The Twin Prime Conjecture states that there are infinitely many pairs of prime numbers which are separated by just two, like 3 and 5, and 29 and 31. "The Twin Prime Conjecture is one of those annoying unsolved problems in number theory: so simple and elegant to state, but a solution continues to evade the most complex methods and sharpest minds," said Brian Murphy, a number theorist involved in breaking the RSA-155 factoring challenge.