---
id: 5900f4931000cf542c50ffa4
challengeType: 5
title: 'Problem 293: Pseudo-Fortunate Numbers'
---
## Description
An even positive integer N will be called admissible, if it is a power of 2 or its distinct prime factors are consecutive primes.
The first twelve admissible numbers are 2,4,6,8,12,16,18,24,30,32,36,48.
If N is admissible, the smallest integer M > 1 such that N+M is prime, will be called the pseudo-Fortunate number for N.
For example, N=630 is admissible since it is even and its distinct prime factors are the consecutive primes 2,3,5 and 7.
The next prime number after 631 is 641; hence, the pseudo-Fortunate number for 630 is M=11.
It can also be seen that the pseudo-Fortunate number for 16 is 3.
Find the sum of all distinct pseudo-Fortunate numbers for admissible numbers N less than 109.
## Instructions
## Tests
```yml
tests:
- text: euler293() should return 2209.
testString: assert.strictEqual(euler293(), 2209, 'euler293() should return 2209.');
```
## Challenge Seed
```js
function euler293() {
// Good luck!
return true;
}
euler293();
```