Sieve Procedure for the Möbius prime-functions, the Infinitude of Primes and the Prime Number Theorem

Details Sieve Procedure for the Möbius prime-functions, the Infinitude of Primes and the Prime Number Theorem Sieve Procedure for the Möbius prime-functions, the Infinitude of Primes and the Prime Number Theorem

2010-04-08

arxiv.org/abs/1004.1563v2

Mathematics

General Mathematics

16 pages, critically reviewed both proofs of the Prime Number Theorem, added details and new results

Scientific paper

Using a sieve procedure akin to the sieve of Eratosthenes we show how for each prime $p$ to build the corresponding M\"obius prime-function, which in the limit of infinitely large primes becomes identical to the original M\"obius function. Discussing this limit we present two simple proofs of the Prime Number Theorem. In the framework of this approach we give several proofs of the infinitude of primes.

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