--- In

primenumbers@yahoogroups.com, Phil Carmody <thefatphil@...> wrote:

>

> > First order son primes (p, 3p+2 prime) are more common than

> > Sophie

> > Germains (p,2p+1 prime): approx 36% more common.

> >

> > Why? - If we look at mod 3

> >

> > if p==1mod3 then 2p+1==0mod3

> > if p==2mod3 then 2p+1==2mod3, 50% chance of a 2p+1 is not

> > 0mod3

> >

> > if: p==1mod3 then 3p+2==2mod3

> > if: p==2mod3 then 3p+2==2mod3, 100% chance that 3p+1 is not

> > 0mod3

> >

> >

> > Question: Why are chains of first order son primes not

> > sought by prime

> > hunters, as they might provide longer chains than SG, CC,

> > despite the

> > slight increase in magnitude?

>

> Other generalised relations have been looked at. However, with an

exponent of 3 driving the size, these chains aren't likely to be

longer than ones which are related to powers of 2. Have you tried

looking for both? How easy is it to find a chain of 10, 11, or 12 of

either type?

>

> Phil

>

Thanks for responding, Phil. I haven't explored these at all, I did

not think about their existence until yesterday, when they appeared as

part of the work I am doing on gaps in ordered proper prime fraction

groups - see post 15 on

http://www.mersenneforum.org/showthread.php?t=10574
I am unlikely to explore these chains, as I do not have any computing

power here in Bangladesh. But I agree, chain of 10 to 12 should be

easy to find.

The earliest instance chains are:

SPlen2 3,11

SPlen3 5,17,53

SPlen4 29,89,269,809

SPlen5 1129,3389,10169,30509,91529

SPlen6 10009,30029,90089,270269,810809,2432429

Regards

Robert