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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.

Impact
76 /100
Funded
$8,900
Donors
178
Of goal
59%

Why this matters

Twin primes are the simplest pattern in the primes that still resists proof. A resolution would crown the bounded-gap program and sharpen sieve methods used across analytic number theory.

What a solution unlocks

  • Stronger sieve and GPY-type methods
  • Progress on prime tuples of longer patterns
  • New insight into prime correlations

Downstream impact

Techniques forged here routinely migrate into cryptography, random models of primes, and adjacent conjectures such as Goldbach-type problems.

Also open

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