Find Prime Numbers

Calculator that finds every prime number within a range of values. A prime number is a positive integer, which is divisible only by 1 and by itself. Prime numbers play an important role in number theory and in cryptography. Although for the latter use, very large prime numbers are needed. Here only numbers up to 10¹⁵ can be calculated. These are numbers less than a quadrillion. Cryptography works with even larger values.

Example: the prime numbers between 180 and 200 are: 181 191 193 197 199

At a very wide span or very large numbers, the calculation might take a while.

A well-known ancient method for finding prime numbers is the Sieve of Eratosthenes. This method of a number sieve is not used here. If you are looking for prime numbers in a limited interval with a lower limit significantly far above 1, then this sieve is not very effective. Here, for each number in the specified interval, it is tested whether it is divisible by integers between 2 and the square root of that number. If such a divisor is found, the algorithm aborts; however, if it runs to the end and finds nothing, the value is output as a prime number. This is the common method for testing a number for the prime number property. For large numbers, a lot of calculations are required, which is why they take so long. This gives cryptography its security. Cryptography is often based on the product of two very large prime numbers, which is, of course, an even larger number. Factoring this number again, i.e. breaking it down into its two prime factors, is not yet possible in a reasonable amount of time, even with the fastest computers.

See also prime factor calculation to divide a number into prime numbers which, when multiplied together, result in that number.