Nash value of exponent

[pepi37]

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!

[Citrix]

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

[axn]

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.