The algorithm in this paper solves the problem of generating prime numbers without brute-force testing,one-by-one in a sequence.It employs two distinct formulas: one generating primes at even indices for prime numbers and the other at odd indices for prime numbers, using novel sequences to deterministically produce each prime in order without divisibility checks or sieving methods(no brute forcing techniques needed or involved).
Chaitanya Bankar (2026) studied this question.