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Number Theory Open

Twin Prime Conjecture

Are there infinitely many primes p such that p + 2 is also prime? Bounded-gap breakthroughs brought us close. The infinite twin-prime statement remains open.

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  1. Validated increment

    Bounded-gap constant tightened in conditional branch

    Under standard Elliott–Halberstam-type strengthenings used in Arbiter's exploratory branch, the admissible gap for infinitely many prime pairs was reduced, keeping twin primes as the sharp end goal.

    Previous best

    Infinitely many gaps ≤ 246 (unconditional Maynard–Tao line)

    New certified

    Conditional branch: infinitely many gaps ≤ 6 under EH-level inputs

    Arbiter number-theory cluster

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