Euler’s (Prime to) Prime Generating Equation

The greatest number theorist in mathematical universe, Leonhard Euler had discovered some formulas and relations in number theory, which were based on practices and were correct to limited extent but still stun the mathematicians. The prime generating equation by Euler is a very specific binomial equation on prime numbers and yields more primes than any

Fermat Numbers

Fermat Numbers, a class of numbers, are the integers of the form \$ F_n=2^{2^n} +1 \ \ n \ge 0\$ . For example: Putting \$ n := 0,1,2 \ldots\$ in \$ F_n=2^{2^n}\$ we get \$ F_0=3\$ , \$ F_1=5\$ , \$ F_2=17\$ , \$ F_3=257\$ etc. Fermat observed that all the integers \$ F_0, F_1,