table of primes in arithmetic progressions per Dirichlet’s theorem
Dirichlet’s theorem on primes in arithmetic progressions tells us that given the nth prime pn, there are infinitely many primes of the form mpn+1. Obviously, for p1=2, the primes of that form are merely the odd primes. For the other primes, m has to be even, but not much else appears obvious.
The leftmost column of this table gives the nth prime, the second column from the left gives the smallest prime of the form mpn+1, the third column from the left gives the second smallest prime of that form, etc. Apart from the leftmost column, none of the columns contain a sequence in ascending order.
pn | ||||||||||
2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 |
3 | 7 | 13 | 19 | 31 | 37 | 43 | 61 | 67 | 73 | 79 |
5 | 11 | 31 | 41 | 61 | 71 | 101 | 131 | 151 | 181 | 191 |
7 | 29 | 43 | 71 | 113 | 127 | 197 | 211 | 239 | 281 | 337 |
11 | 23 | 67 | 89 | 199 | 331 | 353 | 397 | 419 | 463 | 617 |
13 | 53 | 79 | 131 | 157 | 313 | 443 | 521 | 547 | 599 | 677 |
17 | 103 | 137 | 239 | 307 | 409 | 443 | 613 | 647 | 919 | 953 |
19 | 191 | 229 | 419 | 457 | 571 | 647 | 761 | 1103 | 1217 | 1483 |
23 | 47 | 139 | 277 | 461 | 599 | 691 | 829 | 967 | 1013 | 1151 |
29 | 59 | 233 | 349 | 523 | 929 | 1103 | 1277 | 1451 | 1567 | 1741 |
31 | 311 | 373 | 683 | 1117 | 1303 | 1427 | 1489 | 1613 | 1861 | 2357 |
37 | 149 | 223 | 593 | 1259 | 1481 | 1777 | 1999 | 2221 | 2591 | 2887 |
41 | 83 | 739 | 821 | 1231 | 1559 | 1723 | 2297 | 2543 | 2707 | 2789 |
43 | 173 | 431 | 947 | 1033 | 1291 | 1549 | 1721 | 1979 | 2237 | 2753 |
47 | 283 | 659 | 941 | 1129 | 1223 | 1693 | 1787 | 2069 | 2351 | 2539 |
53 | 107 | 743 | 1061 | 1697 | 2333 | 2969 | 3181 | 3499 | 3923 | 4241 |
59 | 709 | 827 | 1063 | 1181 | 1889 | 2243 | 2833 | 3187 | 3541 | 3659 |
61 | 367 | 733 | 977 | 1709 | 1831 | 2441 | 3539 | 4027 | 4271 | 4637 |
67 | 269 | 1609 | 1877 | 2011 | 3083 | 3217 | 4021 | 4289 | 4423 | 4691 |
71 | 569 | 853 | 1279 | 1847 | 2131 | 2273 | 2557 | 2699 | 4261 | 5113 |
73 | 293 | 439 | 877 | 1607 | 1753 | 3067 | 3359 | 3797 | 3943 | 4673 |
79 | 317 | 1423 | 2213 | 2371 | 2687 | 3319 | 3793 | 4583 | 5531 | 5689 |
83 | 167 | 499 | 997 | 1163 | 1993 | 2657 | 4483 | 4649 | 5147 | 5479 |
89 | 179 | 1069 | 2137 | 2671 | 3739 | 3917 | 4273 | 4451 | 5519 | 6053 |
97 | 389 | 971 | 1553 | 1747 | 3299 | 3881 | 4463 | 4657 | 5821 | 6791 |
Title | table of primes in arithmetic progressions per Dirichlet’s theorem |
---|---|
Canonical name | TableOfPrimesInArithmeticProgressionsPerDirichletsTheorem |
Date of creation | 2013-03-22 18:13:15 |
Last modified on | 2013-03-22 18:13:15 |
Owner | PrimeFan (13766) |
Last modified by | PrimeFan (13766) |
Numerical id | 4 |
Author | PrimeFan (13766) |
Entry type | Data Structure |
Classification | msc 11N13 |