List of prime numbers
Updated: 5/20/2026, 8:11:08 PM Wikipedia source
This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes. The first 1,000 primes are listed below, followed by lists of notable types of prime numbers in alphabetical order, giving their respective first terms. The number 1 is neither prime nor composite.
Tables
· The first 1,000 prime numbers
1–20
1–20
Col 1
1–20
1
2
2
3
3
5
4
7
5
11
6
13
7
17
8
19
9
23
10
29
11
31
21–40
21–40
Col 1
21–40
1
73
2
79
3
83
4
89
5
97
6
101
7
103
8
107
9
109
10
113
11
127
41–60
41–60
Col 1
41–60
1
179
2
181
3
191
4
193
5
197
6
199
7
211
8
223
9
227
10
229
11
233
61–80
61–80
Col 1
61–80
1
283
2
293
3
307
4
311
5
313
6
317
7
331
8
337
9
347
10
349
11
353
81–100
81–100
Col 1
81–100
1
419
2
421
3
431
4
433
5
439
6
443
7
449
8
457
9
461
10
463
11
467
101–120
101–120
Col 1
101–120
1
547
2
557
3
563
4
569
5
571
6
577
7
587
8
593
9
599
10
601
11
607
121–140
121–140
Col 1
121–140
1
661
2
673
3
677
4
683
5
691
6
701
7
709
8
719
9
727
10
733
11
739
141–160
141–160
Col 1
141–160
1
811
2
821
3
823
4
827
5
829
6
839
7
853
8
857
9
859
10
863
11
877
161–180
161–180
Col 1
161–180
1
947
2
953
3
967
4
971
5
977
6
983
7
991
8
997
9
1009
10
1013
11
1019
181–200
181–200
Col 1
181–200
1
1087
2
1091
3
1093
4
1097
5
1103
6
1109
7
1117
8
1123
9
1129
10
1151
11
1153
201–220
201–220
Col 1
201–220
1
1229
2
1231
3
1237
4
1249
5
1259
6
1277
7
1279
8
1283
9
1289
10
1291
11
1297
221–240
221–240
Col 1
221–240
1
1381
2
1399
3
1409
4
1423
5
1427
6
1429
7
1433
8
1439
9
1447
10
1451
11
1453
241–260
241–260
Col 1
241–260
1
1523
2
1531
3
1543
4
1549
5
1553
6
1559
7
1567
8
1571
9
1579
10
1583
11
1597
261–280
261–280
Col 1
261–280
1
1663
2
1667
3
1669
4
1693
5
1697
6
1699
7
1709
8
1721
9
1723
10
1733
11
1741
281–300
281–300
Col 1
281–300
1
1823
2
1831
3
1847
4
1861
5
1867
6
1871
7
1873
8
1877
9
1879
10
1889
11
1901
301–320
301–320
Col 1
301–320
1
1993
2
1997
3
1999
4
2003
5
2011
6
2017
7
2027
8
2029
9
2039
10
2053
11
2063
321–340
321–340
Col 1
321–340
1
2131
2
2137
3
2141
4
2143
5
2153
6
2161
7
2179
8
2203
9
2207
10
2213
11
2221
341–360
341–360
Col 1
341–360
1
2293
2
2297
3
2309
4
2311
5
2333
6
2339
7
2341
8
2347
9
2351
10
2357
11
2371
361–380
361–380
Col 1
361–380
1
2437
2
2441
3
2447
4
2459
5
2467
6
2473
7
2477
8
2503
9
2521
10
2531
11
2539
381–400
381–400
Col 1
381–400
1
2621
2
2633
3
2647
4
2657
5
2659
6
2663
7
2671
8
2677
9
2683
10
2687
11
2689
401–420
401–420
Col 1
401–420
1
2749
2
2753
3
2767
4
2777
5
2789
6
2791
7
2797
8
2801
9
2803
10
2819
11
2833
421–440
421–440
Col 1
421–440
1
2909
2
2917
3
2927
4
2939
5
2953
6
2957
7
2963
8
2969
9
2971
10
2999
11
3001
441–460
441–460
Col 1
441–460
1
3083
2
3089
3
3109
4
3119
5
3121
6
3137
7
3163
8
3167
9
3169
10
3181
11
3187
461–480
461–480
Col 1
461–480
1
3259
2
3271
3
3299
4
3301
5
3307
6
3313
7
3319
8
3323
9
3329
10
3331
11
3343
481–500
481–500
Col 1
481–500
1
3433
2
3449
3
3457
4
3461
5
3463
6
3467
7
3469
8
3491
9
3499
10
3511
11
3517
501–520
501–520
Col 1
501–520
1
3581
2
3583
3
3593
4
3607
5
3613
6
3617
7
3623
8
3631
9
3637
10
3643
11
3659
521–540
521–540
Col 1
521–540
1
3733
2
3739
3
3761
4
3767
5
3769
6
3779
7
3793
8
3797
9
3803
10
3821
11
3823
541–560
541–560
Col 1
541–560
1
3911
2
3917
3
3919
4
3923
5
3929
6
3931
7
3943
8
3947
9
3967
10
3989
11
4001
561–580
561–580
Col 1
561–580
1
4073
2
4079
3
4091
4
4093
5
4099
6
4111
7
4127
8
4129
9
4133
10
4139
11
4153
581–600
581–600
Col 1
581–600
1
4241
2
4243
3
4253
4
4259
5
4261
6
4271
7
4273
8
4283
9
4289
10
4297
11
4327
601–620
601–620
Col 1
601–620
1
4421
2
4423
3
4441
4
4447
5
4451
6
4457
7
4463
8
4481
9
4483
10
4493
11
4507
621–640
621–640
Col 1
621–640
1
4591
2
4597
3
4603
4
4621
5
4637
6
4639
7
4643
8
4649
9
4651
10
4657
11
4663
641–660
641–660
Col 1
641–660
1
4759
2
4783
3
4787
4
4789
5
4793
6
4799
7
4801
8
4813
9
4817
10
4831
11
4861
661–680
661–680
Col 1
661–680
1
4943
2
4951
3
4957
4
4967
5
4969
6
4973
7
4987
8
4993
9
4999
10
5003
11
5009
681–700
681–700
Col 1
681–700
1
5099
2
5101
3
5107
4
5113
5
5119
6
5147
7
5153
8
5167
9
5171
10
5179
11
5189
701–720
701–720
Col 1
701–720
1
5281
2
5297
3
5303
4
5309
5
5323
6
5333
7
5347
8
5351
9
5381
10
5387
11
5393
721–740
721–740
Col 1
721–740
1
5449
2
5471
3
5477
4
5479
5
5483
6
5501
7
5503
8
5507
9
5519
10
5521
11
5527
741–760
741–760
Col 1
741–760
1
5641
2
5647
3
5651
4
5653
5
5657
6
5659
7
5669
8
5683
9
5689
10
5693
11
5701
761–780
761–780
Col 1
761–780
1
5801
2
5807
3
5813
4
5821
5
5827
6
5839
7
5843
8
5849
9
5851
10
5857
11
5861
781–800
781–800
Col 1
781–800
1
5953
2
5981
3
5987
4
6007
5
6011
6
6029
7
6037
8
6043
9
6047
10
6053
11
6067
801–820
801–820
Col 1
801–820
1
6143
2
6151
3
6163
4
6173
5
6197
6
6199
7
6203
8
6211
9
6217
10
6221
11
6229
821–840
821–840
Col 1
821–840
1
6311
2
6317
3
6323
4
6329
5
6337
6
6343
7
6353
8
6359
9
6361
10
6367
11
6373
841–860
841–860
Col 1
841–860
1
6481
2
6491
3
6521
4
6529
5
6547
6
6551
7
6553
8
6563
9
6569
10
6571
11
6577
861–880
861–880
Col 1
861–880
1
6679
2
6689
3
6691
4
6701
5
6703
6
6709
7
6719
8
6733
9
6737
10
6761
11
6763
881–900
881–900
Col 1
881–900
1
6841
2
6857
3
6863
4
6869
5
6871
6
6883
7
6899
8
6907
9
6911
10
6917
11
6947
901–920
901–920
Col 1
901–920
1
7001
2
7013
3
7019
4
7027
5
7039
6
7043
7
7057
8
7069
9
7079
10
7103
11
7109
921–940
921–940
Col 1
921–940
1
7211
2
7213
3
7219
4
7229
5
7237
6
7243
7
7247
8
7253
9
7283
10
7297
11
7307
941–960
941–960
Col 1
941–960
1
7417
2
7433
3
7451
4
7457
5
7459
6
7477
7
7481
8
7487
9
7489
10
7499
11
7507
961–980
961–980
Col 1
961–980
1
7573
2
7577
3
7583
4
7589
5
7591
6
7603
7
7607
8
7621
9
7639
10
7643
11
7649
981–1000
981–1000
Col 1
981–1000
1
7727
2
7741
3
7753
4
7757
5
7759
6
7789
7
7793
8
7817
9
7823
10
7829
11
7841
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |
| 1–20 | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 |
| 21–40 | 73 | 79 | 83 | 89 | 97 | 101 | 103 | 107 | 109 | 113 | 127 |
| 41–60 | 179 | 181 | 191 | 193 | 197 | 199 | 211 | 223 | 227 | 229 | 233 |
| 61–80 | 283 | 293 | 307 | 311 | 313 | 317 | 331 | 337 | 347 | 349 | 353 |
| 81–100 | 419 | 421 | 431 | 433 | 439 | 443 | 449 | 457 | 461 | 463 | 467 |
| 101–120 | 547 | 557 | 563 | 569 | 571 | 577 | 587 | 593 | 599 | 601 | 607 |
| 121–140 | 661 | 673 | 677 | 683 | 691 | 701 | 709 | 719 | 727 | 733 | 739 |
| 141–160 | 811 | 821 | 823 | 827 | 829 | 839 | 853 | 857 | 859 | 863 | 877 |
| 161–180 | 947 | 953 | 967 | 971 | 977 | 983 | 991 | 997 | 1009 | 1013 | 1019 |
| 181–200 | 1087 | 1091 | 1093 | 1097 | 1103 | 1109 | 1117 | 1123 | 1129 | 1151 | 1153 |
| 201–220 | 1229 | 1231 | 1237 | 1249 | 1259 | 1277 | 1279 | 1283 | 1289 | 1291 | 1297 |
| 221–240 | 1381 | 1399 | 1409 | 1423 | 1427 | 1429 | 1433 | 1439 | 1447 | 1451 | 1453 |
| 241–260 | 1523 | 1531 | 1543 | 1549 | 1553 | 1559 | 1567 | 1571 | 1579 | 1583 | 1597 |
| 261–280 | 1663 | 1667 | 1669 | 1693 | 1697 | 1699 | 1709 | 1721 | 1723 | 1733 | 1741 |
| 281–300 | 1823 | 1831 | 1847 | 1861 | 1867 | 1871 | 1873 | 1877 | 1879 | 1889 | 1901 |
| 301–320 | 1993 | 1997 | 1999 | 2003 | 2011 | 2017 | 2027 | 2029 | 2039 | 2053 | 2063 |
| 321–340 | 2131 | 2137 | 2141 | 2143 | 2153 | 2161 | 2179 | 2203 | 2207 | 2213 | 2221 |
| 341–360 | 2293 | 2297 | 2309 | 2311 | 2333 | 2339 | 2341 | 2347 | 2351 | 2357 | 2371 |
| 361–380 | 2437 | 2441 | 2447 | 2459 | 2467 | 2473 | 2477 | 2503 | 2521 | 2531 | 2539 |
| 381–400 | 2621 | 2633 | 2647 | 2657 | 2659 | 2663 | 2671 | 2677 | 2683 | 2687 | 2689 |
| 401–420 | 2749 | 2753 | 2767 | 2777 | 2789 | 2791 | 2797 | 2801 | 2803 | 2819 | 2833 |
| 421–440 | 2909 | 2917 | 2927 | 2939 | 2953 | 2957 | 2963 | 2969 | 2971 | 2999 | 3001 |
| 441–460 | 3083 | 3089 | 3109 | 3119 | 3121 | 3137 | 3163 | 3167 | 3169 | 3181 | 3187 |
| 461–480 | 3259 | 3271 | 3299 | 3301 | 3307 | 3313 | 3319 | 3323 | 3329 | 3331 | 3343 |
| 481–500 | 3433 | 3449 | 3457 | 3461 | 3463 | 3467 | 3469 | 3491 | 3499 | 3511 | 3517 |
| 501–520 | 3581 | 3583 | 3593 | 3607 | 3613 | 3617 | 3623 | 3631 | 3637 | 3643 | 3659 |
| 521–540 | 3733 | 3739 | 3761 | 3767 | 3769 | 3779 | 3793 | 3797 | 3803 | 3821 | 3823 |
| 541–560 | 3911 | 3917 | 3919 | 3923 | 3929 | 3931 | 3943 | 3947 | 3967 | 3989 | 4001 |
| 561–580 | 4073 | 4079 | 4091 | 4093 | 4099 | 4111 | 4127 | 4129 | 4133 | 4139 | 4153 |
| 581–600 | 4241 | 4243 | 4253 | 4259 | 4261 | 4271 | 4273 | 4283 | 4289 | 4297 | 4327 |
| 601–620 | 4421 | 4423 | 4441 | 4447 | 4451 | 4457 | 4463 | 4481 | 4483 | 4493 | 4507 |
| 621–640 | 4591 | 4597 | 4603 | 4621 | 4637 | 4639 | 4643 | 4649 | 4651 | 4657 | 4663 |
| 641–660 | 4759 | 4783 | 4787 | 4789 | 4793 | 4799 | 4801 | 4813 | 4817 | 4831 | 4861 |
| 661–680 | 4943 | 4951 | 4957 | 4967 | 4969 | 4973 | 4987 | 4993 | 4999 | 5003 | 5009 |
| 681–700 | 5099 | 5101 | 5107 | 5113 | 5119 | 5147 | 5153 | 5167 | 5171 | 5179 | 5189 |
| 701–720 | 5281 | 5297 | 5303 | 5309 | 5323 | 5333 | 5347 | 5351 | 5381 | 5387 | 5393 |
| 721–740 | 5449 | 5471 | 5477 | 5479 | 5483 | 5501 | 5503 | 5507 | 5519 | 5521 | 5527 |
| 741–760 | 5641 | 5647 | 5651 | 5653 | 5657 | 5659 | 5669 | 5683 | 5689 | 5693 | 5701 |
| 761–780 | 5801 | 5807 | 5813 | 5821 | 5827 | 5839 | 5843 | 5849 | 5851 | 5857 | 5861 |
| 781–800 | 5953 | 5981 | 5987 | 6007 | 6011 | 6029 | 6037 | 6043 | 6047 | 6053 | 6067 |
| 801–820 | 6143 | 6151 | 6163 | 6173 | 6197 | 6199 | 6203 | 6211 | 6217 | 6221 | 6229 |
| 821–840 | 6311 | 6317 | 6323 | 6329 | 6337 | 6343 | 6353 | 6359 | 6361 | 6367 | 6373 |
| 841–860 | 6481 | 6491 | 6521 | 6529 | 6547 | 6551 | 6553 | 6563 | 6569 | 6571 | 6577 |
| 861–880 | 6679 | 6689 | 6691 | 6701 | 6703 | 6709 | 6719 | 6733 | 6737 | 6761 | 6763 |
| 881–900 | 6841 | 6857 | 6863 | 6869 | 6871 | 6883 | 6899 | 6907 | 6911 | 6917 | 6947 |
| 901–920 | 7001 | 7013 | 7019 | 7027 | 7039 | 7043 | 7057 | 7069 | 7079 | 7103 | 7109 |
| 921–940 | 7211 | 7213 | 7219 | 7229 | 7237 | 7243 | 7247 | 7253 | 7283 | 7297 | 7307 |
| 941–960 | 7417 | 7433 | 7451 | 7457 | 7459 | 7477 | 7481 | 7487 | 7489 | 7499 | 7507 |
| 961–980 | 7573 | 7577 | 7583 | 7589 | 7591 | 7603 | 7607 | 7621 | 7639 | 7643 | 7649 |
· Lists of primes by type › Fermat primes › Generalized Fermat primes
2
2
a
{\displaystyle a}
2
Generalized Fermat primes with base a
3, 5, 17, 257, 65537, ... (
OEIS: A019434)
4
4
a
{\displaystyle a}
4
Generalized Fermat primes with base a
5, 17, 257, 65537, ...
6
6
a
{\displaystyle a}
6
Generalized Fermat primes with base a
7, 37, 1297, ...
8
8
a
{\displaystyle a}
8
Generalized Fermat primes with base a
(none exist)
10
10
a
{\displaystyle a}
10
Generalized Fermat primes with base a
11, 101, ...
12
12
a
{\displaystyle a}
12
Generalized Fermat primes with base a
13, ...
14
14
a
{\displaystyle a}
14
Generalized Fermat primes with base a
197, ...
16
16
a
{\displaystyle a}
16
Generalized Fermat primes with base a
17, 257, 65537, ...
18
18
a
{\displaystyle a}
18
Generalized Fermat primes with base a
19, ...
20
20
a
{\displaystyle a}
20
Generalized Fermat primes with base a
401, 160001, ...
22
22
a
{\displaystyle a}
22
Generalized Fermat primes with base a
23, ...
24
24
a
{\displaystyle a}
24
Generalized Fermat primes with base a
577, 331777, ...
| | Generalized Fermat primes with base a |
| 2 | 3, 5, 17, 257, 65537, ... ( OEIS: A019434) |
| 4 | 5, 17, 257, 65537, ... |
| 6 | 7, 37, 1297, ... |
| 8 | (none exist) |
| 10 | 11, 101, ... |
| 12 | 13, ... |
| 14 | 197, ... |
| 16 | 17, 257, 65537, ... |
| 18 | 19, ... |
| 20 | 401, 160001, ... |
| 22 | 23, ... |
| 24 | 577, 331777, ... |
References
- List of prime numbers from 1 to 10,006,721https://openlibrary.org/books/OL16553580M
- Tomás Oliveira e Silva, Goldbach conjecture verification Archived 24 May 2011 at the Wayback Machine. Retrieved 16 Julyhttp://www.ieeta.pt/~tos/goldbach.html
- (sequence A080127 in the OEIS)
- "Conditional Calculation of pi(1024)"http://primes.utm.edu/notes/pi(10%5E24).html
- OEIS: A018239 includes 2 = empty product of first 0 primes plus 1, but 2 is excluded in this list.
- phttp://projecteuclid.org/euclid.em/1048515811
- Mathematics of Computationhttps://doi.org/10.2307%2F2005468
- It varies whether L0 = 2 is included in the Lucas numbers.
- wwwhttps://www.mersenne.org/primes/
- t5khttps://t5k.org/notes/by_year.html
- The On-Line Encyclopedia of Integer Sequenceshttps://oeis.org/A121091
- The On-Line Encyclopedia of Integer Sequenceshttps://oeis.org/A121616
- The On-Line Encyclopedia of Integer Sequenceshttps://oeis.org/A121618
- Math. Comphttps://www.ams.org/journals/mcom/2009-78-266/S0025-5718-08-02090-5/S0025-5718-08-02090-5.pdf
- Journal of Recreational Mathematics
- Mathematics of Computationhttps://www.ams.org/journals/mcom/1967-21-098/S0025-5718-1967-0222007-9/S0025-5718-1967-0222007-9.pdf
- nhttps://doi.org/10.1007%2FBF01951947
- t5khttps://t5k.org/lists/2small/0bit.html
- Subproject status at PrimeGridhttps://www.primegrid.com/server_status_subprojects.php
- The new book of prime number recordshttps://books.google.com/books?id=72eg8bFw40kC&q=ribenboim