Prime Numbers

What is a Prime Number?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself — it can't be formed by multiplying two smaller natural numbers together. Every prime number other than 2 is odd, so it's sometimes called an odd prime.

Examples of a Prime Number

Here are the prime numbers less than 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 — sequence A000040 in the OEIS.

Types of Prime Numbers

Prime numbers fall into quite a few named categories:

Additive Primes
Balanced Primes
Carol Primes
Chen Primes
Circular Primes
Cousin Primes
Double Mersenne Primes
Factorial Primes
Fermat Primes
Fibonacci Primes
Mersenne Primes
Odd Primes
Palindromic Primes
Permutable Primes
Sexy Primes
Twin Primes

How Can You Tell if a Number is Prime?

Find all the factors of the number.
If it has only two factors — 1 and itself — it's prime.
If it has more than two factors, it's not prime; it's composite.

Rather do this by hand? Use the Is a Number Prime? checker or see a number's full prime factorization.

Recognizing Prime Numbers

Recognizing Prime numbers

List of the First 150 Prime Numbers

#	Prime
1	2
2	3
3	5
4	7
5	11
6	13
7	17
8	19
9	23
10	29
11	31
12	37
13	41
14	43
15	47
16	53
17	59
18	61
19	67
20	71
21	73
22	79
23	83
24	89
25	97
26	101
27	103
28	107
29	109
30	113
31	127
32	131
33	137
34	139
35	149
36	151
37	157
38	163
39	167
40	173
41	179
42	181
43	191
44	193
45	197
46	199
47	211
48	223
49	227
50	229
51	233
52	239
53	241
54	251
55	257
56	263
57	269
58	271
59	277
60	281
61	283
62	293
63	307
64	311
65	313
66	317
67	331
68	337
69	347
70	349
71	353
72	359
73	367
74	373
75	379
76	383
77	389
78	397
79	401
80	409
81	419
82	421
83	431
84	433
85	439
86	443
87	449
88	457
89	461
90	463
91	467
92	479
93	487
94	491
95	499
96	503
97	509
98	521
99	523
100	541
101	547
102	557
103	563
104	569
105	571
106	577
107	587
108	593
109	599
110	601
111	607
112	613
113	617
114	619
115	631
116	641
117	643
118	647
119	653
120	659
121	661
122	673
123	677
124	683
125	691
126	701
127	709
128	719
129	727
130	733
131	739
132	743
133	751
134	757
135	761
136	769
137	773
138	787
139	797
140	809
141	811
142	821
143	823
144	827
145	829
146	839
147	853
148	857
149	859
150	863

#	Prime
1	2
2	3
3	5
4	7
5	11
6	13
7	17
8	19
9	23
10	29
11	31
12	37
13	41
14	43
15	47
16	53
17	59
18	61
19	67
20	71
21	73
22	79
23	83
24	89
25	97
26	101
27	103
28	107
29	109
30	113
31	127
32	131
33	137
34	139
35	149
36	151
37	157
38	163
39	167
40	173
41	179
42	181
43	191
44	193
45	197
46	199
47	211
48	223
49	227
50	229
51	233
52	239
53	241
54	251
55	257
56	263
57	269
58	271
59	277
60	281
61	283
62	293
63	307
64	311
65	313
66	317
67	331
68	337
69	347
70	349
71	353
72	359
73	367
74	373
75	379
76	383
77	389
78	397
79	401
80	409
81	419
82	421
83	431
84	433
85	439
86	443
87	449
88	457
89	461
90	463
91	467
92	479
93	487
94	491
95	499
96	503
97	509
98	521
99	523
100	541
101	547
102	557
103	563
104	569
105	571
106	577
107	587
108	593
109	599
110	601
111	607
112	613
113	617
114	619
115	631
116	641
117	643
118	647
119	653
120	659
121	661
122	673
123	677
124	683
125	691
126	701
127	709
128	719
129	727
130	733
131	739
132	743
133	751
134	757
135	761
136	769
137	773
138	787
139	797
140	809
141	811
142	821
143	823
144	827
145	829
146	839
147	853
148	857
149	859
150	863

#	Prime
1	2
2	3
3	5
4	7
5	11
6	13
7	17
8	19
9	23
10	29
11	31
12	37
13	41
14	43
15	47
16	53
17	59
18	61
19	67
20	71
21	73
22	79
23	83
24	89
25	97
26	101
27	103
28	107
29	109
30	113
31	127
32	131
33	137
34	139
35	149
36	151
37	157
38	163
39	167
40	173
41	179
42	181
43	191
44	193
45	197
46	199
47	211
48	223
49	227
50	229
51	233
52	239
53	241
54	251
55	257
56	263
57	269
58	271
59	277
60	281
61	283
62	293
63	307
64	311
65	313
66	317
67	331
68	337
69	347
70	349
71	353
72	359
73	367
74	373
75	379
76	383
77	389
78	397
79	401
80	409
81	419
82	421
83	431
84	433
85	439
86	443
87	449
88	457
89	461
90	463
91	467
92	479
93	487
94	491
95	499
96	503
97	509
98	521
99	523
100	541
101	547
102	557
103	563
104	569
105	571
106	577
107	587
108	593
109	599
110	601
111	607
112	613
113	617
114	619
115	631
116	641
117	643
118	647
119	653
120	659
121	661
122	673
123	677
124	683
125	691
126	701
127	709
128	719
129	727
130	733
131	739
132	743
133	751
134	757
135	761
136	769
137	773
138	787
139	797
140	809
141	811
142	821
143	823
144	827
145	829
146	839
147	853
148	857
149	859
150	863

#	Prime
1	2
2	3
3	5
4	7
5	11
6	13
7	17
8	19
9	23
10	29
11	31
12	37
13	41
14	43
15	47
16	53
17	59
18	61
19	67
20	71
21	73
22	79
23	83
24	89
25	97
26	101
27	103
28	107
29	109
30	113
31	127
32	131
33	137
34	139
35	149
36	151
37	157
38	163
39	167
40	173
41	179
42	181
43	191
44	193
45	197
46	199
47	211
48	223
49	227
50	229
51	233
52	239
53	241
54	251
55	257
56	263
57	269
58	271
59	277
60	281
61	283
62	293
63	307
64	311
65	313
66	317
67	331
68	337
69	347
70	349
71	353
72	359
73	367
74	373
75	379
76	383
77	389
78	397
79	401
80	409
81	419
82	421
83	431
84	433
85	439
86	443
87	449
88	457
89	461
90	463
91	467
92	479
93	487
94	491
95	499
96	503
97	509
98	521
99	523
100	541
101	547
102	557
103	563
104	569
105	571
106	577
107	587
108	593
109	599
110	601
111	607
112	613
113	617
114	619
115	631
116	641
117	643
118	647
119	653
120	659
121	661
122	673
123	677
124	683
125	691
126	701
127	709
128	719
129	727
130	733
131	739
132	743
133	751
134	757
135	761
136	769
137	773
138	787
139	797
140	809
141	811
142	821
143	823
144	827
145	829
146	839
147	853
148	857
149	859
150	863