prime number

prime number: see number theory.

---

prime number

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 (see fundamental theorem of arithmetic).

---

An integer greater than 1 that is not evenly divisible by any number other than itself, and, of course, 1. Prime numbers are considered a fundamental building block of numbers, especially number theory, a branch of mathematics.

The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Except for 2, all primes are odd numbers. As the numbers get higher, prime numbers tend to be found in pairs that are close together; for example, 29,669 and 29,671 are primes. The largest prime number thus far, which contains more than 65,000 digits, was discovered in 1986.