Date: Apr 24, 2013 11:23 AM
Author: HOPEINCHRIST
Subject: Re: primes in the arithmetic sequence 1, 31, 61, 91, 121, ... 30k+1 ...

On Monday, April 22, 2013 1:31:09 AM UTC-5, David Bernier wrote:
> I was looking for a simple arithmetic sequence with many 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+20121 1,097,495,520,301 = 61*27617*651473. // n+20301 So, it should be possible to have a block of six 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 consecutive numbers from that arithmetic sequence that are all 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.

In the linear sense there are many sequences, because prime numbers are sequence themselves. We have and are publishing now world first ever contiuouos prime number sieve at 6.

Seperatly all numbers lend to a constant value of 1.44. ( the encriopted code fornon prime number 119 is 1.428-1.44=0.012 and for 121 it is 1.452-1.44=.012 . The problem is that some of you are so "starched up" by your colleges , its hard to communicate , Then there are your dysfunctionals and perverts, a whole sequence of them. We should be published by 10 days this final paper

Hope Research By the grace of our Lord Jesus Christ