Hello, I have informed the responsible institutions 6 months ago before posting this message on public key cryptography. Below, I'm presenting an introduction to R-sequence theory, allowing more accurate analysis of verification of groups of primes (and more) and distribution of primes. No direct algorithm is enclosed. Equivalence Conjecture might still be untrue. The rest of the analysis has taken over 4 years. References: 1. http://mishabucko.files.wordpress.com/2011/12/paper_new2.pdf 2. http://mishabucko.files.wordpress.com/2011/12/conj.pdf 3. http://mishabucko.wordpress.com/2011/12/09/24-11-1984-conjecture/ Best regards, Misha