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Search. Search. Appearance. ... More details are in the article for the name. n is a natural number (including 0) ... All prime numbers from 31 to 6,469,693,189 for ...
It is either the field of rational numbers or a finite field with a prime number of elements, whence the name. [168] Often a second, additional meaning is intended by using the word prime, namely that any object can be, essentially uniquely, decomposed into its prime components.
The table below lists the largest currently known prime numbers and probable primes (PRPs) as tracked by the PrimePages and by Henri & Renaud Lifchitz's PRP Records. Numbers with more than 2,000,000 digits are shown.
The following table lists the progression of the largest known prime number in ascending order. [3] Here M p = 2 p − 1 is the Mersenne number with exponent p, where p is a prime number. The longest record-holder known was M 19 = 524,287, which was the largest known prime for 144 years. No records are known prior to 1456.
See List of prime numbers for definitions and examples of many classes of primes. Pages in category "Classes of prime numbers" The following 75 pages are in this category, out of 75 total.
The following is a list of all currently known Mersenne primes and perfect numbers, along with their corresponding exponents p. As of 2024, there are 52 known Mersenne primes (and therefore perfect numbers), the largest 18 of which have been discovered by the distributed computing project Great Internet Mersenne Prime Search, or GIMPS. [2]
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All Mersenne primes are of the form M p = 2 p − 1, where p is a prime number itself. The smallest Mersenne prime in this table is 2 1398269 − 1. The first column is the rank of the Mersenne prime in the (ordered) sequence of all Mersenne primes; [33] GIMPS has found all known Mersenne primes beginning with the 35th. #
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