Recently I announced the discovery of a super-prime power series of the form k*2^n-1, n variable, k fixed, with over 200 primes to the Yahoo Primeform group.

http://tech.groups.yahoo.com/group/primeform/message/11407
An analysis of the primes discovered to date shows that there are significantly more even n in the list of primes (119) than odd (94). The complete list of the 213 primes to date is at:

http://www.mersenneforum.org/showthread.php?t=18407 message 5.

I have been fascinated for some while at the ability of k.4^n+/-1 to generate long Cunningham chains, and I am wondering if the predominance of even members of the super-prime power series is connected to the fact that no prime p is p-1 modulo a square base, 4 being 2^2 of course.

I had done some initial work on generalised Cunningham chains back in 2007, and - found good length chains quickly for b=4 and 9, see

http://www.mersenneforum.org/showthread.php?t=9021
Comments, remarks, brickbats welcome

Robert