Thread: "Rare" Primes
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Old 2008-08-20, 18:14   #11
biwema
 
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Mar 2004

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Quote:
Originally Posted by Jens K Andersen View Post
It's easy to construct rare prime forms by picking a quickly growing function with one or a few early primes. You mention Generalized Fermat 10^2^n+1, but there is no base b with more than 7 known primes b^2^n+1, and finding one with more than 10 looks very hard. The record is 7 for b=2072005925466 at http://primepuzzles.net/puzzles/puzz_399.htm
Maybe there is even a Generalized Fermat with more than 7 primes in the range b<10^15 or so. The sequence above assumes that n=0..6 of b^2^n+1 is prime. Maybe there is a generalized Fermat which has more than 7 primes that are not consecutive. For example if n=0,1,2,3,4,5,7,8 is prime.
The probability of that szenario is still pretty small.
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