```Date: Apr 22, 2013 2:31 AM
Author: David Bernier
Subject: primes in the arithmetic sequence 1, 31, 61, 91, 121, ... 30k+1 ...

I was looking for a simple arithmetic sequence withmany primes "crowded together", i.e. quasi-consecutive ...Suppose we let n = 1,097,495,500,000 ; then I get this:n+19941 is prime, n+19971 is prime, n+20001 is prime,n+20031 is prime, n+20061 is prime, n+20091 is prime,n+20121 is composite,n+20151 is prime, n+20181 is prime, n+20211 is prime,n+20241 is prime, n+20271 is prime, n+20301 is composite.1,097,495,520,121 = 7*11*13*23*47669527    // n+201211,097,495,520,301 = 61*27617*651473.       // n+20301So, it should be possible to have a block ofsix consecutive numbers from the arithmectic sequence:1, 31, 61, 91, 121, ... 30k+1 ...that are all prime, then a composite number,followed by a second block of six consecutivenumbers from that arithmetic sequence that areall prime ...  (probably?)I.e. Out of thirteen consecutive integers from the sequence      of the 30k+1, can we get at least 12 primes out      of the thirteen numbers, for the right choice      of the 13 consecutive numbers ?David Bernier? isprime(n+19941)%37 = 1? isprime(n+19971)%38 = 1? isprime(n+20001)%39 = 1? isprime(n+20031)%47 = 1? isprime(n+20061)%48 = 1? isprime(n+20091)%49 = 1? isprime(n+20121)%40 = 0? isprime(n+20151)%41 = 1? isprime(n+20181)%42 = 1? isprime(n+20211)%43 = 1? isprime(n+20241)%44 = 1? isprime(n+20271)%45 = 1? isprime(n+20301)%46 = 0-- Jesus is an Anarchist.  -- J.R.
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