
Glossary: Prime Pages: Top 5000: 
GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) Though actually not a true class of primes, the primes of the form k^{.}2^{n}+1 with 2^{n} > k are often called the Proth primes. They are named after the self taught farmer François Proth who lived near Verdun, France (18521879). He stated four theorems (or tests) for primality (see [Williams98]). The one we are interested in is the following:
Finally, notice that we do not define any prime of the form k^{.}2^{n}+1 (with no restriction on the relative sizes of n and k) to be a Proth primebecause then every odd prime would be a Proth prime.
Chris K. Caldwell © 19992019 (all rights reserved)
