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Full Version: number theory EPNT : extended prime number theorem
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For those intrested in number theory and/or power sums the following seems to be true and new ??

tommy's extended prime number theorem ( EPNT )

let n and k be positive integers with n - 50 > k^2 > 0 and n sufficiently large then for the odd primes we have when p is the biggest odd prime =< n

3^k + 5^k + 7^k + 11^k + ... + p^k
~ [n^(k+1)] / [(k+1) ( ln(n) - ln(k) ) ]