What Connection Do Mersenne Primes Have to Perfect Numbers?

💡 The Answer

• Euclid discovered that if 2^p−1 is prime, then 2^(p−1)(2^p−1) is a perfect number.
• A perfect number equals the sum of its proper divisors, like 6=1+2+3.
• Euler later proved that every even perfect number corresponds to a Mersenne prime.
• This link ties together two ancient areas of number theory.