Prime Numbers List

A prime number is a whole number greater than 1 whose only positive divisors are 1 and itself. The first 200 primes are listed below, generated by the same primality test the Calxy prime factorization calculator uses.

Definition

2 is the only even prime. 1 is not prime, because a prime must have exactly two distinct positive divisors. Numbers greater than 1 that are not prime are composite.

By the fundamental theorem of arithmetic, every integer greater than 1 is a product of primes in exactly one way, apart from the order of the factors. There are infinitely many primes (Euclid).

Sources: OpenStax: Contemporary Mathematics §3.1 Prime and Composite Numbers; NIST Digital Library of Mathematical Functions: DLMF §27.2 Functions of Number Theory (primes)

The first 200 prime numbers

The 200th prime is 1223. The first 168 entries are exactly the primes below 1000, ending at 997.

Primes in rows of ten
#	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
1	2	3	5	7	11	13	17	19	23	29
11	31	37	41	43	47	53	59	61	67	71
21	73	79	83	89	97	101	103	107	109	113
31	127	131	137	139	149	151	157	163	167	173
41	179	181	191	193	197	199	211	223	227	229
51	233	239	241	251	257	263	269	271	277	281
61	283	293	307	311	313	317	331	337	347	349
71	353	359	367	373	379	383	389	397	401	409
81	419	421	431	433	439	443	449	457	461	463
91	467	479	487	491	499	503	509	521	523	541
101	547	557	563	569	571	577	587	593	599	601
111	607	613	617	619	631	641	643	647	653	659
121	661	673	677	683	691	701	709	719	727	733
131	739	743	751	757	761	769	773	787	797	809
141	811	821	823	827	829	839	853	857	859	863
151	877	881	883	887	907	911	919	929	937	941
161	947	953	967	971	977	983	991	997	1009	1013
171	1019	1021	1031	1033	1039	1049	1051	1061	1063	1069
181	1087	1091	1093	1097	1103	1109	1117	1123	1129	1151
191	1153	1163	1171	1181	1187	1193	1201	1213	1217	1223

Sources: OEIS Foundation: A000040 The prime numbers

How many primes there are

π(x) counts the primes up to x. The prime number theorem says π(x) is approximately x ÷ ln x for large x.

Prime-counting function π(x)
x	π(x)	x ÷ ln x
10	4	4.3
100	25	21.7
500	95	80.5
1,000	168	144.8

Definition

The first 200 prime numbers

How many primes there are

References

Frequently asked questions