Twin Prime Finder

About this calculator

A twin prime pair is two prime numbers that differ by exactly 2, such as (11, 13), (17, 19), or (29, 31). This tool searches upward from the number you enter, testing each candidate for primality (checking divisibility by all integers up to its square root) until it finds two consecutive primes p and p+2 — the smallest such pair at or above your starting value.

Twin primes are one of the oldest unsolved problems in number theory: the Twin Prime Conjecture claims there are infinitely many such pairs, and while Yitang Zhang's 2013 breakthrough proved infinitely many primes exist within a bounded gap (later narrowed to 246 by the Polymath project), the conjecture itself remains open. Math students, competitive programmers, and cryptography hobbyists use tools like this to explore prime distribution and test conjectures by hand rather than running a full sieve.