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

2010/04/08 by R. M. Abrarov, Abrarov, R. M., Sanjar M. Abrarov +1
Mathematics · #11A41 #11N05 #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1004.1563

openalex publication_date 2010/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using a sieve procedure akin to the sieve of Eratosthenes we show how for each prime p to build the corresponding Möbius prime-function, which in the limit of infinitely large primes becomes identical to the original Möbius 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.

Citations

• Formulas for Positive, Negative and Zero Values of the Möbius Function

Related

• Asymptotic sieve for primes
• Infinitely Many Primes Using Generating Functions
• Development of sieve of Eratosthenes and sieve of Sundaram's proof
• Generating Prime Numbers -- A Fast New Method
• An algorithmic implementation of the Pi function based on a new sieve