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Some sources only list the smallest prime in each cycle, ... All prime numbers from 31 to 6,469,693,189 for free download. Lists of Primes at the Prime Pages.
A prime number is a natural number that has exactly two distinct natural number divisors: the number 1 and itself. To find all the prime numbers less than or equal to a given integer n by Eratosthenes' method: Create a list of consecutive integers from 2 through n: (2, 3, 4, ..., n). Initially, let p equal 2, the smallest prime number.
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 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.
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 .
Rowland (2008) proved that this sequence contains only ones and prime numbers. However, it does not contain all the prime numbers, since the terms gcd(n + 1, a n) are always odd and so never equal to 2. 587 is the smallest prime (other than 2) not appearing in the first 10,000 outcomes that are different from 1. Nevertheless, in the same paper ...
43 is a Heegner number. [4] 43 is the largest prime which divides the order of the Janko group J 4. 43 is a repdigit in base 6 (111). 43 is the largest natural number that is not an (original) McNugget number. [5] 43 is the smallest prime number expressible as the sum of 2, 3, 4, or 5 different primes: 43 = 41 + 2; 43 = 11 + 13 + 19; 43 = 2 ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.