## You are here

HomeFortunate number

## Primary tabs

# 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 A005235 in Sloane’s OEIS. Some Fortunate numbers occur more than once, such as 23, which occurs for both the fifth and eighth primorials. Even so, the inequality $F_{n}>n$ always holds. These numbers are named after the anthropologist Reo Fortune, who conjectured on their primality.

## Mathematics Subject Classification

11A41*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections