
Perfect - Compute a Perfect Number from q                    13 Aug 1994


      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.

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