A prime number that is one less than some power of two (or what mathematicians write as 2 p – 1) is called a Mersenne prime, after the French monk Marin Mersenne, who investigated them more than ...

Some of them are prime while some are not; highly efficient algorithms have been devised to check them for primality. GIMPS seeks Mersenne primes using a clever method called the Lucas-Lehmer test ...

The largest known prime number has been discovered by an amateur researcher and former Nvidia employee. The new number is 2 136,279,841 – 1, which beats the previous title holder (2 82,589,933 ...

For example, the Goldbach conjecture states that any even number greater than 2 can be expressed by the sum of two prime numbers (4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, and so on).

We have known for millennia that an infinite number of prime numbers, i.e., 2, 3, 5, 7, 11, etc., can be divided by themselves and the number 1 only.

A fragment of the Rhind papyrus, which shows the knowledge about prime numbers in ancient Egypt. Credit: The Trustees of the British Museum For example, the number 4 has five partitions: 4, 3 + 1, 2 + ...