> 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.
_________________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
