If 2^{n}-1 is a prime number, then
2^{(n-1)}(2^{n}-1) is a perfect number

6, 1, 2, 3 28, 1, 2, 14, 4, 7 496, 1, 2, 248, 4, 124, 8, 62, 16, 31 8128, 1, 2, 4064, 4, 2032, 8, 1016, 16, 508, 32, 254, 64, 127 33,550,336 8,589,869,056 Next number has 37 digits! Note that 28 = 1^{3}+ 3^{3}496 = 1^{3}+ 3^{3}+ 5^{3}+ 7^{3}8128 = 1^{3}+ 3^{3}+ 5^{3}+ 7^{3}+ 9^{3}+ 11^{3}+ 13^{3}+ 15^{3}would the next perfect number be equal to this... ???? = 1^{3}+ 3^{3}+ 5^{3}+ 7^{3}+ 9^{3}+ 11^{3}+ 13^{3}+ 15^{3}+ 17^{3}+ 19^{3}+ 21^{3}+ 23^{3}+ 25^{3}+ 27^{3}+ 29^{3}+ 31^{3}And then this number? ???? = 1^{3}+ 3^{3}+ 5^{3}+ 7^{3}+ 9^{3}+ 11^{3}+ 13^{3}+ 15^{3}+ 17^{3}+ 19^{3}+ 21^{3}+ 23^{3}+ 25^{3}+ 27^{3}+ 29^{3}+ 31^{3}+ 33^{3}+ 35^{3}+ 37^{3}+ 39^{3}+ 41^{3}+ 43^{3}+ 45^{3}+ 47^{3}+ 49^{3}+ 51^{3}+ 53^{3}+ 55^{3}+ 57^{3}+ 59^{3}+ 61^{3}+ 63^{3}

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Fun With Math-General Stuff Main Page Units and Prefixes Really Big Number Names Numeric Terms Glossary Proposed New Digits For Base 12, 16, 20 Systems Base Names Formulas: Geometry Number Series Perfect Numbers-definition Perfect Numbers Hexadecimal Math Table 0-10 + 0-10 and 0-10 x 0-10 Hex Decimal Integer Conversion Table How To Compute The Square Root Roman Numerals Binary Math Table Roman Numeral Math Tables What's 13 times 7? Prove That 1 = 2 Number Tricks It's Impossible Pi In Your Face Wind Chill Factor Relative Heat Index Computerized Long Form Math Fractional Tables: Addition Fractional Tables: Multiplication

Related:

Fun With Math Fun With Math-General Stuff Fun With Math-All About The Numbers

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The Del: Dave's Entertainment Library! Celebrities a2z Hit Song Titles Stuff! Calendars Picture Gallery SDN Media News and More

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