2010-06-01, 23:05 | #1 |
"Vincent"
Apr 2010
Over the rainbow
101100011001_{2} Posts |
aliquot and mersenne
is it verified that for the 48 mersenne know prime,
Mx*(M(x-1)+1) end in a cycle of a 1 period? M2*(M1+1) =6 know cycle M3*(M2+1) = 28 M5*(M4+1) = 496 M7*(M6+1) = 8128 ... .... M43112609*(M43112608+1) =?? will be a cycle too? and it seem that they are perfect drivers too Last fiddled with by firejuggler on 2010-06-01 at 23:10 |
2010-06-01, 23:47 | #2 |
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
1000010110101_{2} Posts |
Yes, it's proven.
A number whose aliquot sequence is a cycle with a period of one is just a roundabout way to refer to a perfect number. A link has been proven (quite a long time ago too!) between Mersenne primes and even perfect numbers: If and only if is prime, then is a perfect number. All even perfect numbers are of the form . (Note that , so this is the same as your forms like M7*(M6+1), just using the more common form) And perfect drivers are, by definition, perfect numbers. So yes, is a perfect number, and so it's also a perfect driver, and the aliquot sequence will cycle back to itself immediately. Further reading: http://en.wikipedia.org/wiki/Perfect_number http://en.wikipedia.org/wiki/Mersenne_number http://en.wikipedia.org/wiki/Aliquot_sequence http://mersennewiki.org/index.php/Aliquot_Sequences Last fiddled with by Mini-Geek on 2010-06-01 at 23:52 |
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