- #1
kingtaf
- 8
- 0
Show that if (2^p) -1 is prime then (2^(p-1)) * ((2^p) - 1) is perfect
kingtaf said:Show that if (2^p) -1 is prime then (2^(p-1)) * ((2^p) - 1) is perfect
Glenn L said:The results of these findings are quite remarkable
A perfect number is a positive integer that is equal to the sum of its proper divisors (the divisors excluding the number itself). For example, 6 is a perfect number because its proper divisors are 1, 2, and 3, and 1 + 2 + 3 = 6.
As of 2021, there are 51 known perfect numbers, and it is believed that there are an infinite number of them. The first four perfect numbers are 6, 28, 496, and 8128.
The largest known perfect number is 282,589,933 - 1, which has 24,862,048 digits and was discovered in 2018. It is also known as M82,589,933.
So far, no odd perfect numbers have been discovered. It is not known if any odd perfect numbers exist, but it is believed that if they do, they must be very large and have at least 300 digits.
Perfect numbers have been studied by mathematicians for thousands of years and have been associated with many interesting patterns and properties. They have also been used in number theory and cryptography. However, their significance in practical applications is limited.