## What is a prime perfect number?

We discuss a relative of the perfect numbers for which it is possible to prove that there are. infinitely many examples. Call a natural number n prime-perfect if n and σ(n) share the. same set of distinct prime divisors. For example, all even perfect numbers are prime-perfect.

### What are Mersenne primes used for?

The search for Mersenne primes is an active field in number theory and computer science. It is also one of the major applications for distributed computing, a process in which thousands of computers are linked through the Internet and cooperate in solving a problem.

Is perfect number a prime number?

Equivalently, a perfect number is a number that is half the sum of all of its positive divisors including itself; in symbols, σ1(n) = 2n where σ1 is the sum-of-divisors function. For instance, 28 is perfect as 1 + 2 + 4 + 7 + 14 + 28 = 56 = 2 × 28. —what is now called a Mersenne prime.

Why is 12 the perfect number?

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. Twelve is also the kissing number in three dimensions.

## What is the largest known Mersenne prime?

2^82,589,933 – 1
The Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 2^82,589,933 – 1, having 24,862,048 digits. A computer volunteered by Patrick Laroche from Ocala, Florida, made the find on December 7, 2018.

### Are 2 and 15 coprime numbers?

HCF of 2 and 15 is 1 No they are co primes # two integers a and b are said to be relatively prime, mutually prime, or coprime if the only positive integer that divides both of them is 1.

Which is the perfect number prime or Mersenne?

Perfect Number Table: Prime, p Mersenne Prime, 2 p -1 Perfect Number, 2 p-1 (2 p -1) 2 3 6 3 7 28 5 31 496 7 127 8128

When do you have an even perfect number?

N = 2p-1(2p -1) where p is a prime for which 2p -1 is a Mersenne prime. That is, we have an even Perfect Number of the form N whenever the Mersenne Number 2 p -1 is a prime number.

## Which is the prime number for all primes n?

Many early writers felt that the numbers of the form 2 n -1 were prime for all primes n, but in 1536 Hudalricus Regius showed that 2 11 -1 = 2047 was not prime (it is 23. 89). By 1603 Pietro Cataldi had correctly verified that 2 17 -1 and 2 19 -1 were both prime, but then incorrectly stated 2 n -1 was also prime for 23, 29, 31 and 37.

### Which is the formula for a perfect number?

A Perfect Number “n”, is a positive integer which is equal to the sum of its factors, excluding “n” itself. Euclid, over two thousand years ago, showed that all even perfect numbers can be represented by, N = 2 p-1(2 p -1) where p is a prime for which 2 p -1 is a Mersenne prime.

What is a prime perfect number? We discuss a relative of the perfect numbers for which it is possible to prove that there are. infinitely many examples. Call a natural number n prime-perfect if n and σ(n) share the. same set of distinct prime divisors. For example, all even perfect numbers are prime-perfect. What are…