25335The primeness of even n compared to odd n in k*2^n+/-1
- Aug 19, 2013Recently 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.
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
Comments, remarks, brickbats welcome
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