find two peefect numbers between 1 and 100
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Answer:
A perfect number is defined to be one which is equal to the sum of its aliquot parts. The four perfect numbers 6, 28, 496 and 8128 seem to have been known from ancient times and there is no record of these discoveries.
A Perfect Number N is defined as any positive integer where the sum of its divisors minus the number itself equals the number. The first few of these, already known to the ancient Greeks, are 6, 28, 496, and 8128.
Euclid, over two thousand years ago, showed that all even perfect numbers can be represented by,
N=2p-1(2p -1) where p is a prime for which 2p -1 is a prime number.
That is, we have an even Perfect Number of the form N whenever the Mersenne Number 2p -1 is a prime. Undoubtedly Mersenne was familiar with Euclid’s book in coming up with his primes.
The following gives a table of the first nine Mersenne Primes and Perfect Numbers
Perfect Number, 2p-1(2p -1)
6 and 28
hope you understand