Prime Number

This calculator will help check — if the given number is prime. Interactive table of small and large prime numbers.

Definition: A prime number is a natural number (>0), which has no more than two distinct divisors: 1 and the number itself.
Natural numbers, except for 1, that are not prime numbers are called composite.
One is neither a prime number nor composite.
Examples of prime numbers: 3, 5, 7, 11, 17
Let's take, for example, the number 3. 3 is divisible, without a remainder, only by 1 and itself, therefore the number 3 is a prime number.

There are infinitely many prime numbers. The oldest known proof of this fact was given by Euclid in «Elements» (book IX, proposition 20). Its proof can be briefly reproduced as follows:

Suppose that the number of prime numbers is finite. We multiply them and add one. The resulting number is not divisible by any of the finite set of prime numbers because the remainder of the division by any of them gives one. Thus, the number must be divisible by some prime number not included in this set. Contradiction.

Mutually mathematicians proposed other proofs. One of them (presented by Euler) shows that the sum of the reciprocals of the first n prime numbers grows indefinitely with the increase n.