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 $x 2 + y 2$ (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	$2$	$- i \cdot(1+ i) 2$
5	$2+ i$ $1+2 i$	(p) (p)
8	$2+2 i$	$- i \cdot(1+ i) 3$
9	$3$	(p)
10	$1+3 i$ $3+ i$	$(1+ i)\cdot(2+ i)$ $(1+ i)\cdot(2- i)$
13	$3+2 i$ $2+3 i$	(p) (p)
16	$4$	$-(1+ i) 4$
17	$1+4 i$ $4+ i$	(p) (p)
18	$3+3 i$	$(1+ i)\cdot3$
20	$2+4 i$ $4+2 i$	$(1+ i) 2 \cdot(2- i)$ $- i \cdot(1+ i) 2 \cdot(2+ i)$
25	$3+4 i$ $4+3 i$ $5$	$(2+ i) 2$ $i \cdot(2- i) 2$ $(2+ i)\cdot(2- i)$
26	$1+5 i$ $5+ i$	$(1+ i)\cdot(3+2 i)$ $(1+ i)\cdot(3-2 i)$
29	$2+5 i$ $5+2 i$	(p) (p)
32	$4+4 i$	$-(1+ i) 5$
34	$3+5 i$ $5+3 i$	$(1+ i)\cdot(4+ i)$ $(1+ i)\cdot(4- i)$
36	$6$	$- i \cdot(1+ i) 2 \cdot3$
37	$1+6 i$ $6+ i$	(p) (p)
40	$2+6 i$ $6+2 i$	$- i \cdot(1+ i) 3 \cdot(2+ i)$ $- i \cdot(1+ i) 3 \cdot(2- i)$
41	$4+5 i$ $5+4 i$	(p) (p)
45	$3+6 i$ $6+3 i$	$i \cdot(2- i)\cdot3$ $(2+ i)\cdot3$
49	$7$	(p)
50	$1+7 i$ $5+5 i$ $7+ i$	$i \cdot(1+ i)\cdot(2- i) 2$ $(1+ i)\cdot(2+ i)\cdot(2- i)$ $- i \cdot(1+ i)\cdot(2+ i) 2$
52	$4+6 i$ $6+4 i$	$(1+ i) 2 \cdot(3-2 i)$ $- i \cdot(1+ i) 2 \cdot(3+2 i)$
53	$2+7 i$ $7+2 i$	(p) (p)
58	$3+7 i$ $7+3 i$	$(1+ i)\cdot(5+2 i)$ $(1+ i)\cdot(5-2 i)$
61	$5+6 i$ $6+5 i$	(p) (p)
64	$8$	$i \cdot(1+ i) 6$
65	$1+8 i$ $4+7 i$ $7+4 i$ $8+ i$	$i \cdot(2+ i)\cdot(3-2 i)$ $(2+ i)\cdot(3+2 i)$ $i \cdot(2- i)\cdot(3-2 i)$ $(2- i)\cdot(3+2 i)$
68	$2+8 i$ $8+2 i$	$(1+ i) 2 \cdot(4- i)$ $- i \cdot(1+ i) 2 \cdot(4+ i)$
72	$6+6 i$	$- i \cdot(1+ i) 3 \cdot3$
73	$3+8 i$ $8+3 i$	(p) (p)
74	$5+7 i$ $7+5 i$	$(1+ i)\cdot(6+ i)$ $(1+ i)\cdot(6- i)$
80	$4+8 i$ $8+4 i$	$- i \cdot(1+ i) 4 \cdot(2- i)$ $-(1+ i) 4 \cdot(2+ i)$
81	$9$	$32$
82	$1+9 i$ $9+ i$	$(1+ i)\cdot(5+4 i)$ $(1+ i)\cdot(5-4 i)$
85	$2+9 i$ $6+7 i$ $7+6 i$ $9+2 i$	$i \cdot(2- i)\cdot(4+ i)$ $i \cdot(2- i)\cdot(4- i)$ $(2+ i)\cdot(4+ i)$ $(2+ i)\cdot(4- i)$
89	$5+8 i$ $8+5 i$	(p) (p)
90	$3+9 i$ $9+3 i$	$(1+ i)\cdot(2+ i)\cdot3$ $(1+ i)\cdot(2- i)\cdot3$
97	$4+9 i$ $9+4 i$	(p) (p)
98	$7+7 i$	$(1+ i)\cdot7$
100	$6+8 i$ $8+6 i$ $10$	$- i \cdot(1+ i) 2 \cdot(2+ i) 2$ $(1+ i) 2 \cdot(2- i) 2$ $- i \cdot(1+ i) 2 \cdot(2+ i)\cdot(2- i)$
101	$1+10 i$ $10+ i$	(p) (p)
104	$2+10 i$ $10+2 i$	$- i \cdot(1+ i) 3 \cdot(3+2 i)$ $- i \cdot(1+ i) 3 \cdot(3-2 i)$
106	$5+9 i$ $9+5 i$	$(1+ i)\cdot(7+2 i)$ $(1+ i)\cdot(7-2 i)$
109	$3+10 i$ $10+3 i$	(p) (p)
113	$7+8 i$ $8+7 i$	(p) (p)
116	$4+10 i$ $10+4 i$	$(1+ i) 2 \cdot(5-2 i)$ $- i \cdot(1+ i) 2 \cdot(5+2 i)$
117	$6+9 i$ $9+6 i$	$i \cdot3\cdot(3-2 i)$ $3\cdot(3+2 i)$
121	$11$	(p)
122	$1+11 i$ $11+ i$	$(1+ i)\cdot(6+5 i)$ $(1+ i)\cdot(6-5 i)$
125	$2+11 i$ $5+10 i$ $10+5 i$ $11+2 i$	$(2+ i) 3$ $i \cdot(2+ i)\cdot(2- i) 2$ $(2+ i) 2 \cdot(2- i)$ $i \cdot(2- i) 3$
128	$8+8 i$	$i \cdot(1+ i) 7$
130	$3+11 i$ $7+9 i$ $9+7 i$ $11+3 i$	$i \cdot(1+ i)\cdot(2- i)\cdot(3-2 i)$ $(1+ i)\cdot(2- i)\cdot(3+2 i)$ $(1+ i)\cdot(2+ i)\cdot(3-2 i)$ $- i \cdot(1+ i)\cdot(2+ i)\cdot(3+2 i)$
136	$6+10 i$ $10+6 i$	$- i \cdot(1+ i) 3 \cdot(4+ i)$ $- i \cdot(1+ i) 3 \cdot(4- i)$
137	$4+11 i$ $11+4 i$	(p) (p)
144	$12$	$-(1+ i) 4 \cdot3$
145	$1+12 i$ $8+9 i$ $9+8 i$ $12+ i$	$i \cdot(2- i)\cdot(5+2 i)$ $(2+ i)\cdot(5+2 i)$ $i \cdot(2- i)\cdot(5-2 i)$ $(2+ i)\cdot(5-2 i)$
146	$5+11 i$ $11+5 i$	$(1+ i)\cdot(8+3 i)$ $(1+ i)\cdot(8-3 i)$
148	$2+12 i$ $12+2 i$	$(1+ i) 2 \cdot(6- i)$ $- i \cdot(1+ i) 2 \cdot(6+ i)$
149	$7+10 i$ $10+7 i$	(p) (p)
153	$3+12 i$ $12+3 i$	$i \cdot3\cdot(4- i)$ $3\cdot(4+ i)$
157	$6+11 i$ $11+6 i$	(p) (p)
160	$4+12 i$ $12+4 i$	$-(1+ i) 5 \cdot(2+ i)$ $-(1+ i) 5 \cdot(2- i)$
162	$9+9 i$	$(1+ i)\cdot3 2$
164	$8+10 i$ $10+8 i$	$(1+ i) 2 \cdot(5-4 i)$ $- i \cdot(1+ i) 2 \cdot(5+4 i)$
169	$5+12 i$ $12+5 i$ $13$	$(3+2 i) 2$ $i \cdot(3-2 i) 2$ $(3+2 i)\cdot(3-2 i)$
170	$1+13 i$ $7+11 i$ $11+7 i$ $13+ i$	$(1+ i)\cdot(2+ i)\cdot(4+ i)$ $(1+ i)\cdot(2+ i)\cdot(4- i)$ $(1+ i)\cdot(2- i)\cdot(4+ i)$ $(1+ i)\cdot(2- i)\cdot(4- i)$
173	$2+13 i$ $13+2 i$	(p) (p)
178	$3+13 i$ $13+3 i$	$(1+ i)\cdot(8+5 i)$ $(1+ i)\cdot(8-5 i)$
180	$6+12 i$ $12+6 i$	$(1+ i) 2 \cdot(2- i)\cdot3$ $- i \cdot(1+ i) 2 \cdot(2+ i)\cdot3$
181	$9+10 i$ $10+9 i$	(p) (p)
185	$4+13 i$ $8+11 i$ $11+8 i$ $13+4 i$	$i \cdot(2- i)\cdot(6+ i)$ $i \cdot(2- i)\cdot(6- i)$ $(2+ i)\cdot(6+ i)$ $(2+ i)\cdot(6- i)$
193	$7+12 i$ $12+7 i$	(p) (p)
194	$5+13 i$ $13+5 i$	$(1+ i)\cdot(9+4 i)$ $(1+ i)\cdot(9-4 i)$
196	$14$	$- i \cdot(1+ i) 2 \cdot7$
197	$1+14 i$ $14+ i$	(p) (p)
200	$2+14 i$ $10+10 i$ $14+2 i$	$(1+ i) 3 \cdot(2- i) 2$ $- i \cdot(1+ i) 3 \cdot(2+ i)\cdot(2- i)$ $-(1+ i) 3 \cdot(2+ i) 2$
202	$9+11 i$ $11+9 i$	$(1+ i)\cdot(10+ i)$ $(1+ i)\cdot(10- i)$
205	$3+14 i$ $6+13 i$ $13+6 i$ $14+3 i$	$i \cdot(2+ i)\cdot(5-4 i)$ $(2+ i)\cdot(5+4 i)$ $i \cdot(2- i)\cdot(5-4 i)$ $(2- i)\cdot(5+4 i)$
208	$8+12 i$ $12+8 i$	$- i \cdot(1+ i) 4 \cdot(3-2 i)$ $-(1+ i) 4 \cdot(3+2 i)$
212	$4+14 i$ $14+4 i$	$(1+ i) 2 \cdot(7-2 i)$ $- i \cdot(1+ i) 2 \cdot(7+2 i)$
218	$7+13 i$ $13+7 i$	$(1+ i)\cdot(10+3 i)$ $(1+ i)\cdot(10-3 i)$
221	$5+14 i$ $10+11 i$ $11+10 i$ $14+5 i$	$i \cdot(3-2 i)\cdot(4+ i)$ $(3+2 i)\cdot(4+ i)$ $i \cdot(3-2 i)\cdot(4- i)$ $(3+2 i)\cdot(4- i)$
225	$9+12 i$ $12+9 i$ $15$	$(2+ i) 2 \cdot3$ $i \cdot(2- i) 2 \cdot3$ $(2+ i)\cdot(2- i)\cdot3$
226	$1+15 i$ $15+ i$	$(1+ i)\cdot(8+7 i)$ $(1+ i)\cdot(8-7 i)$
229	$2+15 i$ $15+2 i$	(p) (p)
232	$6+14 i$ $14+6 i$	$- i \cdot(1+ i) 3 \cdot(5+2 i)$ $- i \cdot(1+ i) 3 \cdot(5-2 i)$
233	$8+13 i$ $13+8 i$	(p) (p)
234	$3+15 i$ $15+3 i$	$(1+ i)\cdot3\cdot(3+2 i)$ $(1+ i)\cdot3\cdot(3-2 i)$
241	$4+15 i$ $15+4 i$	(p) (p)
242	$11+11 i$	$(1+ i)\cdot11$
244	$10+12 i$ $12+10 i$	$(1+ i) 2 \cdot(6-5 i)$ $- i \cdot(1+ i) 2 \cdot(6+5 i)$
245	$7+14 i$ $14+7 i$	$i \cdot(2- i)\cdot7$ $(2+ i)\cdot7$
250	$5+15 i$ $9+13 i$ $13+9 i$ $15+5 i$	$(1+ i)\cdot(2+ i) 2 \cdot(2- i)$ $i \cdot(1+ i)\cdot(2- i) 3$ $- i \cdot(1+ i)\cdot(2+ i) 3$ $(1+ i)\cdot(2+ i)\cdot(2- i) 2$

Norm 251–500
Norm	Integer	Factorization
256	$16$	$(1+ i) 8$
257	$1+16 i$ $16+ i$	(p) (p)
260	$2+16 i$ $8+14 i$ $14+8 i$ $16+2 i$	$(1+ i) 2 \cdot(2+ i)\cdot(3-2 i)$ $- i \cdot(1+ i) 2 \cdot(2+ i)\cdot(3+2 i)$ $(1+ i) 2 \cdot(2- i)\cdot(3-2 i)$ $- i \cdot(1+ i) 2 \cdot(2- i)\cdot(3+2 i)$
261	$6+15 i$ $15+6 i$	$i \cdot3\cdot(5-2 i)$ $3\cdot(5+2 i)$
265	$3+16 i$ $11+12 i$ $12+11 i$ $16+3 i$	$i \cdot(2- i)\cdot(7+2 i)$ $i \cdot(2- i)\cdot(7-2 i)$ $(2+ i)\cdot(7+2 i)$ $(2+ i)\cdot(7-2 i)$
269	$10+13 i$ $13+10 i$	(p) (p)
272	$4+16 i$ $16+4 i$	$- i \cdot(1+ i) 4 \cdot(4- i)$ $-(1+ i) 4 \cdot(4+ i)$
274	$7+15 i$ $15+7 i$	$(1+ i)\cdot(11+4 i)$ $(1+ i)\cdot(11-4 i)$
277	$9+14 i$ $14+9 i$	(p) (p)
281	$5+16 i$ $16+5 i$	(p) (p)
288	$12+12 i$	$-(1+ i) 5 \cdot3$
289	$8+15 i$ $15+8 i$ $17$	$i \cdot(4- i) 2$ $(4+ i) 2$ $(4+ i)\cdot(4- i)$
290	$1+17 i$ $11+13 i$ $13+11 i$ $17+ i$	$i \cdot(1+ i)\cdot(2- i)\cdot(5-2 i)$ $(1+ i)\cdot(2+ i)\cdot(5-2 i)$ $(1+ i)\cdot(2- i)\cdot(5+2 i)$ $- i \cdot(1+ i)\cdot(2+ i)\cdot(5+2 i)$
292	$6+16 i$ $16+6 i$	$(1+ i) 2 \cdot(8-3 i)$ $- i \cdot(1+ i) 2 \cdot(8+3 i)$
293	$2+17 i$ $17+2 i$	(p) (p)
296	$10+14 i$ $14+10 i$	$- i \cdot(1+ i) 3 \cdot(6+ i)$ $- i \cdot(1+ i) 3 \cdot(6- i)$
298	$3+17 i$ $17+3 i$	$(1+ i)\cdot(10+7 i)$ $(1+ i)\cdot(10-7 i)$
305	$4+17 i$ $7+16 i$ $16+7 i$ $17+4 i$	$i \cdot(2+ i)\cdot(6-5 i)$ $(2+ i)\cdot(6+5 i)$ $i \cdot(2- i)\cdot(6-5 i)$ $(2- i)\cdot(6+5 i)$
306	$9+15 i$ $15+9 i$	$(1+ i)\cdot3\cdot(4+ i)$ $(1+ i)\cdot3\cdot(4- i)$
313	$12+13 i$ $13+12 i$	(p) (p)
314	$5+17 i$ $17+5 i$	$(1+ i)\cdot(11+6 i)$ $(1+ i)\cdot(11-6 i)$
317	$11+14 i$ $14+11 i$	(p) (p)
320	$8+16 i$ $16+8 i$	$-(1+ i) 6 \cdot(2- i)$ $i \cdot(1+ i) 6 \cdot(2+ i)$
324	$18$	$- i \cdot(1+ i) 2 \cdot3 2$
325	$1+18 i$ $6+17 i$ $10+15 i$ $15+10 i$ $17+6 i$ $18+ i$	$(2+ i) 2 \cdot(3+2 i)$ $i \cdot(2- i) 2 \cdot(3+2 i)$ $i \cdot(2+ i)\cdot(2- i)\cdot(3-2 i)$ $(2+ i)\cdot(2- i)\cdot(3+2 i)$ $(2+ i) 2 \cdot(3-2 i)$ $i \cdot(2- i) 2 \cdot(3-2 i)$
328	$2+18 i$ $18+2 i$	$- i \cdot(1+ i) 3 \cdot(5+4 i)$ $- i \cdot(1+ i) 3 \cdot(5-4 i)$
333	$3+18 i$ $18+3 i$	$i \cdot3\cdot(6- i)$ $3\cdot(6+ i)$
337	$9+16 i$ $16+9 i$	(p) (p)
338	$7+17 i$ $13+13 i$ $17+7 i$	$i \cdot(1+ i)\cdot(3-2 i) 2$ $(1+ i)\cdot(3+2 i)\cdot(3-2 i)$ $- i \cdot(1+ i)\cdot(3+2 i) 2$
340	$4+18 i$ $12+14 i$ $14+12 i$ $18+4 i$	$(1+ i) 2 \cdot(2- i)\cdot(4+ i)$ $(1+ i) 2 \cdot(2- i)\cdot(4- i)$ $- i \cdot(1+ i) 2 \cdot(2+ i)\cdot(4+ i)$ $- i \cdot(1+ i) 2 \cdot(2+ i)\cdot(4- i)$
346	$11+15 i$ $15+11 i$	$(1+ i)\cdot(13+2 i)$ $(1+ i)\cdot(13-2 i)$
349	$5+18 i$ $18+5 i$	(p) (p)
353	$8+17 i$ $17+8 i$	(p) (p)
356	$10+16 i$ $16+10 i$	$(1+ i) 2 \cdot(8-5 i)$ $- i \cdot(1+ i) 2 \cdot(8+5 i)$
360	$6+18 i$ $18+6 i$	$- i \cdot(1+ i) 3 \cdot(2+ i)\cdot3$ $- i \cdot(1+ i) 3 \cdot(2- i)\cdot3$
361	$19$	(p)
362	$1+19 i$ $19+ i$	$(1+ i)\cdot(10+9 i)$ $(1+ i)\cdot(10-9 i)$
365	$2+19 i$ $13+14 i$ $14+13 i$ $19+2 i$	$i \cdot(2- i)\cdot(8+3 i)$ $(2+ i)\cdot(8+3 i)$ $i \cdot(2- i)\cdot(8-3 i)$ $(2+ i)\cdot(8-3 i)$
369	$12+15 i$ $15+12 i$	$i \cdot3\cdot(5-4 i)$ $3\cdot(5+4 i)$
370	$3+19 i$ $9+17 i$ $17+9 i$ $19+3 i$	$(1+ i)\cdot(2+ i)\cdot(6+ i)$ $(1+ i)\cdot(2+ i)\cdot(6- i)$ $(1+ i)\cdot(2- i)\cdot(6+ i)$ $(1+ i)\cdot(2- i)\cdot(6- i)$
373	$7+18 i$ $18+7 i$	(p) (p)
377	$4+19 i$ $11+16 i$ $16+11 i$ $19+4 i$	$i \cdot(3-2 i)\cdot(5+2 i)$ $(3+2 i)\cdot(5+2 i)$ $i \cdot(3-2 i)\cdot(5-2 i)$ $(3+2 i)\cdot(5-2 i)$
386	$5+19 i$ $19+5 i$	$(1+ i)\cdot(12+7 i)$ $(1+ i)\cdot(12-7 i)$
388	$8+18 i$ $18+8 i$	$(1+ i) 2 \cdot(9-4 i)$ $- i \cdot(1+ i) 2 \cdot(9+4 i)$
389	$10+17 i$ $17+10 i$	(p) (p)
392	$14+14 i$	$- i \cdot(1+ i) 3 \cdot7$
394	$13+15 i$ $15+13 i$	$(1+ i)\cdot(14+ i)$ $(1+ i)\cdot(14- i)$
397	$6+19 i$ $19+6 i$	(p) (p)
400	$12+16 i$ $16+12 i$ $20$	$-(1+ i) 4 \cdot(2+ i) 2$ $- i \cdot(1+ i) 4 \cdot(2- i) 2$ $-(1+ i) 4 \cdot(2+ i)\cdot(2- i)$
401	$1+20 i$ $20+ i$	(p) (p)
404	$2+20 i$ $20+2 i$	$(1+ i) 2 \cdot(10- i)$ $- i \cdot(1+ i) 2 \cdot(10+ i)$
405	$9+18 i$ $18+9 i$	$i \cdot(2- i)\cdot3 2$ $(2+ i)\cdot3 2$
409	$3+20 i$ $20+3 i$	(p) (p)
410	$7+19 i$ $11+17 i$ $17+11 i$ $19+7 i$	$i \cdot(1+ i)\cdot(2- i)\cdot(5-4 i)$ $(1+ i)\cdot(2- i)\cdot(5+4 i)$ $(1+ i)\cdot(2+ i)\cdot(5-4 i)$ $- i \cdot(1+ i)\cdot(2+ i)\cdot(5+4 i)$
416	$4+20 i$ $20+4 i$	$-(1+ i) 5 \cdot(3+2 i)$ $-(1+ i) 5 \cdot(3-2 i)$
421	$14+15 i$ $15+14 i$	(p) (p)
424	$10+18 i$ $18+10 i$	$- i \cdot(1+ i) 3 \cdot(7+2 i)$ $- i \cdot(1+ i) 3 \cdot(7-2 i)$
425	$5+20 i$ $8+19 i$ $13+16 i$ $16+13 i$ $19+8 i$ $20+5 i$	$i \cdot(2+ i)\cdot(2- i)\cdot(4- i)$ $(2+ i) 2 \cdot(4+ i)$ $i \cdot(2- i) 2 \cdot(4+ i)$ $(2+ i) 2 \cdot(4- i)$ $i \cdot(2- i) 2 \cdot(4- i)$ $(2+ i)\cdot(2- i)\cdot(4+ i)$
433	$12+17 i$ $17+12 i$	(p) (p)
436	$6+20 i$ $20+6 i$	$(1+ i) 2 \cdot(10-3 i)$ $- i \cdot(1+ i) 2 \cdot(10+3 i)$
441	$21$	$3\cdot7$
442	$1+21 i$ $9+19 i$ $19+9 i$ $21+ i$	$i \cdot(1+ i)\cdot(3-2 i)\cdot(4- i)$ $(1+ i)\cdot(3+2 i)\cdot(4- i)$ $(1+ i)\cdot(3-2 i)\cdot(4+ i)$ $- i \cdot(1+ i)\cdot(3+2 i)\cdot(4+ i)$
445	$2+21 i$ $11+18 i$ $18+11 i$ $21+2 i$	$i \cdot(2+ i)\cdot(8-5 i)$ $(2+ i)\cdot(8+5 i)$ $i \cdot(2- i)\cdot(8-5 i)$ $(2- i)\cdot(8+5 i)$
449	$7+20 i$ $20+7 i$	(p) (p)
450	$3+21 i$ $15+15 i$ $21+3 i$	$i \cdot(1+ i)\cdot(2- i) 2 \cdot3$ $(1+ i)\cdot(2+ i)\cdot(2- i)\cdot3$ $- i \cdot(1+ i)\cdot(2+ i) 2 \cdot3$
452	$14+16 i$ $16+14 i$	$(1+ i) 2 \cdot(8-7 i)$ $- i \cdot(1+ i) 2 \cdot(8+7 i)$
457	$4+21 i$ $21+4 i$	(p) (p)
458	$13+17 i$ $17+13 i$	$(1+ i)\cdot(15+2 i)$ $(1+ i)\cdot(15-2 i)$
461	$10+19 i$ $19+10 i$	(p) (p)
464	$8+20 i$ $20+8 i$	$- i \cdot(1+ i) 4 \cdot(5-2 i)$ $-(1+ i) 4 \cdot(5+2 i)$
466	$5+21 i$ $21+5 i$	$(1+ i)\cdot(13+8 i)$ $(1+ i)\cdot(13-8 i)$
468	$12+18 i$ $18+12 i$	$(1+ i) 2 \cdot3\cdot(3-2 i)$ $- i \cdot(1+ i) 2 \cdot3\cdot(3+2 i)$
477	$6+21 i$ $21+6 i$	$i \cdot3\cdot(7-2 i)$ $3\cdot(7+2 i)$
481	$9+20 i$ $15+16 i$ $16+15 i$ $20+9 i$	$i \cdot(3-2 i)\cdot(6+ i)$ $i \cdot(3-2 i)\cdot(6- i)$ $(3+2 i)\cdot(6+ i)$ $(3+2 i)\cdot(6- i)$
482	$11+19 i$ $19+11 i$	$(1+ i)\cdot(15+4 i)$ $(1+ i)\cdot(15-4 i)$
484	$22$	$- i \cdot(1+ i) 2 \cdot11$
485	$1+22 i$ $14+17 i$ $17+14 i$ $22+ i$	$i \cdot(2- i)\cdot(9+4 i)$ $(2+ i)\cdot(9+4 i)$ $i \cdot(2- i)\cdot(9-4 i)$ $(2+ i)\cdot(9-4 i)$
488	$2+22 i$ $22+2 i$	$- i \cdot(1+ i) 3 \cdot(6+5 i)$ $- i \cdot(1+ i) 3 \cdot(6-5 i)$
490	$7+21 i$ $21+7 i$	$(1+ i)\cdot(2+ i)\cdot7$ $(1+ i)\cdot(2- i)\cdot7$
493	$3+22 i$ $13+18 i$ $18+13 i$ $22+3 i$	$i \cdot(4+ i)\cdot(5-2 i)$ $i \cdot(4- i)\cdot(5-2 i)$ $(4+ i)\cdot(5+2 i)$ $(4- i)\cdot(5+2 i)$
500	$4+22 i$ $10+20 i$ $20+10 i$ $22+4 i$	$- i \cdot(1+ i) 2 \cdot(2+ i) 3$ $(1+ i) 2 \cdot(2+ i)\cdot(2- i) 2$ $- i \cdot(1+ i) 2 \cdot(2+ i) 2 \cdot(2- i)$ $(1+ i) 2 \cdot(2- i) 3$

Norm 501–750
Norm	Integer	Factorization
505	$8+21 i$ $12+19 i$ $19+12 i$ $21+8 i$	$i \cdot(2- i)\cdot(10+ i)$ $i \cdot(2- i)\cdot(10- i)$ $(2+ i)\cdot(10+ i)$ $(2+ i)\cdot(10- i)$
509	$5+22 i$ $22+5 i$	(p) (p)
512	$16+16 i$	$(1+ i) 9$
514	$15+17 i$ $17+15 i$	$(1+ i)\cdot(16+ i)$ $(1+ i)\cdot(16- i)$
520	$6+22 i$ $14+18 i$ $18+14 i$ $22+6 i$	$(1+ i) 3 \cdot(2- i)\cdot(3-2 i)$ $- i \cdot(1+ i) 3 \cdot(2- i)\cdot(3+2 i)$ $- i \cdot(1+ i) 3 \cdot(2+ i)\cdot(3-2 i)$ $-(1+ i) 3 \cdot(2+ i)\cdot(3+2 i)$
521	$11+20 i$ $20+11 i$	(p) (p)
522	$9+21 i$ $21+9 i$	$(1+ i)\cdot3\cdot(5+2 i)$ $(1+ i)\cdot3\cdot(5-2 i)$
529	$23$	(p)
530	$1+23 i$ $13+19 i$ $19+13 i$ $23+ i$	$(1+ i)\cdot(2+ i)\cdot(7+2 i)$ $(1+ i)\cdot(2+ i)\cdot(7-2 i)$ $(1+ i)\cdot(2- i)\cdot(7+2 i)$ $(1+ i)\cdot(2- i)\cdot(7-2 i)$
533	$2+23 i$ $7+22 i$ $22+7 i$ $23+2 i$	$i \cdot(3+2 i)\cdot(5-4 i)$ $(3+2 i)\cdot(5+4 i)$ $i \cdot(3-2 i)\cdot(5-4 i)$ $(3-2 i)\cdot(5+4 i)$
538	$3+23 i$ $23+3 i$	$(1+ i)\cdot(13+10 i)$ $(1+ i)\cdot(13-10 i)$
541	$10+21 i$ $21+10 i$	(p) (p)
544	$12+20 i$ $20+12 i$	$-(1+ i) 5 \cdot(4+ i)$ $-(1+ i) 5 \cdot(4- i)$
545	$4+23 i$ $16+17 i$ $17+16 i$ $23+4 i$	$i \cdot(2- i)\cdot(10+3 i)$ $i \cdot(2- i)\cdot(10-3 i)$ $(2+ i)\cdot(10+3 i)$ $(2+ i)\cdot(10-3 i)$
548	$8+22 i$ $22+8 i$	$(1+ i) 2 \cdot(11-4 i)$ $- i \cdot(1+ i) 2 \cdot(11+4 i)$
549	$15+18 i$ $18+15 i$	$i \cdot3\cdot(6-5 i)$ $3\cdot(6+5 i)$
554	$5+23 i$ $23+5 i$	$(1+ i)\cdot(14+9 i)$ $(1+ i)\cdot(14-9 i)$
557	$14+19 i$ $19+14 i$	(p) (p)
562	$11+21 i$ $21+11 i$	$(1+ i)\cdot(16+5 i)$ $(1+ i)\cdot(16-5 i)$
565	$6+23 i$ $9+22 i$ $22+9 i$ $23+6 i$	$i \cdot(2+ i)\cdot(8-7 i)$ $(2+ i)\cdot(8+7 i)$ $i \cdot(2- i)\cdot(8-7 i)$ $(2- i)\cdot(8+7 i)$
569	$13+20 i$ $20+13 i$	(p) (p)
576	$24$	$i \cdot(1+ i) 6 \cdot3$
577	$1+24 i$ $24+ i$	(p) (p)
578	$7+23 i$ $17+17 i$ $23+7 i$	$(1+ i)\cdot(4+ i) 2$ $(1+ i)\cdot(4+ i)\cdot(4- i)$ $(1+ i)\cdot(4- i) 2$
580	$2+24 i$ $16+18 i$ $18+16 i$ $24+2 i$	$(1+ i) 2 \cdot(2- i)\cdot(5+2 i)$ $- i \cdot(1+ i) 2 \cdot(2+ i)\cdot(5+2 i)$ $(1+ i) 2 \cdot(2- i)\cdot(5-2 i)$ $- i \cdot(1+ i) 2 \cdot(2+ i)\cdot(5-2 i)$
584	$10+22 i$ $22+10 i$	$- i \cdot(1+ i) 3 \cdot(8+3 i)$ $- i \cdot(1+ i) 3 \cdot(8-3 i)$
585	$3+24 i$ $12+21 i$ $21+12 i$ $24+3 i$	$i \cdot(2+ i)\cdot3\cdot(3-2 i)$ $(2+ i)\cdot3\cdot(3+2 i)$ $i \cdot(2- i)\cdot3\cdot(3-2 i)$ $(2- i)\cdot3\cdot(3+2 i)$
586	$15+19 i$ $19+15 i$	$(1+ i)\cdot(17+2 i)$ $(1+ i)\cdot(17-2 i)$
592	$4+24 i$ $24+4 i$	$- i \cdot(1+ i) 4 \cdot(6- i)$ $-(1+ i) 4 \cdot(6+ i)$
593	$8+23 i$ $23+8 i$	(p) (p)
596	$14+20 i$ $20+14 i$	$(1+ i) 2 \cdot(10-7 i)$ $- i \cdot(1+ i) 2 \cdot(10+7 i)$
601	$5+24 i$ $24+5 i$	(p) (p)
605	$11+22 i$ $22+11 i$	$i \cdot(2- i)\cdot11$ $(2+ i)\cdot11$
610	$9+23 i$ $13+21 i$ $21+13 i$ $23+9 i$	$i \cdot(1+ i)\cdot(2- i)\cdot(6-5 i)$ $(1+ i)\cdot(2- i)\cdot(6+5 i)$ $(1+ i)\cdot(2+ i)\cdot(6-5 i)$ $- i \cdot(1+ i)\cdot(2+ i)\cdot(6+5 i)$
612	$6+24 i$ $24+6 i$	$(1+ i) 2 \cdot3\cdot(4- i)$ $- i \cdot(1+ i) 2 \cdot3\cdot(4+ i)$
613	$17+18 i$ $18+17 i$	(p) (p)
617	$16+19 i$ $19+16 i$	(p) (p)
625	$7+24 i$ $15+20 i$ $20+15 i$ $24+7 i$ $25$	$-(2- i) 4$ $(2+ i) 3 \cdot(2- i)$ $i \cdot(2+ i)\cdot(2- i) 3$ $- i \cdot(2+ i) 4$ $(2+ i) 2 \cdot(2- i) 2$
626	$1+25 i$ $25+ i$	$(1+ i)\cdot(13+12 i)$ $(1+ i)\cdot(13-12 i)$
628	$12+22 i$ $22+12 i$	$(1+ i) 2 \cdot(11-6 i)$ $- i \cdot(1+ i) 2 \cdot(11+6 i)$
629	$2+25 i$ $10+23 i$ $23+10 i$ $25+2 i$	$i \cdot(4- i)\cdot(6+ i)$ $i \cdot(4- i)\cdot(6- i)$ $(4+ i)\cdot(6+ i)$ $(4+ i)\cdot(6- i)$
634	$3+25 i$ $25+3 i$	$(1+ i)\cdot(14+11 i)$ $(1+ i)\cdot(14-11 i)$
637	$14+21 i$ $21+14 i$	$i \cdot(3-2 i)\cdot7$ $(3+2 i)\cdot7$
640	$8+24 i$ $24+8 i$	$i \cdot(1+ i) 7 \cdot(2+ i)$ $i \cdot(1+ i) 7 \cdot(2- i)$
641	$4+25 i$ $25+4 i$	(p) (p)
648	$18+18 i$	$- i \cdot(1+ i) 3 \cdot3 2$
650	$5+25 i$ $11+23 i$ $17+19 i$ $19+17 i$ $23+11 i$ $25+5 i$	$(1+ i)\cdot(2+ i)\cdot(2- i)\cdot(3+2 i)$ $(1+ i)\cdot(2+ i) 2 \cdot(3-2 i)$ $i \cdot(1+ i)\cdot(2- i) 2 \cdot(3-2 i)$ $- i \cdot(1+ i)\cdot(2+ i) 2 \cdot(3+2 i)$ $(1+ i)\cdot(2- i) 2 \cdot(3+2 i)$ $(1+ i)\cdot(2+ i)\cdot(2- i)\cdot(3-2 i)$
653	$13+22 i$ $22+13 i$	(p) (p)
656	$16+20 i$ $20+16 i$	$- i \cdot(1+ i) 4 \cdot(5-4 i)$ $-(1+ i) 4 \cdot(5+4 i)$
657	$9+24 i$ $24+9 i$	$i \cdot3\cdot(8-3 i)$ $3\cdot(8+3 i)$
661	$6+25 i$ $25+6 i$	(p) (p)
666	$15+21 i$ $21+15 i$	$(1+ i)\cdot3\cdot(6+ i)$ $(1+ i)\cdot3\cdot(6- i)$
673	$12+23 i$ $23+12 i$	(p) (p)
674	$7+25 i$ $25+7 i$	$(1+ i)\cdot(16+9 i)$ $(1+ i)\cdot(16-9 i)$
676	$10+24 i$ $24+10 i$ $26$	$- i \cdot(1+ i) 2 \cdot(3+2 i) 2$ $(1+ i) 2 \cdot(3-2 i) 2$ $- i \cdot(1+ i) 2 \cdot(3+2 i)\cdot(3-2 i)$
677	$1+26 i$ $26+ i$	(p) (p)
680	$2+26 i$ $14+22 i$ $22+14 i$ $26+2 i$	$- i \cdot(1+ i) 3 \cdot(2+ i)\cdot(4+ i)$ $- i \cdot(1+ i) 3 \cdot(2+ i)\cdot(4- i)$ $- i \cdot(1+ i) 3 \cdot(2- i)\cdot(4+ i)$ $- i \cdot(1+ i) 3 \cdot(2- i)\cdot(4- i)$
685	$3+26 i$ $18+19 i$ $19+18 i$ $26+3 i$	$i \cdot(2- i)\cdot(11+4 i)$ $(2+ i)\cdot(11+4 i)$ $i \cdot(2- i)\cdot(11-4 i)$ $(2+ i)\cdot(11-4 i)$
689	$8+25 i$ $17+20 i$ $20+17 i$ $25+8 i$	$i \cdot(3-2 i)\cdot(7+2 i)$ $(3+2 i)\cdot(7+2 i)$ $i \cdot(3-2 i)\cdot(7-2 i)$ $(3+2 i)\cdot(7-2 i)$
692	$4+26 i$ $26+4 i$	$(1+ i) 2 \cdot(13-2 i)$ $- i \cdot(1+ i) 2 \cdot(13+2 i)$
697	$11+24 i$ $16+21 i$ $21+16 i$ $24+11 i$	$i \cdot(4+ i)\cdot(5-4 i)$ $(4+ i)\cdot(5+4 i)$ $i \cdot(4- i)\cdot(5-4 i)$ $(4- i)\cdot(5+4 i)$
698	$13+23 i$ $23+13 i$	$(1+ i)\cdot(18+5 i)$ $(1+ i)\cdot(18-5 i)$
701	$5+26 i$ $26+5 i$	(p) (p)
706	$9+25 i$ $25+9 i$	$(1+ i)\cdot(17+8 i)$ $(1+ i)\cdot(17-8 i)$
709	$15+22 i$ $22+15 i$	(p) (p)
712	$6+26 i$ $26+6 i$	$- i \cdot(1+ i) 3 \cdot(8+5 i)$ $- i \cdot(1+ i) 3 \cdot(8-5 i)$
720	$12+24 i$ $24+12 i$	$- i \cdot(1+ i) 4 \cdot(2- i)\cdot3$ $-(1+ i) 4 \cdot(2+ i)\cdot3$
722	$19+19 i$	$(1+ i)\cdot19$
724	$18+20 i$ $20+18 i$	$(1+ i) 2 \cdot(10-9 i)$ $- i \cdot(1+ i) 2 \cdot(10+9 i)$
725	$7+26 i$ $10+25 i$ $14+23 i$ $23+14 i$ $25+10 i$ $26+7 i$	$(2+ i) 2 \cdot(5+2 i)$ $i \cdot(2+ i)\cdot(2- i)\cdot(5-2 i)$ $i \cdot(2- i) 2 \cdot(5+2 i)$ $(2+ i) 2 \cdot(5-2 i)$ $(2+ i)\cdot(2- i)\cdot(5+2 i)$ $i \cdot(2- i) 2 \cdot(5-2 i)$
729	$27$	$33$
730	$1+27 i$ $17+21 i$ $21+17 i$ $27+ i$	$i \cdot(1+ i)\cdot(2- i)\cdot(8-3 i)$ $(1+ i)\cdot(2+ i)\cdot(8-3 i)$ $(1+ i)\cdot(2- i)\cdot(8+3 i)$ $- i \cdot(1+ i)\cdot(2+ i)\cdot(8+3 i)$
733	$2+27 i$ $27+2 i$	(p) (p)
738	$3+27 i$ $27+3 i$	$(1+ i)\cdot3\cdot(5+4 i)$ $(1+ i)\cdot3\cdot(5-4 i)$
740	$8+26 i$ $16+22 i$ $22+16 i$ $26+8 i$	$(1+ i) 2 \cdot(2- i)\cdot(6+ i)$ $(1+ i) 2 \cdot(2- i)\cdot(6- i)$ $- i \cdot(1+ i) 2 \cdot(2+ i)\cdot(6+ i)$ $- i \cdot(1+ i) 2 \cdot(2+ i)\cdot(6- i)$
745	$4+27 i$ $13+24 i$ $24+13 i$ $27+4 i$	$i \cdot(2+ i)\cdot(10-7 i)$ $(2+ i)\cdot(10+7 i)$ $i \cdot(2- i)\cdot(10-7 i)$ $(2- i)\cdot(10+7 i)$
746	$11+25 i$ $25+11 i$	$(1+ i)\cdot(18+7 i)$ $(1+ i)\cdot(18-7 i)$

Norm 751–1000
Norm	Integer	Factorization
754	$5+27 i$ $15+23 i$ $23+15 i$ $27+5 i$	$i \cdot(1+ i)\cdot(3-2 i)\cdot(5-2 i)$ $(1+ i)\cdot(3+2 i)\cdot(5-2 i)$ $(1+ i)\cdot(3-2 i)\cdot(5+2 i)$ $- i \cdot(1+ i)\cdot(3+2 i)\cdot(5+2 i)$
757	$9+26 i$ $26+9 i$	(p) (p)
761	$19+20 i$ $20+19 i$	(p) (p)
765	$6+27 i$ $18+21 i$ $21+18 i$ $27+6 i$	$i \cdot(2- i)\cdot3\cdot(4+ i)$ $i \cdot(2- i)\cdot3\cdot(4- i)$ $(2+ i)\cdot3\cdot(4+ i)$ $(2+ i)\cdot3\cdot(4- i)$
769	$12+25 i$ $25+12 i$	(p) (p)
772	$14+24 i$ $24+14 i$	$(1+ i) 2 \cdot(12-7 i)$ $- i \cdot(1+ i) 2 \cdot(12+7 i)$
773	$17+22 i$ $22+17 i$	(p) (p)
776	$10+26 i$ $26+10 i$	$- i \cdot(1+ i) 3 \cdot(9+4 i)$ $- i \cdot(1+ i) 3 \cdot(9-4 i)$
778	$7+27 i$ $27+7 i$	$(1+ i)\cdot(17+10 i)$ $(1+ i)\cdot(17-10 i)$
784	$28$	$-(1+ i) 4 \cdot7$
785	$1+28 i$ $16+23 i$ $23+16 i$ $28+ i$	$i \cdot(2+ i)\cdot(11-6 i)$ $(2+ i)\cdot(11+6 i)$ $i \cdot(2- i)\cdot(11-6 i)$ $(2- i)\cdot(11+6 i)$
788	$2+28 i$ $28+2 i$	$(1+ i) 2 \cdot(14- i)$ $- i \cdot(1+ i) 2 \cdot(14+ i)$
793	$3+28 i$ $8+27 i$ $27+8 i$ $28+3 i$	$i \cdot(3+2 i)\cdot(6-5 i)$ $(3+2 i)\cdot(6+5 i)$ $i \cdot(3-2 i)\cdot(6-5 i)$ $(3-2 i)\cdot(6+5 i)$
794	$13+25 i$ $25+13 i$	$(1+ i)\cdot(19+6 i)$ $(1+ i)\cdot(19-6 i)$
797	$11+26 i$ $26+11 i$	(p) (p)
800	$4+28 i$ $20+20 i$ $28+4 i$	$- i \cdot(1+ i) 5 \cdot(2- i) 2$ $-(1+ i) 5 \cdot(2+ i)\cdot(2- i)$ $i \cdot(1+ i) 5 \cdot(2+ i) 2$
801	$15+24 i$ $24+15 i$	$i \cdot3\cdot(8-5 i)$ $3\cdot(8+5 i)$
802	$19+21 i$ $21+19 i$	$(1+ i)\cdot(20+ i)$ $(1+ i)\cdot(20- i)$
808	$18+22 i$ $22+18 i$	$- i \cdot(1+ i) 3 \cdot(10+ i)$ $- i \cdot(1+ i) 3 \cdot(10- i)$
809	$5+28 i$ $28+5 i$	(p) (p)
810	$9+27 i$ $27+9 i$	$(1+ i)\cdot(2+ i)\cdot3 2$ $(1+ i)\cdot(2- i)\cdot3 2$
818	$17+23 i$ $23+17 i$	$(1+ i)\cdot(20+3 i)$ $(1+ i)\cdot(20-3 i)$
820	$6+28 i$ $12+26 i$ $26+12 i$ $28+6 i$	$(1+ i) 2 \cdot(2+ i)\cdot(5-4 i)$ $- i \cdot(1+ i) 2 \cdot(2+ i)\cdot(5+4 i)$ $(1+ i) 2 \cdot(2- i)\cdot(5-4 i)$ $- i \cdot(1+ i) 2 \cdot(2- i)\cdot(5+4 i)$
821	$14+25 i$ $25+14 i$	(p) (p)
829	$10+27 i$ $27+10 i$	(p) (p)
832	$16+24 i$ $24+16 i$	$-(1+ i) 6 \cdot(3-2 i)$ $i \cdot(1+ i) 6 \cdot(3+2 i)$
833	$7+28 i$ $28+7 i$	$i \cdot(4- i)\cdot7$ $(4+ i)\cdot7$
841	$20+21 i$ $21+20 i$ $29$	$i \cdot(5-2 i) 2$ $(5+2 i) 2$ $(5+2 i)\cdot(5-2 i)$
842	$1+29 i$ $29+ i$	$(1+ i)\cdot(15+14 i)$ $(1+ i)\cdot(15-14 i)$
845	$2+29 i$ $13+26 i$ $19+22 i$ $22+19 i$ $26+13 i$ $29+2 i$	$-(2- i)\cdot(3-2 i) 2$ $i \cdot(2- i)\cdot(3+2 i)\cdot(3-2 i)$ $i \cdot(2+ i)\cdot(3-2 i) 2$ $(2- i)\cdot(3+2 i) 2$ $(2+ i)\cdot(3+2 i)\cdot(3-2 i)$ $- i \cdot(2+ i)\cdot(3+2 i) 2$
848	$8+28 i$ $28+8 i$	$- i \cdot(1+ i) 4 \cdot(7-2 i)$ $-(1+ i) 4 \cdot(7+2 i)$
850	$3+29 i$ $11+27 i$ $15+25 i$ $25+15 i$ $27+11 i$ $29+3 i$	$(1+ i)\cdot(2+ i) 2 \cdot(4- i)$ $i \cdot(1+ i)\cdot(2- i) 2 \cdot(4- i)$ $(1+ i)\cdot(2+ i)\cdot(2- i)\cdot(4+ i)$ $(1+ i)\cdot(2+ i)\cdot(2- i)\cdot(4- i)$ $- i \cdot(1+ i)\cdot(2+ i) 2 \cdot(4+ i)$ $(1+ i)\cdot(2- i) 2 \cdot(4+ i)$
853	$18+23 i$ $23+18 i$	(p) (p)
857	$4+29 i$ $29+4 i$	(p) (p)
865	$9+28 i$ $17+24 i$ $24+17 i$ $28+9 i$	$i \cdot(2- i)\cdot(13+2 i)$ $i \cdot(2- i)\cdot(13-2 i)$ $(2+ i)\cdot(13+2 i)$ $(2+ i)\cdot(13-2 i)$
866	$5+29 i$ $29+5 i$	$(1+ i)\cdot(17+12 i)$ $(1+ i)\cdot(17-12 i)$
872	$14+26 i$ $26+14 i$	$- i \cdot(1+ i) 3 \cdot(10+3 i)$ $- i \cdot(1+ i) 3 \cdot(10-3 i)$
873	$12+27 i$ $27+12 i$	$i \cdot3\cdot(9-4 i)$ $3\cdot(9+4 i)$
877	$6+29 i$ $29+6 i$	(p) (p)
881	$16+25 i$ $25+16 i$	(p) (p)
882	$21+21 i$	$(1+ i)\cdot3\cdot7$
884	$10+28 i$ $20+22 i$ $22+20 i$ $28+10 i$	$(1+ i) 2 \cdot(3-2 i)\cdot(4+ i)$ $- i \cdot(1+ i) 2 \cdot(3+2 i)\cdot(4+ i)$ $(1+ i) 2 \cdot(3-2 i)\cdot(4- i)$ $- i \cdot(1+ i) 2 \cdot(3+2 i)\cdot(4- i)$
890	$7+29 i$ $19+23 i$ $23+19 i$ $29+7 i$	$i \cdot(1+ i)\cdot(2- i)\cdot(8-5 i)$ $(1+ i)\cdot(2- i)\cdot(8+5 i)$ $(1+ i)\cdot(2+ i)\cdot(8-5 i)$ $- i \cdot(1+ i)\cdot(2+ i)\cdot(8+5 i)$
898	$13+27 i$ $27+13 i$	$(1+ i)\cdot(20+7 i)$ $(1+ i)\cdot(20-7 i)$
900	$18+24 i$ $24+18 i$ $30$	$- i \cdot(1+ i) 2 \cdot(2+ i) 2 \cdot3$ $(1+ i) 2 \cdot(2- i) 2 \cdot3$ $- i \cdot(1+ i) 2 \cdot(2+ i)\cdot(2- i)\cdot3$
901	$1+30 i$ $15+26 i$ $26+15 i$ $30+ i$	$i \cdot(4+ i)\cdot(7-2 i)$ $i \cdot(4- i)\cdot(7-2 i)$ $(4+ i)\cdot(7+2 i)$ $(4- i)\cdot(7+2 i)$
904	$2+30 i$ $30+2 i$	$- i \cdot(1+ i) 3 \cdot(8+7 i)$ $- i \cdot(1+ i) 3 \cdot(8-7 i)$
905	$8+29 i$ $11+28 i$ $28+11 i$ $29+8 i$	$i \cdot(2+ i)\cdot(10-9 i)$ $(2+ i)\cdot(10+9 i)$ $i \cdot(2- i)\cdot(10-9 i)$ $(2- i)\cdot(10+9 i)$
909	$3+30 i$ $30+3 i$	$i \cdot3\cdot(10- i)$ $3\cdot(10+ i)$
914	$17+25 i$ $25+17 i$	$(1+ i)\cdot(21+4 i)$ $(1+ i)\cdot(21-4 i)$
916	$4+30 i$ $30+4 i$	$(1+ i) 2 \cdot(15-2 i)$ $- i \cdot(1+ i) 2 \cdot(15+2 i)$
922	$9+29 i$ $29+9 i$	$(1+ i)\cdot(19+10 i)$ $(1+ i)\cdot(19-10 i)$
925	$5+30 i$ $14+27 i$ $21+22 i$ $22+21 i$ $27+14 i$ $30+5 i$	$i \cdot(2+ i)\cdot(2- i)\cdot(6- i)$ $(2+ i) 2 \cdot(6+ i)$ $i \cdot(2- i) 2 \cdot(6+ i)$ $(2+ i) 2 \cdot(6- i)$ $i \cdot(2- i) 2 \cdot(6- i)$ $(2+ i)\cdot(2- i)\cdot(6+ i)$
928	$12+28 i$ $28+12 i$	$-(1+ i) 5 \cdot(5+2 i)$ $-(1+ i) 5 \cdot(5-2 i)$
929	$20+23 i$ $23+20 i$	(p) (p)
932	$16+26 i$ $26+16 i$	$(1+ i) 2 \cdot(13-8 i)$ $- i \cdot(1+ i) 2 \cdot(13+8 i)$
936	$6+30 i$ $30+6 i$	$- i \cdot(1+ i) 3 \cdot3\cdot(3+2 i)$ $- i \cdot(1+ i) 3 \cdot3\cdot(3-2 i)$
937	$19+24 i$ $24+19 i$	(p) (p)
941	$10+29 i$ $29+10 i$	(p) (p)
949	$7+30 i$ $18+25 i$ $25+18 i$ $30+7 i$	$i \cdot(3-2 i)\cdot(8+3 i)$ $(3+2 i)\cdot(8+3 i)$ $i \cdot(3-2 i)\cdot(8-3 i)$ $(3+2 i)\cdot(8-3 i)$
953	$13+28 i$ $28+13 i$	(p) (p)
954	$15+27 i$ $27+15 i$	$(1+ i)\cdot3\cdot(7+2 i)$ $(1+ i)\cdot3\cdot(7-2 i)$
961	$31$	(p)
962	$1+31 i$ $11+29 i$ $29+11 i$ $31+ i$	$(1+ i)\cdot(3+2 i)\cdot(6+ i)$ $(1+ i)\cdot(3+2 i)\cdot(6- i)$ $(1+ i)\cdot(3-2 i)\cdot(6+ i)$ $(1+ i)\cdot(3-2 i)\cdot(6- i)$
964	$8+30 i$ $30+8 i$	$(1+ i) 2 \cdot(15-4 i)$ $- i \cdot(1+ i) 2 \cdot(15+4 i)$
965	$2+31 i$ $17+26 i$ $26+17 i$ $31+2 i$	$i \cdot(2+ i)\cdot(12-7 i)$ $(2+ i)\cdot(12+7 i)$ $i \cdot(2- i)\cdot(12-7 i)$ $(2- i)\cdot(12+7 i)$
968	$22+22 i$	$- i \cdot(1+ i) 3 \cdot11$
970	$3+31 i$ $21+23 i$ $23+21 i$ $31+3 i$	$i \cdot(1+ i)\cdot(2- i)\cdot(9-4 i)$ $(1+ i)\cdot(2+ i)\cdot(9-4 i)$ $(1+ i)\cdot(2- i)\cdot(9+4 i)$ $- i \cdot(1+ i)\cdot(2+ i)\cdot(9+4 i)$
976	$20+24 i$ $24+20 i$	$- i \cdot(1+ i) 4 \cdot(6-5 i)$ $-(1+ i) 4 \cdot(6+5 i)$
977	$4+31 i$ $31+4 i$	(p) (p)
980	$14+28 i$ $28+14 i$	$(1+ i) 2 \cdot(2- i)\cdot7$ $- i \cdot(1+ i) 2 \cdot(2+ i)\cdot7$
981	$9+30 i$ $30+9 i$	$i \cdot3\cdot(10-3 i)$ $3\cdot(10+3 i)$
985	$12+29 i$ $16+27 i$ $27+16 i$ $29+12 i$	$i \cdot(2- i)\cdot(14+ i)$ $i \cdot(2- i)\cdot(14- i)$ $(2+ i)\cdot(14+ i)$ $(2+ i)\cdot(14- i)$
986	$5+31 i$ $19+25 i$ $25+19 i$ $31+5 i$	$(1+ i)\cdot(4+ i)\cdot(5+2 i)$ $(1+ i)\cdot(4- i)\cdot(5+2 i)$ $(1+ i)\cdot(4+ i)\cdot(5-2 i)$ $(1+ i)\cdot(4- i)\cdot(5-2 i)$
997	$6+31 i$ $31+6 i$	(p) (p)
1000	$10+30 i$ $18+26 i$ $26+18 i$ $30+10 i$	$- i \cdot(1+ i) 3 \cdot(2+ i) 2 \cdot(2- i)$ $(1+ i) 3 \cdot(2- i) 3$ $-(1+ i) 3 \cdot(2+ i) 3$ $- i \cdot(1+ i) 3 \cdot(2+ i)\cdot(2- i) 2$

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.

External links

Table of Gaussian integer factorizations

Conventions

Factorizations

See also

References

External links

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