What are the first 7 perfect numbers?

What are the first 7 perfect numbers?

The first few of these, already known to the ancient Greeks, are 6, 28, 496, and 8128. A Perfect Number “n”, is a positive integer which is equal to the sum of its factors, excluding “n” itself….Perfect Number Table:

Prime, p Mersenne Prime, 2p -1 Perfect Number, 2p-1(2p -1)
3 7 28
5 31 496
7 127 8128
13 8191 33550336

What is the formula for perfect numbers?

“Perfect numbers” are equal to the sum of their “proper” divisors (positive integers that divide a number evenly, not counting itself). For example, 6 = 3 + 2 + 1, and 28 = 14 + 7 + 4 + 2 + 1.

Why is 1, 2 the perfect number?

Mathematical properties Twelve is a sublime number, a number that has a perfect number of divisors, and the sum of its divisors is also a perfect number. Since there is a subset of 12’s proper divisors that add up to 12 (all of them but with 4 excluded), 12 is a semiperfect number.

What are the 4 perfect numbers?

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.

What is a perfect number example?

perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128. The discovery of such numbers is lost in prehistory.

Why 12 is a lucky number?

Number 12 represents Dharma and esoteric spiritual knowledge. And it is deemed sacred as well as auspicious. Moreover, this Number has the powers of Surya (Sun – 1) and Chandra (Moon – 2). However, when combined, it mirrors the traits of Number 3, ruled by Jupiter (Guru).

What is a perfect number?

A perfect number is defined as a positive integer which is equal to the sum of its positive divisors, excluding the number itself.

What is the formula for the first 4 perfect numbers?

For example, the first four perfect numbers are generated by the formula 2p−1(2p − 1), with p a prime number, as follows: Prime numbers of the form 2p − 1 are known as Mersenne primes, after the seventeenth-century monk Marin Mersenne, who studied number theory and perfect numbers.

What are some good resources for finding odd perfect numbers?

Weisstein, Eric W. “Perfect Number”. MathWorld. OddPerfect.org A projected distributed computing project to search for odd perfect numbers. Perfect Numbers, math forum at Drexel.

When were perfect numbers first discovered?

It is not known when Perfect Numbers were first discovered, or when they were studied, it is thought that they may even have been known to the Egyptians, and may have even been known before.