A perfect number is one whose proper divisors sum to the number itself.
e.g. The number 6 has proper divisors 1, 2 and 3 and 1 + 2 + 3 = 6
28 = 1 + 2 + 4 + 7 + 14
496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 +248
8128 = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 + 1016 + 2032 + 4064
The first significant result on perfect numbers was by Euclid:
If, for some k > 1 , 2k-1 is prime then 2(k-1) (2k-1) is a perfect number
The mathematician was able to show that all even perfect numbers are of this form.
It is not known to this day whether there are any odd perfect numbers.
The largest known prime is 220996011-1 which has 6320430 decimal digits So the Largest Known Perfect number would be
220996010 (220996011-1)
