# What are the first 5 Mersenne prime numbers?

## What are the first 5 Mersenne prime numbers?

, 3, 5, 7, 13, 17, 19, 31, 61, 89, (OEIS A000043). Mersenne primes were first studied because of the remarkable properties that every Mersenne prime corresponds to exactly one perfect number.

## What is the fifth Mersenne prime?

The fifth, M13 = 8191, was discovered anonymously before 1461; the next two (M17 and M19) were found by Pietro Cataldi in 1588. After nearly two centuries, M31 was verified to be prime by Leonhard Euler in 1772.

What are the first 5 positive prime numbers?

For example, the first 5 prime numbers are 2, 3, 5, 7, and 11. By contrast, numbers with more than 2 factors are call composite numbers.

### How do you check if a number is a Mersenne prime?

Mersenne Prime is a prime number that is one less than a power of two. In other words, any prime is Mersenne Prime if it is of the form 2k-1 where k is an integer greater than or equal to 2. First few Mersenne Primes are 3, 7, 31 and 127.

### What is the 5th perfect number?

List of perfect numbers

Rank p Perfect number
5 13 33550336
6 17 8589869056
7 19 137438691328
8 31 2305843008139952128

What are the 6 prime numbers?

List of prime numbers to 100. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

## What are the two prime numbers of Mersenne?

List of Known Mersenne Prime Numbers # 2 p -1 Digits Date Discovered Perfect Number 1 2 2 -1 1 c. 500 BCE 2 1 · (2 2 -1) 2 2 3 -1 1 c. 500 BCE 2 2 · (2 3 -1) 3 2 5 -1 2 c. 275 BCE 2 4 · (2 5 -1) 4 2 7 -1 3 c. 275 BCE 2 6 · (2 7 -1)

## Which is the smallest Mersenne number with prime exponent n?

More generally, numbers of the form M n = 2 n − 1 without the primality requirement may be called Mersenne numbers. Sometimes, however, Mersenne numbers are defined to have the additional requirement that n be prime. The smallest composite Mersenne number with prime exponent n is 2 11 − 1 = 2047 = 23 × 89.

Which is a theorem of the Mersenne prime theorem?

Finally, we offer the following for your perusal: Theorem Four: Let p = 3 (mod 4) be prime. 2 p +1 is also prime if and only if 2 p +1 divides M p. [ Proof ].

### What did Marin Mersenne conjecture about the numbers?

Enter French monk Marin Mersenne (1588-1648). Mersenne stated in the preface to his Cogitata Physica-Mathematica (1644) that the numbers 2 n -1 were prime for and were composite for all other positive integers n < 257. Mersenne’s (incorrect) conjecture fared only slightly better than Regius’, but still got his name attached to these numbers.