The online computer game “Is this prime?” tests a player’s knowledge of prime numbers—and just surpassed 2,999,999 attempts. Give it a whirl.

Prime numbers are infinite, and proving anything about patterns in them is notoriously difficult. Mathematicians continue to chip away at pair primes, which are primes that are two apart: 11 and ...

Fortunately, Édouard Lucas developed a prime number test in 1878, later proved by Derrick Henry Lehmer in 1930. Their work resulted in an efficient algorithm for evaluating potential Mersenne ...

For centuries, prime numbers have fascinated mathematicians, from ancient artifacts to modern tech. Now, cloud computing and global collaborations are pushing the search for record-breaking primes ...

If a prime number is the sum of two squares, then it’s not a Gaussian prime. So when you note that 13 = 4+9, and that 89 = 25+64, you’re observing that 13 and 89 are not Gaussian primes.

For example, 7 is a prime number since I'm left with a remainder or a fractional component if I divide 7 by anything other than itself or 1. 6 is not a prime because I can divide 6 by 2 and get 3.

25 = 5 * 5 In other words, 25’s “prime signature” is 5 * 5. Only 25 has that signature and 5 * 5 only comes out to 25. If you think about the entire range of whole numbers—that is, the ...

They are sketched by a mathematical formula called the Möbius function, which takes a polynomial as an input and outputs 1 if the polynomial has an even number of prime factors, −1 if it has an ...

These numbers, which are only divisible by 1 and themselves, form the atoms of number theory, so to speak, and have fascinated humankind for thousands of years.

Prime numbers are divisible only by 1 and themselves. They serve as the “atoms” of mathematics, capable of decomposing other numbers into factors (like 12 = 2 × 2 × 3).