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This is a list of articles about prime numbers. 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.
The table below lists the largest currently known prime numbers and probable primes ... 13 June 2023 6,170,560 30 7×2 20267500 + 1 21 July 2022 6,101,127 31
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. The primes up to and including 2 148 + 1 17 {\displaystyle {\tfrac {2^{148}+1}{17}}} are found without a computer, while the primes starting with 180×(M ...
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.
Twenty-three is the ninth prime number, the smallest odd prime that is not a twin prime. [1] It is, however, a cousin prime with 19, and a sexy prime with 17 and 29; while also being the largest member of the first prime sextuplet (7, 11, 13, 17, 19, 23). [2]
The progressions of numbers that are 0, 3, or 6 mod 9 contain at most one prime number (the number 3); the remaining progressions of numbers that are 2, 4, 5, 7, and 8 mod 9 have infinitely many prime numbers, with similar numbers of primes in each progression.
As of 2023, the only known Fermat primes are F 0 = 3, F 1 = 5, ... then every generalized Fermat number will be divisible by 2. The smallest prime number () ...
A balanced prime is by definition the second prime in a CPAP-3. As of 2023 ... primes above and below. Algebraically, the th prime number is a balanced ...