2006-11-02 08:40:41 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
A "perfect number" is a number whose factors add up to itself.
6 = 1 + 2 + 3
28 = 1 + 2 + 4 + 7 + 14
The next two are 496 and 8128.
Euclid discovered that the first four perfect numbers are generated by the formula (2^(n−1)) * (2^n − 1):
for n = 2: (2^1)(2^2 − 1) = 6
for n = 3: (2^2)(2^3 − 1) = 28
for n = 5: (2^4)(2^5 − 1) = 496
for n = 7: (2^6)(2^7 − 1) = 8128
Noticing that 2^n − 1 is a prime number in each instance, Euclid proved that the formula (2^(n−1))*(2^n − 1) gives an even perfect number whenever 2^n − 1 is prime.
Two millennia after Euclid, Euler proved that the formula (2^(n−1))*(2^n − 1) will yield all the even perfect numbers.
It is unknown whether there are any odd perfect numbers, and it has been theorized that none exist.
2006-11-02 08:48:59 · answer #1 · answered by PM 3 · 1⤊ 0⤋
A perfect number is one whose factors (not including the number itself) add up to the number. The first two are 6 and 28:
6 = 1 + 2 + 3
28 = 1 + 2 + 4 + 7 + 14
The next two are 496 and 8128 (where my sn number comes from!)
Much is known and much is unknown about perfect numbers, and they are very interesting. I encourage you to check out the site below.
2006-11-02 08:44:03 · answer #2 · answered by topher8128 2 · 1⤊ 0⤋
A perfect number is a number that can be divided by a number and get that number ex 25=5 x 5, so 25 is a perfect number
2006-11-02 08:49:04 · answer #3 · answered by Jessica B 3 · 0⤊ 1⤋
A number whose factors (other than itself, of course) add up to the number.
Example : 28, since 1+2+4+7+14 = 28.
Here's a nice, detailed article on the history of perfect numbers : http://www-gap.dcs.st-and.ac.uk/~history...
And here's an entry from the largest math encyclopedia evar : http://mathworld.wolfram.com/perfectnumb...
P.S. One of the great mysteries in math is whether there exists an odd perfect number. Figure it out, and you'll be famous forever :)
2006-11-02 08:49:46 · answer #4 · answered by Brite Tiger 6 · 0⤊ 0⤋
the question is too vague
the numbers: 2,3, 7, and 13 are the perfect numbers in my book.
2006-11-02 08:43:36 · answer #5 · answered by neff8684 5 · 0⤊ 0⤋
on a digital clock, 11:11 is as good as it gets. Only time all day all 4 numbers are the same, and they are parallel
2006-11-02 08:43:27 · answer #6 · answered by Jim G 7 · 0⤊ 0⤋
There is no such thing as a perfect number
2006-11-02 08:42:21 · answer #7 · answered by rach_b_2003 1 · 0⤊ 0⤋
21 you can do whatever you want!
2006-11-02 08:42:20 · answer #8 · answered by Hockey rocks! 1 · 0⤊ 0⤋