- 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. ---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.

> ---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

>