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

## Description
<section id='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.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler293()</code> should return 2209.
    testString: assert.strictEqual(euler293(), 2209);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler293() {
  // Good luck!
  return true;
}

euler293();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>