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I had a thought of constructing a infinite decimal out of prime numbers,like the following: $$0.235711131719...$$ Is there a prove that show it's rational or irrational?

John
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John He
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  • I asked this question (I do not remember when) and the answer was that it is irrational. – Peter May 28 '19 at 18:30
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    Dirichtlet's theorem is enough ensuring that every finite digit string (not beginning with a $0$) appears in this number which clearly implies that it cannot be rational. – Peter May 28 '19 at 18:34
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    @Peter Just to complete your answer, given a string of numbers $a_1 a_2\cdots a_n$ we can use Dirichlet theorem to find a prime $a_1 a_2\cdots a_n 1 \bmod (10^{n+1})$. – Julian Mejia May 28 '19 at 18:55
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    It looks transcendental. – herb steinberg May 28 '19 at 19:00

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