
Glossary: Prime Pages: Top 5000: 
GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) Any prime generalized Fermat number F_{b,n} = (with b an integer greater than one) is called a generalized Fermat prime (because they are Fermat primes in the special case b=2). Why is the exponent a power of two? Because if m is an odd divisor of n, then b^{n/m}+1 divides b^{n}+1, so for the latter to be prime, m must be one. Because the exponent is a power of two, it seems reasonable to conjecture that the number of Generalized Fermat primes is finite for every fixed base b.
See Also: Fermats, Mersennes, Cullens Related pages (outside of this work)
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Chris K. Caldwell © 19992019 (all rights reserved)
