Any positive integer greater than 1 and exactly divisible only by 1 and itself. The sequence of prime numbers begins 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 but follows no discernible pattern. The issues of the regularities and irregularities in the distribution of primes are among the most important questions in number theory. Primes have been recognized at least since Pythagoras. It has been known that there are infinitely many of them at least since Euclid. The prime-number factors of an integer are the prime numbers whose product is that integer (seefundamental theorem of arithmetic).