Polignac's conjecture

Polignac's conjecture, also known as the "French conjecture," is a statement in number theory formulated by the French mathematician Alphonse de Polignac in 1849. The conjecture posits that for every positive even integer \( k \), there are infinitely many prime pairs \( p \) and \( p + k \) such that both \( p \) and \( p + k \) are prime numbers.