Re: forprime in arithmetic progressions?

[Remy José Cano <cano.remy.jose@gmail.com>]

Dear friends,

What do you think? about the performance of this stub:

------------------------[ Start ]-----------------------------------

a(n)=sum(k=0,n, k*(n+1)^k ); \\ if n>0 can be interpreted as the
greatest possible permutation without repetition of digits that can be
written in the base n+1.

\\ Initial state.
n=4;
s=3181; \\ s= a(0)+a(1)+a(2)+a(3)+a(4);

\\ Search loop.
while(1,ispseudoprime(s+=a(n++))&&break)

------------------------[ End ]-----------------------------------

The purpose with such loop is to find a counter example for an
hypothesis on "s", which states that with the exception of s(1), s(2),
s(3) and s(4), there are no other primes in such sequence.

I am trying such test empirically, although more desirable of course
it would be a formal proof...

After running it on an AMD64 4GB Linux64 GP 2.9.4 environment during
131mins., (at purpose with the definition of a(n) compiled separately
using GP2C),
the execution reached n>4096 without breaking the loop by code instruction...

[ This is, I only had stop it via CTRL+C sometimes to check the progress ]

Cheers,

Remy.

P.S.: I am about to update my installation to GP 2.10 when finished
this in order to be able of using forsquarefree( ) in another pending
tasks... Merci.