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 number theory EPNT : extended prime number theorem tommy1729 Ultimate Fellow Posts: 1,438 Threads: 349 Joined: Feb 2009 08/23/2012, 02:44 PM (This post was last modified: 08/23/2012, 02:47 PM by tommy1729.) Hi 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) ) ] regards tommy1729 « Next Oldest | Next Newest »

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