Prime numbers, vital in mathematics and competitive exams, can be quickly identified using a systematic approach. This method ...

Using a notion called integer partitions, mathematicians have discovered a new way to detect prime numbers while also ...

Around 300 BCE, Euclid proved that there are infinitely many prime numbers. Mathematicians have since built on his theorem, ... or a perfect square—makes the problem much harder.

His idea was to identify all the primes up to a given point by gradually “sieving out” the numbers that aren’t prime. His sieve starts by crossing out all the multiples of 2 (except 2 itself), then ...

A prime number is an integer that can’t be divided by any integer other than itself and 1. ... by definition, no prime number has an integer square root or any other factor besides itself and 1.

Prime numbers, when expressed as that number of dots, can be arranged only in a single row or column, rather than a square or rectangle. David Eppstein/Wikimedia Commons ...

Prime numbers, when expressed as that number of dots, can be arranged only in a single row or column, rather than a square or rectangle. David Eppstein/Wikimedia Commons.

Let’s break that down a bit. The square brackets ⌊ and ⌋ indicate that you should round down the value inside them. So, for example, ⌊ 1.7 ⌋ = 1 and ⌊ 1.12111167545 ⌋ = 1.

Prime numbers, fundamental to number theory and mathematics, have intrigued humans for millennia. Mersenne primes, of the form 2 p –1, are central to the search for large primes.