47 lines
1.1 KiB
Markdown
47 lines
1.1 KiB
Markdown
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---
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id: 5900f4931000cf542c50ffa4
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title: 'Problem 293: Pseudo-Fortunate Numbers'
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challengeType: 5
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forumTopicId: 301945
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dashedName: problem-293-pseudo-fortunate-numbers
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---
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# --description--
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An even positive integer N will be called admissible, if it is a power of 2 or its distinct prime factors are consecutive primes.
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The first twelve admissible numbers are 2,4,6,8,12,16,18,24,30,32,36,48.
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If N is admissible, the smallest integer M > 1 such that N+M is prime, will be called the pseudo-Fortunate number for N.
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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.
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Find the sum of all distinct pseudo-Fortunate numbers for admissible numbers N less than 109.
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# --hints--
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`euler293()` should return 2209.
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```js
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assert.strictEqual(euler293(), 2209);
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```
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# --seed--
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## --seed-contents--
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```js
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function euler293() {
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return true;
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}
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euler293();
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```
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# --solutions--
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```js
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// solution required
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```
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