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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.
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.
A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, ... Largest known prime number;
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As of October 2024 the largest known prime number is a Mersenne prime with 41,024,320 decimal digits. [1] [2] There are infinitely many primes, as demonstrated by Euclid around 300 BC. No known simple formula separates prime numbers from composite numbers.
For example, 3 is a Mersenne prime as it is a prime number and is expressible as 2 2 − 1. [1] [2] The numbers p corresponding to Mersenne primes must themselves be prime, although the vast majority of primes p do not lead to Mersenne primes—for example, 2 11 − 1 = 2047 = 23 × 89. [3]
The number 2,147,483,647 remained the largest known prime until 1867. [ 4 ] In computing, this number is the largest value that a signed 32-bit integer field can hold.
Mathematics: 10,223 × 2 31,172,165 + 1 is a 9,383,761-digit Proth prime, the largest known Proth prime [85] and non-Mersenne prime as of 2021. [86] Digit growth in the largest known prime. Mathematics: 2 82,589,933 − 1 is a 24,862,048-digit Mersenne prime; the largest known prime of any kind as of 2020. [86]