Prime numbers and factors online calculator (really fast). Give it an integer number, and you got the answers: Is the number prime? If not, what are prime factors? What are results of dividing by prime factors ? What is next/previous prime number ? All of those questions answered here. Used computation method makes this prime number calculator one of the fastest in the web.

Enter number |

Is prime | no, it is NOT prime... | |

Factorization | 2 × 11 | |

Grouped factors | 2 × 11 | |

Lower primes | 19, 17, 13, 11, 7, 5, 3, 2 | |

Higher primes | 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 | |

Processing time (performance) | 0 |

22 11 1 | 2 11 |

- A prime number is a natural number that has exactly two divisors: number one and itself, eg. 2, 3, 5, 7, 11.
- Colloquially, it is often to found vague definition saying that prime number is "number that is divisible only by one and by itself," but it is not compatible with the formal definition used in mathematics. The reason is number one. It is "divisible by one and itself", but has only one divisor.
- Each natural number greater than one can be expresed as factor of prime numbers. Searching for these numbers is called
**factorization**. - One of algorithms searching for all prime numbers belong to given range is
**sieve of Eratosthenes**. Name of algorithm is derived from ancient Greek philosopher - Eratostenes (greek Ἐρατοσθένης Eratosthenes), who is credited with its discovery. Algorithm has computational complexity O((n log n)(log log n)). - The biggest known prime number (data from 2013 year) is 2
_{57 885 161}- 1. This number has 17 425 170 digits in decimal system. It was discovered on 25 January 2013 by Curtis Cooper. - There is internet project GIMPS, which deals with searching for as big as possible prime numbers. Project is created by volunteers and based on distributed computing and open source software.
- Prime numbers are important for
**asymmetric cryptography**. In this case we use fact, that it is very easy to compute multiplication of many prime numbers, but it's very hard to inverse this process (i.e. factorize). This kinds of operations are often called**one directional**. Example of cryptografic algorithm, which is based on prime numbers operations is RSA. - There are at least a few algorithms to check if given number is prime or not. These type of algorithms are called
**primality tests**. Examples are Miller-Rabin or Solovay-Strassen tests.

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