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The largest known prime number is 2 136,279,841 − 1, a number which has 41,024,320 digits when written in the decimal system. It was found on October 12, 2024, on a cloud-based virtual machine volunteered by Luke Durant, a 36-year-old researcher from San Jose, California, to the Great Internet Mersenne Prime Search (GIMPS).
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.
Former Nvidia programmer Luke Durant’s search led to the groundbreaking discovery of the world’s largest known prime number in ... officially called M136279841, consists of an astounding ...
A different computation found that there are 18,435,599,767,349,200,867,866 primes ... Also called primes congruent to d modulo a. ... "New Largest Known Prime Number".
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Mersenne primes and perfect numbers are two deeply interlinked types of natural numbers in number theory. Mersenne primes, named after the friar Marin Mersenne, are prime numbers that can be expressed as 2 p − 1 for some positive integer p. For example, 3 is a Mersenne prime as it is a prime number and is expressible as 2 2 − 1.
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] Mathematics: 2 82,589,932 × (2 82,589,933 − 1) is a 49,724,095-digit perfect number, the largest known as of 2020. [87] Mathematics – History: 10 8×10 16, largest named number in Archimedes' Sand Reckoner.
Euler ascertained that 2 31 − 1 = 2147483647 is a prime number; and this is the greatest at present known to be such, and, consequently, the last of the above perfect numbers [i.e., 2 30 (2 31 − 1)], which depends upon this, is the greatest perfect number known at present, and probably the greatest that ever will be discovered; for as they ...