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 2018-09-08, 21:13 #1 pepi37     Dec 2011 After milion nines:) 1,249 Posts Nash value of exponent We all know there is k ( on any base) that can have low nash value or high nash value. When I start searching prime in fixed exponent type, I also noticed some exponent have on same k range little more exponent that survive sieve from another. But difference is small , maybe ( or max) 2-3%. So if someone here know the answer: is on any base some exponent that will produce significant lower sieve files, or will every be case Iike I observed. And of course, if such exponent exist, how to compute more of them. Thanks!
 2018-09-09, 03:52 #2 Citrix     Jun 2003 2·3·257 Posts For k*b^n+-1, I think you are talking about fixed b and n and variable k? Some of this is randomness involved with distribution of factors. When n has a lot of small factors and k is a power then they could have a factor. e.g. 4*5^10-1 will have factors 2*5^5+1 and 2*5^5-1
2018-09-09, 04:56   #3
axn

Jun 2003

459310 Posts

Quote:
 Originally Posted by pepi37 So if someone here know the answer: is on any base some exponent that will produce significant lower sieve files, or will every be case Iike I observed.
The short answer is no. Except for minor statistical noise, there is not going to be meaningful difference between different exponents.

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