(2−i)2
(1+i)·(2+i)·(2−i)
−i·(1+i)·(2+i)2
52 4+6i
6+4i		 (1+i)2·(3−2i)
−i·(1+i)2·(3+2i)
53 2+7i
7+2i		 (p)
(p)
58 3+7i
7+3i		 (1+i)·(5+2i)
(1+i)·(5−2i)
61 5+6i
6+5i		 (p)
(p)
64 8 i·(1+i)6
65 1+8i
4+7i
7+4i
8+i		 i·(2+i)·(3−2i)
(2+i)·(3+2i)
i·(2−i)·(3−2i)
(2−i)·(3+2i)
68 2+8i
8+2i		 (1+i)2·(4−i)
−i·(1+i)2·(4+i)
72 6+6i −i·(1+i)3·3
73 3+8i
8+3i		 (p)
(p)
74 5+7i
7+5i		 (1+i)·(6+i)
(1+i)·(6−i)
80 4+8i
8+4i		 −i·(1+i)4·(2−i)
−(1+i)4·(2+i)
81 9 32
82 1+9i
9+i		 (1+i)·(5+4i)
(1+i)·(5−4i)
85 2+9i
6+7i
7+6i
9+2i		 i·(2−i)·(4+i)
i·(2−i)·(4−i)
(2+i)·(4+i)
(2+i)·(4−i)
89 5+8i
8+5i		 (p)
(p)
90 3+9i
9+3i		 (1+i)·(2+i)·3
(1+i)·(2−i)·3
97 4+9i
9+4i		 (p)
(p)
98 7+7i (1+i)·7
100 6+8i
8+6i
10		 −i·(1+i)2·(2+i)2
(1+i)2·(2−i)2
−i·(1+i)2·(2+i)·(2−i)
101 1+10i
10+i		 (p)
(p)
104 2+10i
10+2i		 −i·(1+i)3·(3+2i)
−i·(1+i)3·(3−2i)
106 5+9i
9+5i		 (1+i)·(7+2i)
(1+i)·(7−2i)
109 3+10i
10+3i		 (p)
(p)
113 7+8i
8+7i		 (p)
(p)
116 4+10i
10+4i		 (1+i)2·(5−2i)
−i·(1+i)2·(5+2i)
117 6+9i
9+6i		 i·3·(3−2i)
3·(3+2i)
121 11 (p)
122 1+11i
11+i		 (1+i)·(6+5i)
(1+i)·(6−5i)
125 2+11i
5+10i
10+5i
11+2i		 (2+i)3
i·(2+i)·(2−i)2
(2+i)2·(2−i)
i·(2−i)3
128 8+8i i·(1+i)7
130 3+11i
7+9i
9+7i
11+3i		 i·(1+i)·(2−i)·(3−2i)
(1+i)·(2−i)·(3+2i)
(1+i)·(2+i)·(3−2i)
−i·(1+i)·(2+i)·(3+2i)
136 6+10i
10+6i		 −i·(1+i)3·(4+i)
−i·(1+i)3·(4−i)
137 4+11i
11+4i		 (p)
(p)
144 12 −(1+i)4·3
145 1+12i
8+9i
9+8i
12+i		 i·(2−i)·(5+2i)
(2+i)·(5+2i)
i·(2−i)·(5−2i)
(2+i)·(5−2i)
146 5+11i
11+5i		 (1+i)·(8+3i)
(1+i)·(8−3i)
148 2+12i
12+2i		 (1+i)2·(6−i)
−i·(1+i)2·(6+i)
149 7+10i
10+7i		 (p)
(p)
153 3+12i
12+3i		 i·3·(4−i)
3·(4+i)
157 6+11i
11+6i		 (p)
(p)
160 4+12i
12+4i		 −(1+i)5·(2+i)
−(1+i)5·(2−i)
162 9+9i (1+i)·32
164 8+10i
10+8i		 (1+i)2·(5−4i)
−i·(1+i)2·(5+4i)
169 5+12i
12+5i
13		 (3+2i)2
i·(3−2i)2
(3+2i)·(3−2i)
170 1+13i
7+11i
11+7i
13+i		 (1+i)·(2+i)·(4+i)
(1+i)·(2+i)·(4−i)
(1+i)·(2−i)·(4+i)
(1+i)·(2−i)·(4−i)
173 2+13i
13+2i		 (p)
(p)
178 3+13i
13+3i		 (1+i)·(8+5i)
(1+i)·(8−5i)
180 6+12i
12+6i		 (1+i)2·(2−i)·3
−i·(1+i)2·(2+i)·3
181 9+10i
10+9i		 (p)
(p)
185 4+13i
8+11i
11+8i
13+4i		 i·(2−i)·(6+i)
i·(2−i)·(6−i)
(2+i)·(6+i)
(2+i)·(6−i)
193 7+12i
12+7i		 (p)
(p)
194 5+13i
13+5i		 (1+i)·(9+4i)
(1+i)·(9−4i)
196 14 −i·(1+i)2·7
197 1+14i
14+i		 (p)
(p)
200 2+14i
10+10i
14+2i		 (1+i)3·(2−i)2
−i·(1+i)3·(2+i)·(2−i)
−(1+i)3·(2+i)2
202 9+11i
11+9i		 (1+i)·(10+i)
(1+i)·(10−i)
205 3+14i
6+13i
13+6i
14+3i		 i·(2+i)·(5−4i)
(2+i)·(5+4i)
i·(2−i)·(5−4i)
(2−i)·(5+4i)
208 8+12i
12+8i		 −i·(1+i)4·(3−2i)
−(1+i)4·(3+2i)
212 4+14i
14+4i		 (1+i)2·(7−2i)
−i·(1+i)2·(7+2i)
218 7+13i
13+7i		 (1+i)·(10+3i)
(1+i)·(10−3i)
221 5+14i
10+11i
11+10i
14+5i		 i·(3−2i)·(4+i)
(3+2i)·(4+i)
i·(3−2i)·(4−i)
(3+2i)·(4−i)
225 9+12i
12+9i
15		 (2+i)2·3
i·(2−i)2·3
(2+i)·(2−i)·3
226 1+15i
15+i		 (1+i)·(8+7i)
(1+i)·(8−7i)
229 2+15i
15+2i		 (p)
(p)
232 6+14i
14+6i		 −i·(1+i)3·(5+2i)
−i·(1+i)3·(5−2i)
233 8+13i
13+8i		 (p)
(p)
234 3+15i
15+3i		 (1+i)·3·(3+2i)
(1+i)·3·(3−2i)
241 4+15i
15+4i		 (p)
(p)
242 11+11i (1+i)·11
244 10+12i
12+10i		 (1+i)2·(6−5i)
−i·(1+i)2·(6+5i)
245 7+14i
14+7i		 i·(2−i)·7
(2+i)·7
250 5+15i
9+13i
13+9i
15+5i		 (1+i)·(2+i)2·(2−i)
i·(1+i)·(2−i)3
−i·(1+i)·(2+i)3
(1+i)·(2+i)·(2−i)2
Norm 251–500
Norm Integer Factorization
256 16 (1+i)8
257 1+16i
16+i		 (p)
(p)
260 2+16i
8+14i
14+8i
16+2i		 (1+i)2·(2+i)·(3−2i)
−i·(1+i)2·(2+i)·(3+2i)
(1+i)2·(2−i)·(3−2i)
−i·(1+i)2·(2−i)·(3+2i)
261 6+15i
15+6i		 i·3·(5−2i)
3·(5+2i)
265 3+16i
11+12i
12+11i
16+3i		 i·(2−i)·(7+2i)
i·(2−i)·(7−2i)
(2+i)·(7+2i)
(2+i)·(7−2i)
269 10+13i
13+10i		 (p)
(p)
272 4+16i
16+4i		 −i·(1+i)4·(4−i)
−(1+i)4·(4+i)
274 7+15i
15+7i		 (1+i)·(11+4i)
(1+i)·(11−4i)
277 9+14i
14+9i		 (p)
(p)
281 5+16i
16+5i		 (p)
(p)
288 12+12i −(1+i)5·3
289 8+15i
15+8i
17		 i·(4−i)2
(4+i)2
(4+i)·(4−i)
290 1+17i
11+13i
13+11i
17+i		 i·(1+i)·(2−i)·(5−2i)
(1+i)·(2+i)·(5−2i)
(1+i)·(2−i)·(5+2i)
−i·(1+i)·(2+i)·(5+2i)
292 6+16i
16+6i		 (1+i)2·(8−3i)
−i·(1+i)2·(8+3i)
293 2+17i
17+2i		 (p)
(p)
296 10+14i
14+10i		 −i·(1+i)3·(6+i)
−i·(1+i)3·(6−i)
298 3+17i
17+3i		 (1+i)·(10+7i)
(1+i)·(10−7i)
305 4+17i
7+16i
16+7i
17+4i		 i·(2+i)·(6−5i)
(2+i)·(6+5i)
i·(2−i)·(6−5i)
(2−i)·(6+5i)
306 9+15i
15+9i		 (1+i)·3·(4+i)
(1+i)·3·(4−i)
313 12+13i
13+12i		 (p)
(p)
314 5+17i
17+5i		 (1+i)·(11+6i)
(1+i)·(11−6i)
317 11+14i
14+11i		 (p)
(p)
320 8+16i
16+8i		 −(1+i)6·(2−i)
i·(1+i)6·(2+i)
324 18 −i·(1+i)2·32
325 1+18i
6+17i
10+15i
15+10i
17+6i
18+i		 (2+i)2·(3+2i)
i·(2−i)2·(3+2i)
i·(2+i)·(2−i)·(3−2i)
(2+i)·(2−i)·(3+2i)
(2+i)2·(3−2i)
i·(2−i)2·(3−2i)
328 2+18i
18+2i		 −i·(1+i)3·(5+4i)
−i·(1+i)3·(5−4i)
333 3+18i
18+3i		 i·3·(6−i)
3·(6+i)
337 9+16i
16+9i		 (p)
(p)
338 7+17i
13+13i
17+7i		 i·(1+i)·(3−2i)2
(1+i)·(3+2i)·(3−2i)
−i·(1+i)·(3+2i)2
340 4+18i
12+14i
14+12i
18+4i		 (1+i)2·(2−i)·(4+i)
(1+i)2·(2−i)·(4−i)
−i·(1+i)2·(2+i)·(4+i)
−i·(1+i)2·(2+i)·(4−i)
346 11+15i
15+11i		 (1+i)·(13+2i)
(1+i)·(13−2i)
349 5+18i
18+5i		 (p)
(p)
353 8+17i
17+8i		 (p)
(p)
356 10+16i
16+10i		 (1+i)2·(8−5i)
−i·(1+i)2·(8+5i)
360 6+18i
18+6i		 −i·(1+i)3·(2+i)·3
−i·(1+i)3·(2−i)·3
361 19 (p)
362 1+19i
19+i		 (1+i)·(10+9i)
(1+i)·(10−9i)
365 2+19i
13+14i
14+13i
19+2i		 i·(2−i)·(8+3i)
(2+i)·(8+3i)
i·(2−i)·(8−3i)
(2+i)·(8−3i)
369 12+15i
15+12i		 i·3·(5−4i)
3·(5+4i)
370 3+19i
9+17i
17+9i
19+3i		 (1+i)·(2+i)·(6+i)
(1+i)·(2+i)·(6−i)
(1+i)·(2−i)·(6+i)
(1+i)·(2−i)·(6−i)
373 7+18i
18+7i		 (p)
(p)
377 4+19i
11+16i
16+11i
19+4i		 i·(3−2i)·(5+2i)
(3+2i)·(5+2i)
i·(3−2i)·(5−2i)
(3+2i)·(5−2i)
386 5+19i
19+5i		 (1+i)·(12+7i)
(1+i)·(12−7i)
388 8+18i
18+8i		 (1+i)2·(9−4i)
−i·(1+i)2·(9+4i)
389 10+17i
17+10i		 (p)
(p)
392 14+14i −i·(1+i)3·7
394 13+15i
15+13i		 (1+i)·(14+i)
(1+i)·(14−i)
397 6+19i
19+6i		 (p)
(p)
400 12+16i
16+12i
20		 −(1+i)4·(2+i)2
−i·(1+i)4·(2−i)2
−(1+i)4·(2+i)·(2−i)
401 1+20i
20+i		 (p)
(p)
404 2+20i
20+2i		 (1+i)2·(10−i)
−i·(1+i)2·(10+i)
405 9+18i
18+9i		 i·(2−i)·32
(2+i)·32
409 3+20i
20+3i		 (p)
(p)
410 7+19i
11+17i
17+11i
19+7i		 i·(1+i)·(2−i)·(5−4i)
(1+i)·(2−i)·(5+4i)
(1+i)·(2+i)·(5−4i)
−i·(1+i)·(2+i)·(5+4i)
416 4+20i
20+4i		 −(1+i)5·(3+2i)
−(1+i)5·(3−2i)
421 14+15i
15+14i		 (p)
(p)
424 10+18i
18+10i		 −i·(1+i)3·(7+2i)
−i·(1+i)3·(7−2i)
425 5+20i
8+19i
13+16i
16+13i
19+8i
20+5i		 i·(2+i)·(2−i)·(4−i)
(2+i)2·(4+i)
i·(2−i)2·(4+i)
(2+i)2·(4−i)
i·(2−i)2·(4−i)
(2+i)·(2−i)·(4+i)
433 12+17i
17+12i		 (p)
(p)
436 6+20i
20+6i		 (1+i)2·(10−3i)
−i·(1+i)2·(10+3i)
441 21 3·7
442 1+21i
9+19i
19+9i
21+i		 i·(1+i)·(3−2i)·(4−i)
(1+i)·(3+2i)·(4−i)
(1+i)·(3−2i)·(4+i)
−i·(1+i)·(3+2i)·(4+i)
445 2+21i
11+18i
18+11i
21+2i		 i·(2+i)·(8−5i)
(2+i)·(8+5i)
i·(2−i)·(8−5i)
(2−i)·(8+5i)
449 7+20i
20+7i		 (p)
(p)
450 3+21i
15+15i
21+3i		 i·(1+i)·(2−i)2·3
(1+i)·(2+i)·(2−i)·3
−i·(1+i)·(2+i)2·3
452 14+16i
16+14i		 (1+i)2·(8−7i)
−i·(1+i)2·(8+7i)
457 4+21i
21+4i		 (p)
(p)
458 13+17i
17+13i		 (1+i)·(15+2i)
(1+i)·(15−2i)
461 10+19i
19+10i		 (p)
(p)
464 8+20i
20+8i		 −i·(1+i)4·(5−2i)
−(1+i)4·(5+2i)
466 5+21i
21+5i		 (1+i)·(13+8i)
(1+i)·(13−8i)
468 12+18i
18+12i		 (1+i)2·3·(3−2i)
−i·(1+i)2·3·(3+2i)
477 6+21i
21+6i		 i·3·(7−2i)
3·(7+2i)
481 9+20i
15+16i
16+15i
20+9i		 i·(3−2i)·(6+i)
i·(3−2i)·(6−i)
(3+2i)·(6+i)
(3+2i)·(6−i)
482 11+19i
19+11i		 (1+i)·(15+4i)
(1+i)·(15−4i)
484 22 −i·(1+i)2·11
485 1+22i
14+17i
17+14i
22+i		 i·(2−i)·(9+4i)
(2+i)·(9+4i)
i·(2−i)·(9−4i)
(2+i)·(9−4i)
488 2+22i
22+2i		 −i·(1+i)3·(6+5i)
−i·(1+i)3·(6−5i)
490 7+21i
21+7i		 (1+i)·(2+i)·7
(1+i)·(2−i)·7
493 3+22i
13+18i
18+13i
22+3i		 i·(4+i)·(5−2i)
i·(4−i)·(5−2i)
(4+i)·(5+2i)
(4−i)·(5+2i)
500 4+22i
10+20i
20+10i
22+4i		 −i·(1+i)2·(2+i)3
(1+i)2·(2+i)·(2−i)2
−i·(1+i)2·(2+i)2·(2−i)
(1+i)2·(2−i)3
Norm 501–750
Norm Integer Factorization
505 8+21i
12+19i
19+12i
21+8i		 i·(2−i)·(10+i)
i·(2−i)·(10−i)
(2+i)·(10+i)
(2+i)·(10−i)
509 5+22i
22+5i		 (p)
(p)
512 16+16i (1+i)9
514 15+17i
17+15i		 (1+i)·(16+i)
(1+i)·(16−i)
520 6+22i
14+18i
18+14i
22+6i		 (1+i)3·(2−i)·(3−2i)
−i·(1+i)3·(2−i)·(3+2i)
−i·(1+i)3·(2+i)·(3−2i)
−(1+i)3·(2+i)·(3+2i)
521 11+20i
20+11i		 (p)
(p)
522 9+21i
21+9i		 (1+i)·3·(5+2i)
(1+i)·3·(5−2i)
529 23 (p)
530 1+23i
13+19i
19+13i
23+i		 (1+i)·(2+i)·(7+2i)
(1+i)·(2+i)·(7−2i)
(1+i)·(2−i)·(7+2i)
(1+i)·(2−i)·(7−2i)
533 2+23i
7+22i
22+7i
23+2i		 i·(3+2i)·(5−4i)
(3+2i)·(5+4i)
i·(3−2i)·(5−4i)
(3−2i)·(5+4i)
538 3+23i
23+3i		 (1+i)·(13+10i)
(1+i)·(13−10i)
541 10+21i
21+10i		 (p)
(p)
544 12+20i
20+12i		 −(1+i)5·(4+i)
−(1+i)5·(4−i)
545 4+23i
16+17i
17+16i
23+4i		 i·(2−i)·(10+3i)
i·(2−i)·(10−3i)
(2+i)·(10+3i)
(2+i)·(10−3i)
548 8+22i
22+8i		 (1+i)2·(11−4i)
−i·(1+i)2·(11+4i)
549 15+18i
18+15i		 i·3·(6−5i)
3·(6+5i)
554 5+23i
23+5i		 (1+i)·(14+9i)
(1+i)·(14−9i)
557 14+19i
19+14i		 (p)
(p)
562 11+21i
21+11i		 (1+i)·(16+5i)
(1+i)·(16−5i)
565 6+23i
9+22i
22+9i
23+6i		 i·(2+i)·(8−7i)
(2+i)·(8+7i)
i·(2−i)·(8−7i)
(2−i)·(8+7i)
569 13+20i
20+13i		 (p)
(p)
576 24 i·(1+i)6·3
577 1+24i
24+i		 (p)
(p)
578 7+23i
17+17i
23+7i		 (1+i)·(4+i)2
(1+i)·(4+i)·(4−i)
(1+i)·(4−i)2
580 2+24i
16+18i
18+16i
24+2i		 (1+i)2·(2−i)·(5+2i)
−i·(1+i)2·(2+i)·(5+2i)
(1+i)2·(2−i)·(5−2i)
−i·(1+i)2·(2+i)·(5−2i)
584 10+22i
22+10i		 −i·(1+i)3·(8+3i)
−i·(1+i)3·(8−3i)
585 3+24i
12+21i
21+12i
24+3i		 i·(2+i)·3·(3−2i)
(2+i)·3·(3+2i)
i·(2−i)·3·(3−2i)
(2−i)·3·(3+2i)
586 15+19i
19+15i		 (1+i)·(17+2i)
(1+i)·(17−2i)
592 4+24i
24+4i		 −i·(1+i)4·(6−i)
−(1+i)4·(6+i)
593 8+23i
23+8i		 (p)
(p)
596 14+20i
20+14i		 (1+i)2·(10−7i)
−i·(1+i)2·(10+7i)
601 5+24i
24+5i		 (p)
(p)
605 11+22i
22+11i		 i·(2−i)·11
(2+i)·11
610 9+23i
13+21i
21+13i
23+9i		 i·(1+i)·(2−i)·(6−5i)
(1+i)·(2−i)·(6+5i)
(1+i)·(2+i)·(6−5i)
−i·(1+i)·(2+i)·(6+5i)
612 6+24i
24+6i		 (1+i)2·3·(4−i)
−i·(1+i)2·3·(4+i)
613 17+18i
18+17i		 (p)
(p)
617 16+19i
19+16i		 (p)
(p)
625 7+24i
15+20i
20+15i
24+7i
25		 −(2−i)4
(2+i)3·(2−i)
i·(2+i)·(2−i)3
−i·(2+i)4
(2+i)2·(2−i)2
626 1+25i
25+i		 (1+i)·(13+12i)
(1+i)·(13−12i)
628 12+22i
22+12i		 (1+i)2·(11−6i)
−i·(1+i)2·(11+6i)
629 2+25i
10+23i
23+10i
25+2i		 i·(4−i)·(6+i)
i·(4−i)·(6−i)
(4+i)·(6+i)
(4+i)·(6−i)
634 3+25i
25+3i		 (1+i)·(14+11i)
(1+i)·(14−11i)
637 14+21i
21+14i		 i·(3−2i)·7
(3+2i)·7
640 8+24i
24+8i		 i·(1+i)7·(2+i)
i·(1+i)7·(2−i)
641 4+25i
25+4i		 (p)
(p)
648 18+18i −i·(1+i)3·32
650 5+25i
11+23i
17+19i
19+17i
23+11i
25+5i		 (1+i)·(2+i)·(2−i)·(3+2i)
(1+i)·(2+i)2·(3−2i)
i·(1+i)·(2−i)2·(3−2i)
−i·(1+i)·(2+i)2·(3+2i)
(1+i)·(2−i)2·(3+2i)
(1+i)·(2+i)·(2−i)·(3−2i)
653 13+22i
22+13i		 (p)
(p)
656 16+20i
20+16i		 −i·(1+i)4·(5−4i)
−(1+i)4·(5+4i)
657 9+24i
24+9i		 i·3·(8−3i)
3·(8+3i)
661 6+25i
25+6i		 (p)
(p)
666 15+21i
21+15i		 (1+i)·3·(6+i)
(1+i)·3·(6−i)
673 12+23i
23+12i		 (p)
(p)
674 7+25i
25+7i		 (1+i)·(16+9i)
(1+i)·(16−9i)
676 10+24i
24+10i
26		 −i·(1+i)2·(3+2i)2
(1+i)2·(3−2i)2
−i·(1+i)2·(3+2i)·(3−2i)
677 1+26i
26+i		 (p)
(p)
680 2+26i
14+22i
22+14i
26+2i		 −i·(1+i)3·(2+i)·(4+i)
−i·(1+i)3·(2+i)·(4−i)
−i·(1+i)3·(2−i)·(4+i)
−i·(1+i)3·(2−i)·(4−i)
685 3+26i
18+19i
19+18i
26+3i		 i·(2−i)·(11+4i)
(2+i)·(11+4i)
i·(2−i)·(11−4i)
(2+i)·(11−4i)
689 8+25i
17+20i
20+17i
25+8i		 i·(3−2i)·(7+2i)
(3+2i)·(7+2i)
i·(3−2i)·(7−2i)
(3+2i)·(7−2i)
692 4+26i
26+4i		 (1+i)2·(13−2i)
−i·(1+i)2·(13+2i)
697 11+24i
16+21i
21+16i
24+11i		 i·(4+i)·(5−4i)
(4+i)·(5+4i)
i·(4−i)·(5−4i)
(4−i)·(5+4i)
698 13+23i
23+13i		 (1+i)·(18+5i)
(1+i)·(18−5i)
701 5+26i
26+5i		 (p)
(p)
706 9+25i
25+9i		 (1+i)·(17+8i)
(1+i)·(17−8i)
709 15+22i
22+15i		 (p)
(p)
712 6+26i
26+6i		 −i·(1+i)3·(8+5i)
−i·(1+i)3·(8−5i)
720 12+24i
24+12i		 −i·(1+i)4·(2−i)·3
−(1+i)4·(2+i)·3
722 19+19i (1+i)·19
724 18+20i
20+18i		 (1+i)2·(10−9i)
−i·(1+i)2·(10+9i)
725 7+26i
10+25i
14+23i
23+14i
25+10i
26+7i		 (2+i)2·(5+2i)
i·(2+i)·(2−i)·(5−2i)
i·(2−i)2·(5+2i)
(2+i)2·(5−2i)
(2+i)·(2−i)·(5+2i)
i·(2−i)2·(5−2i)
729 27 33
730 1+27i
17+21i
21+17i
27+i		 i·(1+i)·(2−i)·(8−3i)
(1+i)·(2+i)·(8−3i)
(1+i)·(2−i)·(8+3i)
−i·(1+i)·(2+i)·(8+3i)
733 2+27i
27+2i		 (p)
(p)
738 3+27i
27+3i		 (1+i)·3·(5+4i)
(1+i)·3·(5−4i)
740 8+26i
16+22i
22+16i
26+8i		 (1+i)2·(2−i)·(6+i)
(1+i)2·(2−i)·(6−i)
−i·(1+i)2·(2+i)·(6+i)
−i·(1+i)2·(2+i)·(6−i)
745 4+27i
13+24i
24+13i
27+4i		 i·(2+i)·(10−7i)
(2+i)·(10+7i)
i·(2−i)·(10−7i)
(2−i)·(10+7i)
746 11+25i
25+11i		 (1+i)·(18+7i)
(1+i)·(18−7i)
Norm 751–1000
Norm Integer Factorization
754 5+27i
15+23i
23+15i
27+5i		 i·(1+i)·(3−2i)·(5−2i)
(1+i)·(3+2i)·(5−2i)
(1+i)·(3−2i)·(5+2i)
−i·(1+i)·(3+2i)·(5+2i)
757 9+26i
26+9i		 (p)
(p)
761 19+20i
20+19i		 (p)
(p)
765 6+27i
18+21i
21+18i
27+6i		 i·(2−i)·3·(4+i)
i·(2−i)·3·(4−i)
(2+i)·3·(4+i)
(2+i)·3·(4−i)
769 12+25i
25+12i		 (p)
(p)
772 14+24i
24+14i		 (1+i)2·(12−7i)
−i·(1+i)2·(12+7i)
773 17+22i
22+17i		 (p)
(p)
776 10+26i
26+10i		 −i·(1+i)3·(9+4i)
−i·(1+i)3·(9−4i)
778 7+27i
27+7i		 (1+i)·(17+10i)
(1+i)·(17−10i)
784 28 −(1+i)4·7
785 1+28i
16+23i
23+16i
28+i		 i·(2+i)·(11−6i)
(2+i)·(11+6i)
i·(2−i)·(11−6i)
(2−i)·(11+6i)
788 2+28i
28+2i		 (1+i)2·(14−i)
−i·(1+i)2·(14+i)
793 3+28i
8+27i
27+8i
28+3i		 i·(3+2i)·(6−5i)
(3+2i)·(6+5i)
i·(3−2i)·(6−5i)
(3−2i)·(6+5i)
794 13+25i
25+13i		 (1+i)·(19+6i)
(1+i)·(19−6i)
797 11+26i
26+11i		 (p)
(p)
800 4+28i
20+20i
28+4i		 −i·(1+i)5·(2−i)2
−(1+i)5·(2+i)·(2−i)
i·(1+i)5·(2+i)2
801 15+24i
24+15i		 i·3·(8−5i)
3·(8+5i)
802 19+21i
21+19i		 (1+i)·(20+i)
(1+i)·(20−i)
808 18+22i
22+18i		 −i·(1+i)3·(10+i)
−i·(1+i)3·(10−i)
809 5+28i
28+5i		 (p)
(p)
810 9+27i
27+9i		 (1+i)·(2+i)·32
(1+i)·(2−i)·32
818 17+23i
23+17i		 (1+i)·(20+3i)
(1+i)·(20−3i)
820 6+28i
12+26i
26+12i
28+6i		 (1+i)2·(2+i)·(5−4i)
−i·(1+i)2·(2+i)·(5+4i)
(1+i)2·(2−i)·(5−4i)
−i·(1+i)2·(2−i)·(5+4i)
821 14+25i
25+14i		 (p)
(p)
829 10+27i
27+10i		 (p)
(p)
832 16+24i
24+16i		 −(1+i)6·(3−2i)
i·(1+i)6·(3+2i)
833 7+28i
28+7i		 i·(4−i)·7
(4+i)·7
841 20+21i
21+20i
29		 i·(5−2i)2
(5+2i)2
(5+2i)·(5−2i)
842 1+29i
29+i		 (1+i)·(15+14i)
(1+i)·(15−14i)
845 2+29i
13+26i
19+22i
22+19i
26+13i
29+2i		 −(2−i)·(3−2i)2
i·(2−i)·(3+2i)·(3−2i)
i·(2+i)·(3−2i)2
(2−i)·(3+2i)2
(2+i)·(3+2i)·(3−2i)
−i·(2+i)·(3+2i)2
848 8+28i
28+8i		 −i·(1+i)4·(7−2i)
−(1+i)4·(7+2i)
850 3+29i
11+27i
15+25i
25+15i
27+11i
29+3i		 (1+i)·(2+i)2·(4−i)
i·(1+i)·(2−i)2·(4−i)
(1+i)·(2+i)·(2−i)·(4+i)
(1+i)·(2+i)·(2−i)·(4−i)
−i·(1+i)·(2+i)2·(4+i)
(1+i)·(2−i)2·(4+i)
853 18+23i
23+18i		 (p)
(p)
857 4+29i
29+4i		 (p)
(p)
865 9+28i
17+24i
24+17i
28+9i		 i·(2−i)·(13+2i)
i·(2−i)·(13−2i)
(2+i)·(13+2i)
(2+i)·(13−2i)
866 5+29i
29+5i		 (1+i)·(17+12i)
(1+i)·(17−12i)
872 14+26i
26+14i		 −i·(1+i)3·(10+3i)
−i·(1+i)3·(10−3i)
873 12+27i
27+12i		 i·3·(9−4i)
3·(9+4i)
877 6+29i
29+6i		 (p)
(p)
881 16+25i
25+16i		 (p)
(p)
882 21+21i (1+i)·3·7
884 10+28i
20+22i
22+20i
28+10i		 (1+i)2·(3−2i)·(4+i)
−i·(1+i)2·(3+2i)·(4+i)
(1+i)2·(3−2i)·(4−i)
−i·(1+i)2·(3+2i)·(4−i)
890 7+29i
19+23i
23+19i
29+7i		 i·(1+i)·(2−i)·(8−5i)
(1+i)·(2−i)·(8+5i)
(1+i)·(2+i)·(8−5i)
−i·(1+i)·(2+i)·(8+5i)
898 13+27i
27+13i		 (1+i)·(20+7i)
(1+i)·(20−7i)
900 18+24i
24+18i
30		 −i·(1+i)2·(2+i)2·3
(1+i)2·(2−i)2·3
−i·(1+i)2·(2+i)·(2−i)·3
901 1+30i
15+26i
26+15i
30+i		 i·(4+i)·(7−2i)
i·(4−i)·(7−2i)
(4+i)·(7+2i)
(4−i)·(7+2i)
904 2+30i
30+2i		 −i·(1+i)3·(8+7i)
−i·(1+i)3·(8−7i)
905 8+29i
11+28i
28+11i
29+8i		 i·(2+i)·(10−9i)
(2+i)·(10+9i)
i·(2−i)·(10−9i)
(2−i)·(10+9i)
909 3+30i
30+3i		 i·3·(10−i)
3·(10+i)
914 17+25i
25+17i		 (1+i)·(21+4i)
(1+i)·(21−4i)
916 4+30i
30+4i		 (1+i)2·(15−2i)
−i·(1+i)2·(15+2i)
922 9+29i
29+9i		 (1+i)·(19+10i)
(1+i)·(19−10i)
925 5+30i
14+27i
21+22i
22+21i
27+14i
30+5i		 i·(2+i)·(2−i)·(6−i)
(2+i)2·(6+i)
i·(2−i)2·(6+i)
(2+i)2·(6−i)
i·(2−i)2·(6−i)
(2+i)·(2−i)·(6+i)
928 12+28i
28+12i		 −(1+i)5·(5+2i)
−(1+i)5·(5−2i)
929 20+23i
23+20i		 (p)
(p)
932 16+26i
26+16i		 (1+i)2·(13−8i)
−i·(1+i)2·(13+8i)
936 6+30i
30+6i		 −i·(1+i)3·3·(3+2i)
−i·(1+i)3·3·(3−2i)
937 19+24i
24+19i		 (p)
(p)
941 10+29i
29+10i		 (p)
(p)
949 7+30i
18+25i
25+18i
30+7i		 i·(3−2i)·(8+3i)
(3+2i)·(8+3i)
i·(3−2i)·(8−3i)
(3+2i)·(8−3i)
953 13+28i
28+13i		 (p)
(p)
954 15+27i
27+15i		 (1+i)·3·(7+2i)
(1+i)·3·(7−2i)
961 31 (p)
962 1+31i
11+29i
29+11i
31+i		 (1+i)·(3+2i)·(6+i)
(1+i)·(3+2i)·(6−i)
(1+i)·(3−2i)·(6+i)
(1+i)·(3−2i)·(6−i)
964 8+30i
30+8i		 (1+i)2·(15−4i)
−i·(1+i)2·(15+4i)
965 2+31i
17+26i
26+17i
31+2i		 i·(2+i)·(12−7i)
(2+i)·(12+7i)
i·(2−i)·(12−7i)
(2−i)·(12+7i)
968 22+22i −i·(1+i)3·11
970 3+31i
21+23i
23+21i
31+3i		 i·(1+i)·(2−i)·(9−4i)
(1+i)·(2+i)·(9−4i)
(1+i)·(2−i)·(9+4i)
−i·(1+i)·(2+i)·(9+4i)
976 20+24i
24+20i		 −i·(1+i)4·(6−5i)
−(1+i)4·(6+5i)
977 4+31i
31+4i		 (p)
(p)
980 14+28i
28+14i		 (1+i)2·(2−i)·7
−i·(1+i)2·(2+i)·7
981 9+30i
30+9i		 i·3·(10−3i)
3·(10+3i)
985 12+29i
16+27i
27+16i
29+12i		 i·(2−i)·(14+i)
i·(2−i)·(14−i)
(2+i)·(14+i)
(2+i)·(14−i)
986 5+31i
19+25i
25+19i
31+5i		 (1+i)·(4+i)·(5+2i)
(1+i)·(4−i)·(5+2i)
(1+i)·(4+i)·(5−2i)
(1+i)·(4−i)·(5−2i)
997 6+31i
31+6i		 (p)
(p)
1000 10+30i
18+26i
26+18i
30+10i		 −i·(1+i)3·(2+i)2·(2−i)
(1+i)3·(2−i)3
−(1+i)3·(2+i)3
−i·(1+i)3·(2+i)·(2−i)2

See also

References

  • Dresden, Greg; Dymacek, Wayne (2005). "Finding factors of factor rings over the Gaussian integers". American Mathematical Monthly. 112 (7): 602–611. doi:10.2307/30037545. JSTOR 30037545. MR 2158894.
  • Gethner, Ellen; Wagner, Stan; Wick, Brian (1998). "A stroll through the Gaussian primes". Amer. Math. Monthly. 105 (4): 327–337. doi:10.2307/2589708. JSTOR 2589708. MR 1614871.
  • Matsui, Hajime (2000). "A bound for the least Gaussian prime omega with alpha < arg(omega) < beta". Arch. Math. 74 (6): 423–431. doi:10.1007/s000130050463. MR 1753540.
Index: pl ar de en es fr it arz nl ja pt ceb sv uk vi war zh ru af ast az bg zh-min-nan bn be ca cs cy da et el eo eu fa gl ko hi hr id he ka la lv lt hu mk ms min no nn ce uz kk ro simple sk sl sr sh fi ta tt th tg azb tr ur zh-yue hy my ace als am an hyw ban bjn map-bms ba be-tarask bcl bpy bar bs br cv nv eml hif fo fy ga gd gu hak ha hsb io ig ilo ia ie os is jv kn ht ku ckb ky mrj lb lij li lmo mai mg ml zh-classical mr xmf mzn cdo mn nap new ne frr oc mhr or as pa pnb ps pms nds crh qu sa sah sco sq scn si sd szl su sw tl shn te bug vec vo wa wuu yi yo diq bat-smg zu lad kbd ang smn ab roa-rup frp arc gn av ay bh bi bo bxr cbk-zam co za dag ary se pdc dv dsb myv ext fur gv gag inh ki glk gan guw xal haw rw kbp pam csb kw km kv koi kg gom ks gcr lo lbe ltg lez nia ln jbo lg mt mi tw mwl mdf mnw nqo fj nah na nds-nl nrm nov om pi pag pap pfl pcd krc kaa ksh rm rue sm sat sc trv stq nso sn cu so srn kab roa-tara tet tpi to chr tum tk tyv udm ug vep fiu-vro vls wo xh zea ty ak bm ch ny ee ff got iu ik kl mad cr pih ami pwn pnt dz rmy rn sg st tn ss ti din chy ts kcg ve
Prefix: a b c d e f g h i j k l m n o p q r s t u v w x y z 0 1 2 3 4 5 6 7 8 9

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