PERFECT NUMBERS

The Greeks called the number 6 the first "perfect number." A perfect number is one where all the divisors (except the number itself) add up to the number, e.g. the divisors of six are 1, 2, and 3, and 1 + 2 + 3 = 6. Following are the first dozen perfect numbers; number twelve has 77 digits; these are historically important because in the more than 2,000 years that elapsed between the time the Greeks made their determination and 1952, when computers were first used for this purpose, mathematicians discovered a total of only twelve perfect numbers; we now know thirty-seven (the highest having 1,819,050 digits):


6.

28.

496.

8128.

33550336.

8589869056.

137438691328.

2305843008139952128.

2658455991569831744654692615953842176.

191561942608236107294793378084303638130997321548169216

13164036458569648337239753460458722910223472318386943117783728128.

14474011154664524427946373126085988481573677491474835889066354349131199152128.

More on Perfect Numbers
The Mersenne Prime Race
. . . . .as ref'd by Martin Fouts in news:misc.writing

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