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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. 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.
The largest known prime gap with identified probable prime gap ends has length 16,045,848, with 385,713-digit probable primes and merit M = 18.067, found by Andreas Höglund in March 2024. The largest known prime gap with identified proven primes as gap ends has length 1,113,106 and merit 25.90, with 18,662-digit primes found by P. Cami, M ...
Megaprime. A megaprime is a prime number with at least one million decimal digits. [1] Other terms for large primes include "titanic prime", coined by Samuel Yates in the 1980s for a prime with at least 1000 digits [2] (of which the smallest is 10 999 +7), [3] and "gigantic prime" for a prime with at least 10,000 digits [4] (of which the ...
The largest known probable Fibonacci prime is F 10317107. It was found by Ryan Propper in July 2024. [2] It was proved by Nick MacKinnon that the only Fibonacci numbers that are also twin primes are 3, 5, and 13.
Mersenne primes (of form 2^ p − 1 where p is a prime) In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century.
Probable prime. In number theory, a probable prime ( PRP) is an integer that satisfies a specific condition that is satisfied by all prime numbers, but which is not satisfied by most composite numbers. Different types of probable primes have different specific conditions. While there may be probable primes that are composite (called ...
As of 2022, the largest known prime of the form p n # + 1 is 392113# + 1 (n = 33,237) with 169,966 digits, found in 2001 by Daniel Heuer. Euclid 's proof of the infinitude of the prime numbers is commonly misinterpreted as defining the primorial primes, in the following manner: [4]