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Euclid also showed that if the number 2n - 1 is prime then the number 2n-1(2n - 1) is a perfect number. The mathematician Euler (much later in 1747) was able to show that all even perfect numbers are of this form.
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www-history.mcs.st-and.ac.uk/HistTopics/Prime_numbers.h...
www-history.mcs.st-and.ac.uk/HistTopics/Prime_numbers.html
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What is a perfect number? ... For more information, see Perfect Numbers, from the St. Andrews MacTutor Math History archives; or search the Dr. Math archives for the words perfect number (that exact phrase). The archives provide a List of the First 22 Perfect Numbers.
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mathforum.org/dr.math/faq/faq.perfect.html
mathforum.org/dr.math/faq/faq.perfect.html
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Date: 24 Mar 1995 21:13:05 -0500 From: Dr. Sydney Subject: Re: Perfect Numbers Thanks for writing Dr. Math! Perfect numbers are pretty interesting! It turns out that perfect numbers are involved in several unsolved problems of mathematics.
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mathforum.org/dr.math/problems/perfect.html
mathforum.org/dr.math/problems/perfect.html
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Iannucci, D. E. "The Second Largest Prime Divisor of an Odd Perfect Number Exceeds Ten Thousand." Math. Comput. 68, 1749-1760, 1999. ...
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mathworld.wolfram.com/PerfectNumber.html
mathworld.wolfram.com/PerfectNumber.html
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Perfect numbers were given their name by the ancient Greek mathematiticians, who mixed number theory with mysticism. A perfect number is a number that is equal to the sum of all of its (positive) divisors, excluding itself.
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www.stormloader.com/ajy/perfect.html
www.stormloader.com/ajy/perfect.html
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Math Help Forum > University Math Help > Number theory ... Thank you Aftershock, I made a mistake, the converse of even perfect numbers was accomplished by the great Euler. ... Noone has proved that there are no odd perfect numbers. On the contrary, no one has ever found one.
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www.mathhelpforum.com/math-help/number-theory/6628-proo...
www.mathhelpforum.com/math-help/number-theory/6628-proof-perfect-numbers.html
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Math Help Forum > University Math Help > Number theory ... Math Help Forum is a community of maths forums with an emphasis on maths help in all levels of mathematics. Register to post your math questions or just hang out and try some of our math games or visit the arcade.
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www.mathhelpforum.com/math-help/number-theory/13116-pro...
www.mathhelpforum.com/math-help/number-theory/13116-proof-perfect-numbers.html
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So, for n=1 we have 6, for n=2 we have 28, for n=4 we have 496, for n=6 we have 8128 and we have the next four perfect numbers for n=12, 16, 18, 24. Computers have found perfect numbers for different values of n and I know that they have calculated a number for n=216.090 with ; ... Newsgroups: sci.math...
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groups.google.sc/group/sci.math/browse_thread/thread/f5...
groups.google.sc/group/sci.math/browse_thread/thread/f59634f8c2d3f552
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Perfect Numbers and a Few Theorems ... You may have also noticed that the perfect numbers listed above (6, 28, 496, 8128) all end with either the digit 6 or the digit 8--this is also very easy to prove (but no, they do not continue to alternate 6, 8, 6, 8,...). If you like that digit pattern, look at the first four...
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primes.utm.edu/mersenne/index.html
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