Fortunate number

Given a positive integer n, the nth Fortunate number Fn>1 is the difference between the primorial


(where π(x) is the prime counting function and pi is the ith prime numberMathworldPlanetmath) and the nearest prime number above (ignoring the primorial prime that may be there). For example, the 3rd Fortunate number is 7, since the third primorial is 30 since the next highest prime is 37 (the primorial prime 31 is ignored).

The first few Fortunate numbers are 3, 5, 7, 13, 23, 17, 19, 23, 37, 61, 67, 61, 71, 47, 107, 59, 61, 109, 89, 103, 79, 151, etc. listed in njas/sequences/A005235A005235 in Sloane’s OEIS. Some Fortunate numbers occur more than once, such as 23, which occurs for both the fifth and eighth primorials. so, the inequality Fn>n always holds. These numbers are named after the anthropologist Reo Fortune, who conjectured on their primality.

Title Fortunate number
Canonical name FortunateNumber
Date of creation 2013-03-22 17:31:10
Last modified on 2013-03-22 17:31:10
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 5
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A41