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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. [citation needed]
Largest known primes [ edit ] These numbers have been proved prime by computer with a primality test for their form, for example the Lucas–Lehmer primality test for Mersenne numbers . “!” is the factorial , “#” is the primorial , and Φ 3 ( x ) {\displaystyle \Phi _{3}(x)} is the third cyclotomic polynomial , defined as x 2 + x + 1 ...
As of 2024, there are 52 known Mersenne primes. The 13th, 14th, and 52nd have respectively 157, 183, and 41,024,320 digits. This includes the largest known prime 2 136,279,841-1, which is the 52nd Mersenne prime.
He devoted nearly one year and invested a considerable sum of his own money to uncover the world’s largest known prime number. If you need a refresher, a prime number is a whole number that can ...
It thus improved upon the previous record-holding prime, 6,700,417, also discovered by Euler, forty years earlier. 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.
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The largest known prime number, 2 136,279,841 − 1, is a Mersenne prime. [ 1 ] [ 2 ] Since 1997, all newly found Mersenne primes have been discovered by the Great Internet Mersenne Prime Search , a distributed computing project.
As of October 2024, the project has found a total of eighteen Mersenne primes, sixteen of which were the largest known prime number at their respective times of discovery. The largest known prime as of October 2024 is 2 136,279,841 − 1 (or M 136,279,841 for short) and was discovered on October 12, 2024, by Luke Durant.