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All prime numbers from 31 to 6,469,693,189 for free download. Lists of Primes at the Prime Pages. The Nth Prime Page Nth prime through n=10^12, pi(x) through x=3*10^13, Random primes in same range. Interface to a list of the first 98 million primes (primes less than 2,000,000,000) Weisstein, Eric W. "Prime Number Sequences". MathWorld.
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.
Many 19th century mathematicians still considered 1 to be prime, [42] and Derrick Norman Lehmer included 1 in his list of primes less than ten million published in 1914. [43] Lists of primes that included 1 continued to be published as recently as 1956.
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.
As of October 2024, the seven largest known primes are Mersenne primes. [2] The last eighteen record primes were Mersenne primes. [3] [4] The binary representation of any Mersenne prime is composed of all ones, since the binary form of 2 k − 1 is simply k ones. [5] Finding larger prime numbers is sometimes presented as a means to stronger ...
The following is a list of all currently known Mersenne primes and perfect numbers, along with their corresponding exponents p. As of 2024 [update] , 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 ...
Consider any finite list of prime numbers p 1, p 2, ..., p n. It will be shown that there exists at least one additional prime number not included in this list. Let P be the product of all the prime numbers in the list: P = p 1 p 2...p n. Let q = P + 1. Then q is either prime or not:
The PrimePages is a website about prime numbers originally created by Chris Caldwell at the University of Tennessee at Martin [2] who maintained it from 1994 to 2023. The site maintains the list of the "5,000 largest known primes", selected smaller primes of special forms, and many "top twenty" lists for primes of various forms.