20180908, 21:13  #1 
Dec 2011
After milion nines:)
17×83 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) 23%. 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! 
20180909, 03:52  #2 
Jun 2003
1,579 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*5^101 will have factors 2*5^5+1 and 2*5^51 
20180909, 04:56  #3 
Jun 2003
11375_{8} Posts 
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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