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. We are now in our 56th year, we are closing in on 350,000 sequences,Īnd we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”). To support ongoing development and maintenance of the OEIS. Year-end appeal: Please make a donation to the OEIS Foundation