even perfect number

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Offline jas_fluidm

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even perfect number
« on: March 05, 2012, 03:23:41 PM »
Over 2300 years ago Euclid proved that If 2^(k)-1 is a prime number (it would be a Mersenne prime), then 2^(k-1)(2^(k)-1) is a perfect number. A few hundred years ago Euler proved the converse (that every even perfect number has this form).  It is still unknown if there are any odd perfect numbers (but if there are, they are large and have many prime factors).

Offline Masuma Parvin

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Re: even perfect number
« Reply #1 on: March 06, 2012, 04:47:17 PM »
All even perfect numbers are a power of two times a Mersenne prime.

Offline tasnuva

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Re: even perfect number
« Reply #2 on: March 14, 2012, 01:53:45 PM »
Nice post.
Tasnuva Ali
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Department of ETE
Daffodil International university