Fortunate number

Given a positive integer $n$, the $n$th Fortunate number $F_n>1$ is the difference between the primorial

$$\prod _{i=1}^{\pi (n)}{p}_i$$

(where $\pi (x)$ is the prime counting function and $p_i$ is the $i$th prime number) 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 http://www.research.att.com/ 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 $F_n>n$ 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