[Cryptography] Need a list of Solinas/pseudo Mersene Primes.

[Viktor Dukhovni]

> On Aug 31, 2018, at 10:44 AM, Viktor Dukhovni <cryptography at dukhovni.org> wrote:
> 
>> On Aug 30, 2018, at 8:33 PM, Phillip Hallam-Baker <phill at hallambaker.com> wrote:
>> 
>> need a value greater than 2^256, sorry. 2^257-n
>> 
>> So what is the lowest value of n that is prime? Did not see that in safe primes :(
> 
> According to https://www.alpertron.com.ar/ECM.HTM
> 
>  (1 SHL 257) - B(1 SHL 257) = 93
> 
> So you can take n = 93.

If you want the lowest possible "n", and would prefer a lower "n" at the
cost of a slightly higher exponent, then 2^266 - 3 is the best you can do
for exponents modestly above 256.

That was found with:  x=257;x=x+1;x<=272;x*1000 + ((1 SHL x) - B(1 SHL x))
with "266003" the winner.

-- 
	Viktor.