conjectures turn out to be true.

As I wrote in a previous post, the set of safe primes is composed of two subsets: the set of steady primes and the set of tough primes.

The first few safe primes where primes in olive green are steady and the rest are tough |

Conjecture 1: Given p a steady prime and a < p such that it is not a power of 2 mod p then

a^((p-1)/2)= p-1 else if a is a power of 2 mod p then a^((p-1)/2)= 1

Conjecture 2: Given p a steady prime then (p-1)/2 is not a power of 2 mod p and

((p-1)/2)^((p-1)/2) = p-1