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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.
So, 6 is a perfect number because the proper divisors of 6 are 1, 2, and 3, and 1 + 2 + 3 = 6. [2] [4] Euclid proved c. 300 BCE that every prime expressed as M p = 2 p − 1 has a corresponding perfect number M p × (M p +1)/2 = 2 p − 1 × (2 p − 1). For example, the Mersenne prime 2 2 − 1 = 3 leads to the corresponding perfect number 2 2 ...
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 ...
There are other prime-related congruences that provide necessary and sufficient conditions on the primality of certain subsequences of the natural numbers. Many of these alternate statements characterizing primality are related to Wilson's theorem , or are restatements of this classical result given in terms of other special variants of ...
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 ).
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A prime number is a natural number that has no natural number divisors other than the number 1 and itself.. To find all the prime numbers less than or equal to a given integer N, a sieve algorithm examines a set of candidates in the range 2, 3, …, N, and eliminates those that are not prime, leaving the primes at the end.
31×2 15145093 – 1 9 February 2025 4,559,129 65 69×2 14977631 – 1 3 December 2021 4,508,719 66 192971×2 14773498 – 1 7 March 2021 4,447,272 67 4×3 9214845 + 1 10 September 2024 4,396,600 68 9145334×3 9145334 + 1 25 December 2023 4,363,441 69 4×5 6181673 – 1 15 July 2022 4,320,805 70 396101×2 14259638 – 1 3 February 2024 4,292,585 71