By definition a number    is prime if  1$">  and its only divisors are 1 and    itself.

There are infinite prime numbers.

Stanislaw Ulam in 1963 observed that drawing the integers along a spiral (as depicted below) the prime numbers often seem to align along some diagonals. Essentially this depends on the fact that certain quadratic polynomials produce (at least in a limited range) more primes than others.

A spiral with side 256: This construction can be applied to other families of numbers, like abundant, admirable, alternating, apocalyptic, arithmetic, binomials, congruent, deficient, balanced, economical, equidigital, evil, hoax, inconsummate, junction, lucky, nialpdrome, odious, plaindrome, practical, pseudoperfect, self, super-d, tau, triangular, Ulam, wasteful and Zumkeller numbers.

The prime numbers up to 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. more terms