Perfect - Compute a perfect number from an input number q
Version 1.00, last revised: 1994-08-13, 0600 hours
Copyright (c) 1981-1994 by author: Harry J. Smith,
19628 Via Monte Dr., Saratoga, CA 95070.  All rights reserved.

Perfect is a MS Windows program to compute a perfect number from q, the
exponent in a Mersenne prime M(q) = 2^q - 1.  When q = 859433 the
517430-digit number is computed and stored on disk in about 5 minutes on
a 33 MHz i486 machine.

A number is called perfect if it is equal to the sum of its divisors.
Six is perfect: 6 = 1 + 2 + 3.
28 is perfect: 28 = 1 + 2 + 4 + 7 + 14.

M(n) = 2^n - 1 is called a Mersenne number.
If M(q) = is prime then it is called a Mersenne prime and q will be prime also.
If q makes a Mersenne prime then P(q) = 2^(q-1) * (2^q - 1) is a Perfect number.

The first few consecutive perfect numbers are -

P( 2) = 2 * 3 = 6
P( 3) = 4 * 7 = 28
P( 5) = 16 * 31 = 496
P( 7) = 64 * 127 = 8128
P(13) = 4096 * 8191 = 33,550,336
P(17) = 65,536 * 131,071 = 8,589,869,056
P(19) = 262,144 * 524,287 = 137,438,691,328
P(31) = 1,073,741,824 * 2,147,483,647 = 2,305,843,008,139,952,128
P(61) = 1,152,921,504,606,846,976 * 2,305,843,009,213,693,951 =
        2,658,455,991,569,831,744,654,692,615,953,842,176

The Perfect homepage is located at:

	http://pw1.netcom.com/~hjsmith/Perfect/PerfWhat.html