The number of primitive polynomials over GF(2)
of the form xⁿ+x^k+...

	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31
1	2
2	0	1
3	0	1	1
4	0	1	0	1
5	0	0	1	2	3
6	0	1	0	0	1	4
7	0	1	0	2	2	4	9
8	0	0	0	0	1	2	6	7
9	0	0	0	0	2	3	6	12	25
10	0	0	0	1	1	2	2	7	16	31
11	0	0	1	0	1	2	5	11	22	47	87
12	0	0	0	0	0	0	4	3	12	19	34	72
13	0	0	0	0	1	2	3	11	20	38	80	160	315
14	0	0	0	0	0	2	3	7	12	22	42	96	191	381
15	0	1	0	0	2	2	2	9	15	25	63	105	230	445	901
16	0	0	0	0	0	3	1	2	9	20	25	59	132	258	522	1017
17	0	0	0	2	0	4	4	7	16	32	62	120	244	484	960	1920	3855
18	0	0	0	0	0	2	2	4	6	18	25	58	111	248	485	972	1955	3890
19	0	0	0	0	0	2	6	3	13	25	51	101	208	424	868	1728	3456	6912	13797
20	0	0	0	1	0	0	4	1	5	11	27	53	92	195	382	731	1513	3032	5953	12000
21	0	0	1	0	0	2	4	2	16	19	40	75	162	319	668	1337	2627	5286	10568	21202	42344
22	0	1	0	0	0	1	0	2	6	13	27	72	111	235	479	931	1852	3751	7436	15018	30054	60043
23	0	0	0	0	0	5	3	8	8	24	36	100	174	364	682	1414	2826	5561	11138	22326	44604	89256	178431
24	0	0	0	0	1	0	0	4	4	10	10	45	61	123	276	526	1057	2110	4429	8627	17278	34573	69122	138224
25	0	0	0	2	0	1	0	4	11	20	43	87	158	324	613	1254	2520	5158	10098	20292	40566	80953	161973	323892	648031
26	0	0	0	0	0	0	2	3	8	15	27	54	105	223	390	847	1666	3399	6635	13480	26997	53840	107369	215016	429765	860059
27	0	0	0	0	0	1	0	3	7	12	35	61	127	246	516	1017	2022	4055	8174	16306	33065	65605	131229	262814	524847	1051001	2101353
28	0	0	0	1	0	0	2	1	3	9	22	43	85	136	273	553	1115	2336	4574	9217	18520	37292	74178	148021	296200	592827	1185509	2370715
29	0	0	1	0	2	0	0	3	8	14	48	69	130	269	552	1059	2226	4416	9101	17987	36018	71767	143748	287330	575122	1150754	2301175	4602262	9203747
30	0	0	0	0	0	0	1	2	3	9	12	31	79	149	271	550	1137	2200	4386	8742	17475	34934	69538	138955	278259	557741	1113954	2228058	4454574	8908940
31	0	0	0	2	0	2	3	5	9	14	35	74	121	277	522	1061	2109	4263	8516	17014	33708	67558	135354	270794	541456	1082544	2165024	4329536	8658944	17317888	34636833

Notes:

• The primitive polynomial x is not counted anywhere in the above table; all others are counted.
• The diagonal entries are the total number of primitive polynomials; i.e., the sum of the entries to their left.
• Row heading of row n is red if and only if 2ⁿ-1 is prime. In this case every irreducible polynomial is also primitive.
• The corresponding table for irreducible polynomials is also available.
• Created by Frank Ruskey. Please let me know if you make use of this table.