47 lines
1.6 KiB
Markdown
47 lines
1.6 KiB
Markdown
---
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id: 5900f4a11000cf542c50ffb3
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title: 'Problem 308: An amazing Prime-generating Automaton'
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challengeType: 5
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forumTopicId: 301962
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dashedName: problem-308-an-amazing-prime-generating-automaton
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---
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# --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 , 7885 , 1951 , 2338 , 2933 , 7729 , 9523 , 7719 , 117 , 1113 , 1311 , 152 , 17 , 551 . Starting with the seed integer 2, successive iterations of the program produce the sequence: 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, ... 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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# --hints--
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`euler308()` should return 1539669807660924.
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```js
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assert.strictEqual(euler308(), 1539669807660924);
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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 euler308() {
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return true;
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}
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euler308();
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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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