Mathworld Headline News, Primality Testing is Easy Yan, Pseudo Random test of prime numbers, arXiv:math/0603450, 2006. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, vol. Saxena, Resonance 11-2002, A polynomial time algorithm to test if a number is prime or notĮ. Jones, Daihachiro Sato, Hideo Wada and Douglas Wiens, Diophantine representation of the set of prime numbers, The American Mathematical Monthly 83, no. ICON Project, List of first 50000 primes grouped within ten columns Hartmann, Prime number proofs (in German) Granville, It is easy to determine whether a given integer is prime Golomb, A Direct Interpretation of Gandhi's Formula, Mathematics Magazine, Vol. Yildirim, Small gaps between primes and almost primes, arXiv:math/0506067, 2005. Gast, PRIMES is in P: Manindra Agrawal, Neeraj Kayal and Nitin Saxena (in French)ĭ. Garrett, Big Primes, Factoring Big Integers Gallot, The Chronology of Prime Number Records Furstenberg, On the Infinitude of Primes, The American Mathematical Monthly, Vol. Ford, Expositions of the PRIMES is in P theorem. Salvy, On the non-holonomic character of logarithms, powers and the n-th prime function, arXiv:math/0501379, 2005. Euler, Observations on a theorem of Fermat and others on looking at prime numbers, arXiv:math/0501118, 2005-2008. Elk, Prime Number Assignment to a Hexagonal Tessellation of a Plane That Generates Canonical Names for Peri-Condensed Polybenzenes, J. Elie, L'algorithme AKS ou Les nombres premiers sont de classe P Jean-Christophe Hervé, Jun 01 2014Ĭonjecture: Numbers having prime factors =2, Mathematics of Computation 68: (1999), 411-415. Russ Cox, Apr 20 2006Įvery prime p > 3 is a linear combination of previous primes prime(n) with nonzero coefficients c(n) and |c(n)| 1 such that b = p-1 is the only base >= 1 for which the base-b alternate digital sum is 0.Įquivalently: Numbers p > 1 such that the base-b alternate digital sum is 0 for all bases 1 1 is a prime if and only if it is not the sum of positive integers in arithmetic progression with common difference 2.
Second sequence ever computed by electronic computer, on EDSAC, (see Renwick link). a( A000720(n)) = n if (and only if) n is prime. Prime(n) and pi(n) are inverse functions: A000720(a(n)) = n and a(n) is the least number m such that a( A000720(m)) = a(n). This shows that there exist infinitely many prime numbers." - Pieter Moree, Oct 14 2004ġ is not a prime, for if the primes included 1, then the factorization of a natural number n into a product of primes would not be unique, since n = n*1. The paper by Kaoru Motose starts as follows: "Let q be a prime divisor of a Mersenne number 2^p-1 where p is prime. For contributions concerning "almost primes" see A002808.Ī number p is prime if (and only if) it is greater than 1 and has no positive divisors except 1 and p.Ī natural number is prime if and only if it has exactly two (positive) divisors.Ī prime has exactly one proper positive divisor, 1. For all information concerning prime powers, see A000961. 51 is aĬomposite number and can be factored by any of the following numbers: 1, 3, 17, 51.įor a list of the first 1000 prime numbers see our See Is 51 a prime number? No, 51 is NOT a prime number because it has more than two factors. Prime number because it only has two factors, 1 and 17.
Prime number because it only has two factors, 1 and 2. In other words, a prime number only has two factors, 1 and itself. What is a Prime Number?Ī prime number is any integer, or whole number, greater than 1 that is only divisible by 1 and itself. Test for a prime number for any integer, or whole number, less than 10,000,000,000,000 (less than 10 trillion or a maximum of 13 digits).
Factorization or decomposition of composite numbers can be done on the If it is composite the calculator will also find all of the factors of the composite number. This prime number calculator will find if a number is prime or composite.