11.2.16

Kinky Primes

Definition: Kinky primes are pairs of primes of the form (p, q) where p = a1*r + 1 and q = a2*s + 1 such that GCD(a1, a2) > 1 and a1, a2 , r, s are in Z.

Claim: Given a pair of kinky primes (p = a1*r + 1, q = a2*s + 1) the universal exponent mod p*q is phi(p*q)/GCD(a1, a2)

Proof: A slightly kinkier version of the proof presented here

Claim: The set of all bad primes as defined here is a subset of the set of kinky primes.

Proof: Follows from the previous claim.