
Glossary: Prime Pages: Top 5000: 
GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) Recall that a perfect number is an integer that is the sum of its aliquot divisors, that is, all of its positive divisors except itself. Another way to say this is: n is perfect if the sum of all of its positive divisors, denoted sigma(n), is twice n. Any positive integer n which divides the sum of its positive divisors is called multiply perfect or kperfect where k is the index sigma(n)/n. For example, here are the smallest multiply perfect numbers for their index:
Fermat (not Carmichael) was the first to find a 6perfect number (in 1643): 34111227434420791224041472000.You might want to try your hand at proving the following theorems:
See Also: SigmaFunction, PerfectNumber Related pages (outside of this work)
Chris K. Caldwell © 19992020 (all rights reserved)
