number-theory - w3toppers.com

Parallel Algorithms for Generating Prime Numbers (possibly using Hadoop’s map reduce)

Here’s an algorithm that is built on mapping and reducing (folding). It expresses the sieve of Eratosthenes P = {3,5,7, …} \ U {{p2, p2+2p, p2+4p, …} | p in P} for the odd primes (i.e without the 2). The folding tree is indefinitely deepening to the right, like this: where each prime number … Read more

finding a^b^c^… mod m

abc mod m = abc mod n mod m, where n = φ(m) Euler’s totient function. If m is prime, then n = m-1. Edit: as Nabb pointed out, this only holds if a is coprime to m. So you would have to check this first.