
Glossary: Prime Pages: Top 5000: 
GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) In 1877 Pepin proved the following theorem for deciding if Fermat numbers are prime (this is one of the nicest examples of the classical primality proving tests):
If F_{n} is prime, this primality can be shown by Pepin's test, but when F_{n} is composite, Pepin's test does not tell us what the factors will be (only that it is composite). For example, Selfridge and Hurwitz showed that F_{14} was composite in 1963, but it was not until 2010 that its first factor was found.
See Also: Fermats, FermatDivisor Related pages (outside of this work) Chris K. Caldwell © 19992019 (all rights reserved)
