##  [Mertens' Theorem](/mertens-theorem) 

  ##  [Mertens' Theorem](https://mathlogic.quantumdictionary.io/mertens-theorem-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A collection of classical asymptotic results describing the average growth of certain multiplicative summatory functions: notably the product identity product_{p ≤ x}(1 - 1/p) ~ e^{-γ}/log x and related logarithmic sum asymptotics for reciprocals of primes; historically associated conjectures about the Möbius summatory function must be distinguished from these proven statements.