# Mertens' theorem

Mertens used Chebyshev's theorem (a weak version of the prime number theorem) to prove that

.

This is now called **Mertens' Theorem**.

Assuming the Riemann hypothesis, Schoenfeld showed that when *x* > 8, we have the following error bound

where γ is Euler's constant.

**Related pages** (outside of this work)

**References:**

- BS96 (p. 210,234)
E. BachandJ. Shallit,Algorithmic number theory, Foundations of Computing Vol, I: Efficient Algorithms, The MIT Press, Cambridge, MA, 1996. pp. xvi+512,MR 97e:11157(Annotation available)

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