Prime Generating?

Number Theory Level 3

( n + 1 ) 3 − n 3 = P ( 4 n ) (n+1)^{3}-n^{3}=P(4n) , where P ( n ) P(n) is a function that outputs the n th n^\text{th} prime number .

Is the above function true?

True True for P ( 4 ( P ( n ) ) P(4(P(n)) False

Akira Kato by Akira Kato , 22, China

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1 solution

Michael Mendrin
Aug 18, 2016

No polynomial function of n n with integer coefficients can ever be a function that generates only prime numbers for any integer n n

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Otherwise, you couldn't sell large prime numbers for like half a million to security companies.

Ron Lauterbach - 3 years, 7 months ago

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hahaha! That cracked me up!

Syed Hamza Khalid - 2 years, 8 months ago

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