Note on the generation of p0 for RSA keysets

A note has been published by Clayden (1988) regarding the value p₀=s^r-1(mod rs)-r^s-1(mod rs) (where r and s are distinct primes). This value of p₀ can be used in the generation of strong primes for the RSA public key cryptosystem. In another paper, Gordon (1984) requires whichever of p₀ or p₀+rs is odd to generate the strong prime. Clayden´s note gives a proof of the fact that it is always the value of p₀+rs that is odd. He also commented that, as this is not necessarily the case if either r or s is not prime, then the oddness of p₀+rs could be used as an extra test for the primality of both r and s.