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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.
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.
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 following table lists the progression of the largest known prime number in ascending order. [4] 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 first row has been interpreted as the prime numbers between 10 and 20 (i.e., 19, 17, 13, and 11), while a second row appears to add and subtract 1 from 10 and 20 (i.e., 9, 19, 21, and 11); the third row contains amounts that might be halves and doubles, though these are inconsistent. [14]
The fundamental theorem can be derived from Book VII, propositions 30, 31 and 32, and Book IX, proposition 14 of Euclid's Elements.. If two numbers by multiplying one another make some number, and any prime number measure the product, it will also measure one of the original numbers.
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.
It was created in 1979 by Paul Pritchard. [2] Since Pritchard has created a number of other sieve algorithms for finding prime numbers, [3] [4] [5] the sieve of Pritchard is sometimes singled out by being called the wheel sieve (by Pritchard himself [1]) or the dynamic wheel sieve. [6]