Greetings!
There are chains known today of at least 22 primes in arithmetic
progression.
Paul Pritchard has found a number of them.
1968 I searched for such PAP:s as they are known together with Hans Riesel,
but the available computer power at that time was too hard to get.
Later I picked up the old project, and I have a fairly large collection of
PAP:s.
Torbjörn Alm
----- Original Message -----
From: <[EMAIL PROTECTED]>
To: "Gary Untermeyer" <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
Sent: Thursday, April 05, 2001 6:38 AM
Subject: Re: Mersenne: arithmetic progression of consecutive primes
> > From: "Gary Untermeyer" <[EMAIL PROTECTED]>
>
> > Greetings,
>
> > Although this is not a question regarding mersenne primes, I thought I'd
> > throw this out to the readers here.
>
> > Let x be a prime number. Consider the series of numbers that take the
> > following form:
>
> > x, x + n, x + 2n, x + 3n, x + 4n, x + 5n, x + 6n, where n is an
> > even positive whole number.
>
> > In this series of seven numbers, can anyone tell me why, if ALL of these
> > numbers are prime, that the minimum value of n is 210 if all the terms
> > are _consecutive_ prime numbers?
>
> The _consecutive_ hypothesis is not required,
> other than requiring x > 7 and n > 0. If n is not divisible by 7,
> then one of the seven numbers x, x + n, ..., x + 6n
> will be divisible by 7, hence not prime.
> [No two of the seven will be congruent modulo 7,
> so all possible remainders modulo 7 must be represented.]
> Likewise n must be divisible by 2, 3, 5.
>
>
>
>
>
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