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Prime number: Difference between revisions
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A prime is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a [[composite number]]<ref>http://primes.utm.edu/</ref> | A prime is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a [[composite number]]<ref>http://primes.utm.edu/</ref> | ||
<small>Science is so fascinated by prime numbers that special computer programs have been found that are looking for ever bigger prime numbers. It is a so-called Mersenne prime number. A Mersenne prime number is a positive integer that is exactly 1 smaller than a power of two. The prime numbers found today are all Mersenne numbers (to the French monk and mathematician Marin Mersenne). These numbers are in the form: 2 <sup>p</sup>-1, where p is a prime number, and thus odd, for example: 2 <sup>3</sup> - 1 = 7. This method is currently considered the most efficient method for finding new prime numbers. | |||
A simple example of how a prime number can be traced to the source is the following. For example, take the prime number 8191. The origin of this can be found by first adding 1 and checking whether the general rule: 2 <sup>p</sup>-1 applies here. This can be done simply by working with the rules of the logarithms</small> | |||
[[Proth's Theorem]] by François Proth, non Mersene-prime | [[Proth's Theorem]] by François Proth, non Mersene-prime | ||
the largest | the largest is 9,383,761 digits long. | ||
[[Brute-force search]] | [[Brute-force search]] | ||
Latest revision as of 04:07, 25 April 2017
A prime is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number[1]
Science is so fascinated by prime numbers that special computer programs have been found that are looking for ever bigger prime numbers. It is a so-called Mersenne prime number. A Mersenne prime number is a positive integer that is exactly 1 smaller than a power of two. The prime numbers found today are all Mersenne numbers (to the French monk and mathematician Marin Mersenne). These numbers are in the form: 2 p-1, where p is a prime number, and thus odd, for example: 2 3 - 1 = 7. This method is currently considered the most efficient method for finding new prime numbers.
A simple example of how a prime number can be traced to the source is the following. For example, take the prime number 8191. The origin of this can be found by first adding 1 and checking whether the general rule: 2 p-1 applies here. This can be done simply by working with the rules of the logarithms
Proth's Theorem by François Proth, non Mersene-prime
the largest is 9,383,761 digits long.
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