84 lines
1.6 KiB
Markdown
84 lines
1.6 KiB
Markdown
---
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id: 5900f4301000cf542c50ff42
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challengeType: 5
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title: 'Problem 196: Prime triplets'
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forumTopicId: 301834
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---
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## Description
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<section id='description'>
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Build a triangle from all positive integers in the following way:
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1
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2 3
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4 5 6
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7 8 9 1011 12 13 14 15
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16 17 18 19 20 21
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22 23 24 25 26 27 2829 30 31 32 33 34 35 3637 38 39 40 41 42 43 44 45
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46 47 48 49 50 51 52 53 54 55
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56 57 58 59 60 61 62 63 64 65 66
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. . .
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Each positive integer has up to eight neighbours in the triangle.
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A set of three primes is called a prime triplet if one of the three primes has the other two as neighbours in the triangle.
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For example, in the second row, the prime numbers 2 and 3 are elements of some prime triplet.
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If row 8 is considered, it contains two primes which are elements of some prime triplet, i.e. 29 and 31.
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If row 9 is considered, it contains only one prime which is an element of some prime triplet: 37.
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Define S(n) as the sum of the primes in row n which are elements of any prime triplet.
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Then S(8)=60 and S(9)=37.
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You are given that S(10000)=950007619.
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Find S(5678027) + S(7208785).
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler196()</code> should return 322303240771079940.
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testString: assert.strictEqual(euler196(), 322303240771079940);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler196() {
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// Good luck!
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return true;
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}
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euler196();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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