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The 5000 largest known primes at The PrimePages The 10,000 largest known probable primes at primenumbers.net PrimeGrid’s 321 Prime Search , about the discovery of 3×2 6090515 −1
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 , there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes .
PrimePages. 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.
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 following is a list of all currently known Mersenne primes and perfect numbers, along with their corresponding exponents p. As of 2023, there are 51 known Mersenne primes (and therefore perfect numbers), the largest 17 of which have been discovered by the distributed computing project Great Internet Mersenne Prime Search, or GIMPS. [2]
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 smallest is 10 9999 +33603).
Ulam spiral of size 201×201. Black dots represent prime numbers. Diagonal, vertical, and horizontal lines with a high density of prime numbers are clearly visible. For comparison, a spiral with random odd numbers colored black (at the same density of primes in a 200x200 spiral). The Ulam spiral or prime spiral is a graphical depiction of the ...
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a ...