table of primes in arithmetic progressions per Dirichlet’s theorem

Dirichlet’s theorem on primes in arithmetic progressions tells us that given the $n$ th prime $p_{n}$ , there are infinitely many primes of the form $mp_{n}+1$ . Obviously, for $p_{1}=2$ , 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 $n$ th prime, the second column from the left gives the smallest prime of the form $mp_{n}+1$ , 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.

$p_{n}$
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