That so many puzzles about prime numbers still remain seems astonishing—after all, several formulas for calculating prime numbers exist.

It’s also a building block of number theory. Large prime numbers are massively useful in cryptography, which is the study and use of codes.

The newly discovered number is what's known as a Mersenne prime, named for a French monk named Marin Mersenne who studied primes some 350 years ago. Mersenne primes have a simple formula: 2 n -1.

Mathematicians have spent millennia trying to understand prime numbers – those only divisible by themselves and 1 – but so far no one has discovered a pattern for the primes. Now mathematician ...