Prime number

In mathematics, a prime number (or prime) is a natural number greater than one whose only positive divisors are one and itself. Or for short: A prime number is a natural number with exactly two natural divisors. A natural number that is greater than one and is not a prime is called a composite number. The numbers zero and one are neither prime nor composite. The property of being a prime is called primality. Prime numbers are of fundamental importance in number theory.

The largest known prime

The largest known prime, as of September 2005, is

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225964951 − 1 (this number is 7,816,230 digits long); it is the 42nd known Mersenne prime. M25964951 was found on February 18, 2005 by Martin Nowak, a member of a collaborative effort known as GIMPS.

Related Topics:
Number - Mersenne prime - February 18 - 2005 - Martin Nowak - GIMPS

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The next largest known prime is 224036583 − 1 (this number is 7,235,733 digits long); it is the 41st known Mersenne prime.

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M24036583 was found on May 15, 2004 by Josh Findley (member of GIMPS) and it was announced in late May 2004.

Related Topics:
May 15 - 2004 - Josh Findley

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The third largest known prime is 220996011 − 1 (this number is 6,320,430 digits long); it is the 40th known Mersenne prime.

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M20996011 was found on November 17, 2003 by Michael Shafer (and GIMPS) and announced in early December 2003.

Related Topics:
November 17 - 2003 - Michael Shafer

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Historically, the largest known prime has almost always been a Mersenne prime since the dawn of electronic computers, because there exists a particularly fast primality test for numbers of this form, the Lucas-Lehmer test for Mersenne primes.

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The largest known prime that is not a Mersenne prime is 27653 × 29167433 + 1 (2,759,677 digits). This is also the fifth largest known prime of any form. It was found by the Seventeen or Bust project and it brings them one step closer to solving the Sierpinski problem.

Related Topics:
Seventeen or Bust - Sierpinski problem

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Some of the largest primes not known to have any particular form (that is, no simple formula such as that of Mersenne primes) have been found by taking a piece of semi-random binary data, converting it to a number n, multiplying it by 256k for some positive integer k, and searching for possible primes within the interval .

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In fact, as a publicity stunt against the Digital Millennium Copyright Act and other WIPO Copyright Treaty implementations, some people have applied this to various forms of DeCSS code, creating the set of illegal prime numbers. Such numbers, when converted to binary and executed as a computer program, perform acts encumbered by applicable law in one or more jurisdictions.

Related Topics:
Publicity stunt - Digital Millennium Copyright Act - WIPO Copyright Treaty - DeCSS - Illegal prime - Computer program

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