Math Basics

All About Numbers

Is there such a thing as a perfect number?

Yes, there is such a thing as a perfect number, but it is not what we think of as true perfection. To mathematicians, perfect numbers are somewhat rare because they are few and far between. They are defined as a natural number (or positive integer) in which the sum of its positive divisors (or the bottom number in a fraction that divides the number to equal another whole number, and includes 1 but not the number itself) is the number itself. For example, 6 is considered a perfect number because its divisors are 1, 2, and 3—or 1 + 2 + 3 = 6. The next perfect numbers are 28 (1 + 2 + 4 + 7 + 14), 496, 8128, 33550336, 8589869056, 137438691328,2305843008139952128, and so on—with larger and larger perfect numbers being discovered, especially with the help of faster and more memory-packed computers. (For more about perfect numbers, see Mersenne primes, elsewhere in this chapter.)


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