Santilli’s Prime Chains: P_j + 1=aP_j ± b

Chun-Xuan Jiang

Abstract

Santilli’s prime chains: Pj + 1=aPj ± b , j=1,⋯,k−1, (a,b)=1, 2|ab. If a −1 = P1λn Pnλn , P1⋯Pn|b, we have J2(ω)→∞ as ω→∞. There exist infinitely many primes P1 such that P2,⋯, Pk are primes for arbitrary length k. It is the Book proof. This is a generalized Euclid-Euler proof for the existence of infinitely many primes. Therefore Euclid-Euler-Jiang theorem in the distribution of primes is advanced. It is the Book theorem.