
Glossary: Prime Pages: Top 5000: 
GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) 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 is Euler's constant.
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Chris K. Caldwell © 19992019 (all rights reserved)
