---
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 ${10}^9$.

# --hints--

`pseudoFortunateNumbers()` should return `2209`.

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

# --seed--

## --seed-contents--

```js
function pseudoFortunateNumbers() {

  return true;
}

pseudoFortunateNumbers();
```

# --solutions--

```js
// solution required
```