Fortune's conjecture, named for Reo Fortune, states that no Fortunate number is composite. A Fortunate number is defined, for a given positive integer n, as the smallest integer m greater than 1 such that the sum of the primorial of the first n primes and m is itself prime. As of 2017 every known Fortunate number was prime, verified up to n equal to 3000, but the conjecture that this holds for every Fortunate number remains unproven.
Facts
StatementFor a positive integer n, a Fortunate number is defined as the smallest integer m greater than 1 such that the sum of the primorial of the first n primes and m is prime. Fortune's conjecture states that no Fortunate number is composite, meaning every Fortunate number is itself prime. 1 Progress Toward ResolutionAs of 2017 the conjecture had been verified computationally with every known Fortunate number found to be prime, checked up to n equal to 3000, but no general proof exists. 1 Classification
Resolution Status Prize Status
Prize Status (category) Connections
In Branch
Source Fortunate number (Wikipedia)
Sources
1. Fortune's Conjecture (Wikipedia)
Lead section, definition
Fortune conjectured that no Fortunate number is composite.
Lead section, verification status
all known Fortunate numbers are prime, checked up to n = 3000
- Lead section
View the SourceFortunate number (Wikipedia)
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