---
id: 5900f4931000cf542c50ffa4
title: 'Problem 293: Pseudo-Fortunate Numbers'
challengeType: 5
forumTopicId: 301945
dashedName: 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.

# --hints--

`euler293()` should return 2209.

```js
assert.strictEqual(euler293(), 2209);
```

# --seed--

## --seed-contents--

```js
function euler293() {

  return true;
}

euler293();
```

# --solutions--

```js
// solution required
```