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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.
Ω(n), the prime omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities). A prime number has Ω(n) = 1. The first: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (sequence A000040 in the OEIS). There are many special types of prime numbers. A composite number has Ω(n) > 1.
The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m , for which n / m is again an integer (which is necessarily also a divisor of n ). For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21).
Therefore, every prime number other than 2 is an odd number, and is called an odd prime. [10] Similarly, when written in the usual decimal system, all prime numbers larger than 5 end in 1, 3, 7, or 9. The numbers that end with other digits are all composite: decimal numbers that end in 0, 2, 4, 6, or 8 are even, and decimal numbers that end in ...
For example, 3 is a Mersenne prime as it is a prime number and is expressible as 2 2 − 1. [1] [2] The exponents p corresponding to Mersenne primes must themselves be prime, although the vast majority of primes p do not lead to Mersenne primes—for example, 2 11 − 1 = 2047 = 23 × 89. [3]
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.
1566 = number k such that k 64 + 1 is prime; 1567 = number of partitions of 24 with at least one distinct part [200] 1568 = Achilles number [343] 1569 = 2 × 28 2 + 1 = number of different 2 × 2 determinants with integer entries from 0 to 28 [199] 1570 = 2 × 28 2 + 2 = number of points on surface of tetrahedron with edgelength 28 [141] 1571 ...
8435×2 6786180 – 1 7 January 2021 2,042,848 316 51×2 6753404 + 1 26 May 2020 2,032,979 317 93×2 6750726 + 1 18 September 2023 2,032,173 318 69×2 6745775 + 1 21 March 2023 2,030,683 319 9995×2 6711008 – 1 31 December 2020 2,020,219 320 50454356 262144 + 1 1 March 2025 2,019,269 321 50449664 262144 + 1 1 March 2025 2,019,259 322 50366208 ...