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## Prime sequence, is it likely to be extendable

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• Whilst working on another project, I noticed a sequence of primes given by the following pari/gp script: { p=7; for(j=1,1206, i = (j*12)+9; p = 7 +
Message 1 of 3 , Oct 9, 2013
Whilst working on another project, I noticed a sequence of primes given by
the following pari/gp script:

{
p=7;
for(j=1,1206,
i = (j*12)+9;
p = 7 + ((2^i-1)*16);
o=p-sum(x=0,(i-6)/3,4*8^(x))*32-23;
l=lift(Mod(2,p)^o);
if(l == 1,
print([j,i,l,isprime(p/7),[ceil(log(p/7)/log(10))]]);
);
);
}

where p/7 is prime for j = 1, 6, 9, 13, 18, 20, 103, 151 and 1206

My question is, is it likely that this sequence is extendable or is it
likely to be finite?

I've put a fair number of cycles into this, but was unable to find
anything with j > 1206 as yet.

Regards,

Kevin.
• ... Heuristically, we expect an infinty of primes of this form: (2^(12*1+13)-9)/7 is trivially prime!: 4793489 (2^(12*6+13)-9)/7 is 3-PRP! (0.0000s+0.1175s)
Message 2 of 3 , Oct 10, 2013

---In primenumbers@yahoogroups.com, <research@...> wrote:

> is it likely that this sequence is extendable or is it
> likely to be finite?

Heuristically, we expect an infinty of primes of this form:

(2^(12*1+13)-9)/7 is trivially prime!: 4793489
(2^(12*6+13)-9)/7 is 3-PRP! (0.0000s+0.1175s)
(2^(12*9+13)-9)/7 is 3-PRP! (0.0000s+0.1096s)
(2^(12*13+13)-9)/7 is 3-PRP! (0.0000s+0.0605s)
(2^(12*18+13)-9)/7 is 3-PRP! (0.0000s+0.0333s)
(2^(12*20+13)-9)/7 is 3-PRP! (0.0000s+0.0418s)
(2^(12*103+13)-9)/7 is 3-PRP! (0.0013s+0.0458s)
(2^(12*151+13)-9)/7 is 3-PRP! (0.0020s+0.0860s)
(2^(12*1206+13)-9)/7 is 3-PRP! (0.1019s+0.0397s)
(2^(12*7269+13)-9)/7 is 3-PRP! (5.2402s+0.0563s)
David
• Hello David, Thanks for the info. I hadn t spotted the 12*n+13 pattern. Best Regards, Kevin.
Message 3 of 3 , Oct 10, 2013
Hello David,

Thanks for the info. I hadn't spotted the 12*n+13 pattern.

Best Regards,

Kevin.

> ---In primenumbers@yahoogroups.com, <research@...> wrote:
>
>> is it likely that this sequence is extendable or is it
>> likely to be finite?
>
> Heuristically, we expect an infinty of primes of this form:
>
> (2^(12*1+13)-9)/7 is trivially prime!: 4793489
> (2^(12*6+13)-9)/7 is 3-PRP! (0.0000s+0.1175s)
> (2^(12*9+13)-9)/7 is 3-PRP! (0.0000s+0.1096s)
> (2^(12*13+13)-9)/7 is 3-PRP! (0.0000s+0.0605s)
> (2^(12*18+13)-9)/7 is 3-PRP! (0.0000s+0.0333s)
> (2^(12*20+13)-9)/7 is 3-PRP! (0.0000s+0.0418s)
> (2^(12*103+13)-9)/7 is 3-PRP! (0.0013s+0.0458s)
> (2^(12*151+13)-9)/7 is 3-PRP! (0.0020s+0.0860s)
> (2^(12*1206+13)-9)/7 is 3-PRP! (0.1019s+0.0397s)
> (2^(12*7269+13)-9)/7 is 3-PRP! (5.2402s+0.0563s)
>
> David
>
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