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All prime numbers from 31 to 6,469,693,189 for free download. Lists of Primes at the Prime Pages. The Nth Prime Page Nth prime through n=10^12, pi(x) through x=3*10^13, Random primes in same range. Interface to a list of the first 98 million primes (primes less than 2,000,000,000) Weisstein, Eric W. "Prime Number Sequences". MathWorld.
This is due to the Euclid–Euler theorem, partially proved by Euclid and completed by Leonhard Euler: even numbers are perfect if and only if they can be expressed in the form 2 p−1 × (2 p − 1), where 2 p − 1 is a Mersenne prime. In other words, all numbers that fit that expression are perfect, while all even perfect numbers fit that form.
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.
See List of prime numbers for definitions and examples of many classes of primes. Pages in category "Classes of prime numbers" The following 75 pages are in this category, out of 75 total.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
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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.
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