Twin Primes Conjecture

Many of the oldest and most difficult mathematical puzzles are based on prime numbers, which are numbers that can only be divided by one or by themselves. One of these is the theory of the twin primes. One of the oldest unsolved math problems we are aware of is often referred to as Polignac's conjecture, after the mathematician who initially proposed it in 1846, Alphonse de Polignac.

It predicts the existence of an endless number of "twin primes," or prime numbers that differ by 2, such as 3 and 5, 5 and 7, and so forth. If you ask us, it makes sense, but as the numbers rise, primes become mathematically rarer and much trickier to calculate. It is not a simple effort to show that there would always be a pair of primes that differ by a factor of 2, and some of our brightest mathematicians have so far been unable to do it.