2 3 5 7 1 1 13 17 19 23 29

3 1 37 4 1 43 47 53 59 6 1 67 7 1

73 79 83 89 97 10 1 103 107 109 1 13

127 13 1 137 139 149 15 1 157 163 167 173

179 18 1 19 1 193 197 199 2 1 1 223 227 229

233 239 24 1 25 1 257 263 269 27 1 277 28 1

283 293 307 3 1 1 3 13 3 17 33 1 337 347 349

353 359 367 373 379 383 389 397 40 1 409

4 19 42 1 43 1 433 439 443 449 457 46 1 463

467 479 487 49 1 499 503 509 52 1 523 54 1

547 557 563 569 57 1 577 587 593 599 60 1

607 6 13 6 17 6 19 63 1 64 1 643 647 653 659

66 1 673 677 683 69 1 70 1 709 7 19 727 733

739 743 75 1 757 76 1 769 773 787 797 809

8 1 1 82 1 823 827 829 839 853 857 859 863

877 88 1 883 887 907 9 1 1 9 19 929 937 94 1

947 953 967 97 1 977 983 99 1 997 1009 10 13

10 19 102 1 103 1 1033 1039 1049 105 1 106 1 1063 1069

1087 109 1 1093 1097 1 103 1 109 1 1 17 1 123 1 129 1 15 1

1 153 1 163 1 17 1 1 18 1 1 187 1 193 1 20 1 12 13 12 17 1223

1229 123 1 1237 1249 1259 1277 1279 1283 1289 129 1

1297 130 1 1303 1307 13 19 132 1 1327 136 1 1367 1373

138 1 1399 1409 1423 1427 1429 1433 1439 1447 145 1

1453 1459 147 1 148 1 1483 1487 1489 1493 1499 15 1 1

1523 153 1 1543 1549 1553 1559 1567 157 1 1579 1583

1597 160 1 1607 1609 16 13 16 19 162 1 1627 1637 1657

1663 1667 1669 1693 1697 1699 1709 172 1 1723 1733

174 1 1747 1753 1759 1777 1783 1787 1789 180 1 18 1 1

1823 183 1 1847 186 1 1867 187 1 1873 1877 1879 1889

190 1 1907 19 13 193 1 1933 1949 195 1 1973 1979 1987

1993 1997 1999 2003 20 1 1 20 17 2027 2029 2039 2053

2063 2069 208 1 2083 2087 2089 2099 2 1 1 1 2 1 13 2 129

2 13 1 2 137 2 14 1 2 143 2 153 2 16 1 2 179 2203 2207 22 13

222 1 2237 2239 2243 225 1 2267 2269 2273 228 1 2287

2293 2297 2309 23 1 1 2333 2339 234 1 2347 235 1 2357

237 1 2377 238 1 2383 2389 2393 2399 24 1 1 24 17 2423

2437 244 1 2447 2459 2467 2473 2477 2503 252 1 253 1

2539 2543 2549 255 1 2557 2579 259 1 2593 2609 26 17

262 1 2633 2647 2657 2659 2663 267 1 2677 2683 2687

2689 2693 2699 2707 27 1 1 27 13 27 19 2729 273 1 274 1

2749 2753 2767 2777 2789 279 1 2797 280 1 2803 28 19

2833 2837 2843 285 1 2857 286 1 2879 2887 2897 2903

2909 29 17 2927 2939 2953 2957 2963 2969 297 1 2999

300 1 30 1 1 30 19 3023 3037 304 1 3049 306 1 3067 3079

3083 3089 3 109 3 1 19 3 12 1 3 137 3 163 3 167 3 169 3 18 1

3 187 3 19 1 3203 3209 32 17 322 1 3229 325 1 3253 3257

3259 327 1 3299 330 1 3307 33 13 33 19 3323 3329 333 1

3343 3347 3359 336 1 337 1 3373 3389 339 1 3407 34 13

3433 3449 3457 346 1 3463 3467 3469 349 1 3499 35 1 1

35 17 3527 3529 3533 3539 354 1 3547 3557 3559 357 1

358 1 3583 3593 3607 36 13 36 17 3623 363 1 3637 3643

3659 367 1 3673 3677 369 1 3697 370 1 3709 37 19 3727

3733 3739 376 1 3767 3769 3779 3793 3797 3803 382 1

3823 3833 3847 385 1 3853 3863 3877 388 1 3889 3907

39 1 1 39 17 39 19 3923 3929 393 1 3943 3947 3967 3989

400 1 4003 4007 40 13 40 19 402 1 4027 4049 405 1 4057

4073 4079 409 1 4093 4099 4 1 1 1 4 127 4 129 4 133 4 139

4 153 4 157 4 159 4 177 420 1 42 1 1 42 17 42 19 4229 423 1

424 1 4243 4253 4259 426 1 427 1 4273 4283 4289 4297

4327 4337 4339 4349 4357 4363 4373 439 1 4397 4409

442 1 4423 444 1 4447 445 1 4457 4463 448 1 4483 4493

4507 45 13 45 17 45 19 4523 4547 4549 456 1 4567 4583

459 1 4597 4603 462 1 4637 4639 4643 4649 465 1 4657

4663 4673 4679 469 1 4703 472 1 4723 4729 4733 475 1

4759 4783 4787 4789 4793 4799 480 1 48 13 48 17 483 1

486 1 487 1 4877 4889 4903 4909 49 19 493 1 4933 4937

4943 495 1 4957 4967 4969 4973 4987 4993 4999 5003

5009 50 1 1 502 1 5023 5039 505 1 5059 5077 508 1 5087

5099 5 10 1 5 107 5 1 13 5 1 19 5 147 5 153 5 167 5 17 1 5 179

5 189 5 197 5209 5227 523 1 5233 5237 526 1 5273 5279

528 1 5297 5303 5309 5323 5333 5347 535 1 538 1 5387

5393 5399 5407 54 13 54 17 54 19 543 1 5437 544 1 5443

5449 547 1 5477 5479 5483 550 1 5503 5507 55 19 552 1

5527 553 1 5557 5563 5569 5573 558 1 559 1 5623 5639

564 1 5647 565 1 5653 5657 5659 5669 5683 5689 5693

570 1 57 1 1 57 17 5737 574 1 5743 5749 5779 5783 579 1

580 1 5807 58 13 582 1 5827 5839 5843 5849 585 1 5857

586 1 5867 5869 5879 588 1 5897 5903 5923 5927 5939

5953 598 1 5987 6007 60 1 1 6029 6037 6043 6047 6053

6067 6073 6079 6089 609 1 6 10 1 6 1 13 6 12 1 6 13 1 6 133

6 143 6 15 1 6 163 6 173 6 197 6 199 6203 62 1 1 62 17 622 1

6229 6247 6257 6263 6269 627 1 6277 6287 6299 630 1

63 1 1 63 17 6323 6329 6337 6343 6353 6359 636 1 6367

6373 6379 6389 6397 642 1 6427 6449 645 1 6469 6473

648 1 649 1 652 1 6529 6547 655 1 6553 6563 6569 657 1

6577 658 1 6599 6607 66 19 6637 6653 6659 666 1 6673

6679 6689 669 1 670 1 6703 6709 67 19 6733 6737 676 1

6763 6779 678 1 679 1 6793 6803 6823 6827 6829 6833

684 1 6857 6863 6869 687 1 6883 6899 6907 69 1 1 69 17

6947 6949 6959 696 1 6967 697 1 6977 6983 699 1 6997

700 1 70 13 70 19 7027 7039 7043 7057 7069 7079 7 103

7 109 7 12 1 7 127 7 129 7 15 1 7 159 7 177 7 187 7 193 7207

72 1 1 72 13 72 19 7229 7237 7243 7247 7253 7283 7297

7307 7309 732 1 733 1 7333 7349 735 1 7369 7393 74 1 1

74 17 7433 745 1 7457 7459 7477 748 1 7487 7489 7499

7507 75 17 7523 7529 7537 754 1 7547 7549 7559 756 1

7573 7577 7583 7589 759 1 7603 7607 762 1 7639 7643

7649 7669 7673 768 1 7687 769 1 7699 7703 77 17 7723

7727 774 1 7753 7757 7759 7789 7793 78 17 7823 7829

784 1 7853 7867 7873 7877 7879 7883 790 1 7907 79 19

7927 7933 7937 7949 795 1 7963 7993 8009 80 1 1 80 17

8039 8053 8059 8069 808 1 8087 8089 8093 8 10 1 8 1 1 1

8 1 17 8 123 8 147 8 16 1 8 167 8 17 1 8 179 8 19 1 8209 82 19

822 1 823 1 8233 8237 8243 8263 8269 8273 8287 829 1

8293 8297 83 1 1 83 17 8329 8353 8363 8369 8377 8387

8389 84 19 8423 8429 843 1 8443 8447 846 1 8467 850 1

85 13 852 1 8527 8537 8539 8543 8563 8573 858 1 8597

8599 8609 8623 8627 8629 864 1 8647 8663 8669 8677

868 1 8689 8693 8699 8707 87 13 87 19 873 1 8737 874 1

8747 8753 876 1 8779 8783 8803 8807 88 19 882 1 883 1

8837 8839 8849 886 1 8863 8867 8887 8893 8923 8929

8933 894 1 895 1 8963 8969 897 1 8999 900 1 9007 90 1 1

90 13 9029 904 1 9043 9049 9059 9067 909 1 9 103 9 109

9 127 9 133 9 137 9 15 1 9 157 9 16 1 9 173 9 18 1 9 187 9 199

9203 9209 922 1 9227 9239 924 1 9257 9277 928 1 9283

9293 93 1 1 93 19 9323 9337 934 1 9343 9349 937 1 9377

939 1 9397 9403 94 13 94 19 942 1 943 1 9433 9437 9439

946 1 9463 9467 9473 9479 949 1 9497 95 1 1 952 1 9533

9539 9547 955 1 9587 960 1 96 13 96 19 9623 9629 963 1

9643 9649 966 1 9677 9679 9689 9697 97 19 972 1 9733

9739 9743 9749 9767 9769 978 1 9787 979 1 9803 98 1 1

98 17 9829 9833 9839 985 1 9857 9859 987 1 9883 9887

990 1 9907 9923 9929 993 1 994 1 9949 9967 9973

Extended data:

There are infinite prime numbers, also called prime numbers.

A prime number is defined as a natural number greater than 1, and there are no other factors except 1 and itself.

The number of prime numbers is infinite. There is a classic proof in Euclid's Elements of Geometry. It uses a common proof method: reduction to absurdity. The concrete proof is as follows: Suppose there are only a limited number of n prime numbers, which are arranged in the order from small to large as p 1, p2, ..., pn, and let n = P 1× P2×...× PN, then,

Is it a prime number?

if

Is a prime number.

It is greater than p 1, p2, ..., pn, so it is not in the assumed prime set.

If it is a composite number, because any composite number can be decomposed into the product of several prime numbers; The greatest common divisor of n and N+ 1 is 1, so it is impossible to be divisible by p 1, p2, ..., pn, so the prime factor obtained by this complex number decomposition is definitely not in the assumed prime number set. Therefore, whether the number is a prime number or a composite number, it means that there are other prime numbers besides the assumed finite number of prime numbers. So the original assumption doesn't hold water. In other words, there are infinitely many prime numbers.

Other mathematicians have given some different proofs. Euler proved by Riemann function that the sum of reciprocal of all prime numbers is divergent, Ernst Cuomo proved more succinctly, and harry Furstenberg proved by topology.