32dbe23f5e
* fix: clean-up Project Euler 301-320 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
55 lines
1.9 KiB
Markdown
55 lines
1.9 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:
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$$\frac{17}{91}, \frac{78}{85}, \frac{19}{51}, \frac{23}{38}, \frac{29}{33}, \frac{77}{29}, \frac{95}{23}, \frac{77}{19}, \frac{1}{17}, \frac{11}{13}, \frac{13}{11}, \frac{15}{2}, \frac{1}{7}, \frac{55}{1}$$
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Starting with the seed integer 2, successive iterations of the program produce the sequence:
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$$15, 825, 725, 1925, 2275, 425, \ldots, 68, \mathbf{4}, 30, \ldots, 136, \mathbf{8}, 60, \ldots, 544, \mathbf{32}, 240, \ldots$$
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The powers of 2 that appear in this sequence are $2^2, 2^3, 2^5, \ldots$.
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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 ${10001}^{\text{st}}$ prime), how many iterations would be needed until the program produces $2^{10001^{\text{st}}\text{ prime}}$?
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# --hints--
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`primeGeneratingAutomation()` should return `1539669807660924`.
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```js
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assert.strictEqual(primeGeneratingAutomation(), 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 primeGeneratingAutomation() {
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return true;
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}
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primeGeneratingAutomation();
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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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