79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
94 lines
1.8 KiB
Markdown
94 lines
1.8 KiB
Markdown
---
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id: 5900f4a11000cf542c50ffb3
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challengeType: 5
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title: 'Problem 308: An amazing Prime-generating Automaton'
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---
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## Description
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<section id='description'>
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A program written in the programming language Fractran consists of a list of fractions.
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The internal state of the Fractran Virtual Machine is a positive integer, which is initially set to a seed value. Each iteration of a Fractran program multiplies the state integer by the first fraction in the list which will leave it an integer.
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For example, one of the Fractran programs that John Horton Conway wrote for prime-generation consists of the following 14 fractions:1791
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,
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7885
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,
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1951
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,
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2338
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,
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2933
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,
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7729
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,
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9523
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,
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7719
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,
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117
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,
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1113
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,
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1311
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,
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152
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,
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17
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,
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551
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.
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Starting with the seed integer 2, successive iterations of the program produce the sequence:
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15, 825, 725, 1925, 2275, 425, ..., 68, 4, 30, ..., 136, 8, 60, ..., 544, 32, 240, ...
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The powers of 2 that appear in this sequence are 22, 23, 25, ...
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It can be shown that all the powers of 2 in this sequence have prime exponents and that all the primes appear as exponents of powers of 2, in proper order!
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If someone uses the above Fractran program to solve Project Euler Problem 7 (find the 10001st prime), how many iterations would be needed until the program produces 210001st prime ?
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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>euler308()</code> should return 1539669807660924.
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testString: assert.strictEqual(euler308(), 1539669807660924, '<code>euler308()</code> should return 1539669807660924.');
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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 euler308() {
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// Good luck!
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return true;
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}
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euler308();
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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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