This shouldn't be possible

For what value of x x in the equation

x 3 n \lfloor{x^{3^n}} \rfloor

give primes for all positive integer values of n n ? Give to the nearest thousandth.

Edit: I just realised that this is only possible if Riemann's Hypothesis is true. Pretend that it is. Sorry.


The answer is 1.306.

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1 solution

Sharky Kesa
May 4, 2014

This is a very special type of constant known as Mill's constant. The approximate value of Mill's constant is 1.306 1.306 .

Mind blowing!!!

Arvind Chander - 7 years, 1 month ago

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It has an actual proof, you know. It's awesome.

Sharky Kesa - 7 years, 1 month ago

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Please don't say that the proof is too big for the margins of Brilliant. ;)

Andrei Li - 2 years, 10 months ago

Numberphile did a video about it (of course) here .

Trevor B. - 7 years, 1 month ago

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They had to.

Sharky Kesa - 7 years, 1 month ago

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