Re: [PrimeNumbers] Primes not in AP
- Robert wrote:
> are there primes that are not in AP, if AP>2?An AP of primes starting at p cannot have length above p,
because p would divide term p+1 which is p + a*p
where a is the common difference in the AP.
It follows from commonly believed conjectures like
Dickson's conjecture that every prime p is the start
of infinitely many cases of p primes in AP.
The largest p with a known case is 17 where the minimal case is
17 + 341976204789992332560*n for n = 0..16, found by Phil Carmody in 2001:
I don't think it has been proved for any prime that it is in
an AP3 without finding a specific example AP3.
Jens Kruse Andersen