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25335The primeness of even n compared to odd n in k*2^n+/-1

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  • robert44444uk
    Aug 19, 2013
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      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
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