New Largest Prime Found.

[imhotep]

BLOWING ROCK, NC, October 21, 2024 -- The Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 2^136,279,841 - 1, having 41,024,320 decimal digits. Luke Durant, from San Jose, California, found the prime on October 12th.

Luke is currently GIMPS' most prolific contributor. He is joined by thousands of volunteers using free GIMPS software available at www.mersenne.org/download/.

The new prime number, also known as M136279841, is calculated by multiplying together 136,279,841 twos, and then subtracting 1. It is over 16 million digits larger than the previous record prime number, in a special class of extremely rare prime numbers known as Mersenne primes. It is only the 52nd known Mersenne prime ever discovered, each increasingly more difficult to find. Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. GIMPS, founded in 1996, has discovered the last 18 Mersenne primes. Volunteers download a free program to search for these primes, with a $3000 award offered to anyone lucky enough to find a new prime. Prof. Chris Caldwell founded an authoritative web site on the largest known primes which is now maintained by volunteers, and has an excellent history of Mersenne primes.

Further info: https://www.mersenne.org/primes/?press=M136279841

 

[Solo Rider]

#numbers

 

[B.Chat]

ප්‍රථමක සංඛ්‍යා bump

 

[Stimulus mind]

TFS සහෝ.

 

[Voldemort Bro]

munta tiyana prashna deyyane

---

 

[Ozone4]

What is the purpose of finding the largest prime number? Any idea?

 

[imhotep]

What is the purpose of finding the largest prime number? Any idea?

Mersenne primes are of the form 2^n - 1 where n is a prime. They are interesting to Mathematicians as they are in direct correspondence to Perfect numbers.
The Euclid–Euler theorem relates Perfect numbers to Mersenne primes. It states that an even number is perfect if and only if it has the form 2^n−1(2^n − 1), where 2^n − 1 is a prime number. The theorem is named after mathematicians Euclid and Leonhard Euler, who respectively proved the "if" and "only if" aspects of the theorem.

Generally Primes are useful in cryptography. For eg RSA is based on two primes - but note that these are not very large Mersenne primes.
Generalized Mersenne Prime Numbers are used in Elliptical Curve Cryptography and Random Number Generation. I don't know of any use in finding large Mersenne Primes other than for interest and Mathematical research.

PS: Perfect Numbers

A perfect number is defined as a positive integer which is equal to the sum of its positive divisors, excluding the number itself. The smallest perfect number is 6, which is the sum of 1, 2, and 3.
he first 5 perfect numbers are 6, 28, 496, 8128, and 33550336.

 

[Reincarnator]

TFS

 

[Miami-Vice]

 

[Manash]

ok

 

[NRTG]

TFS

 

[priyade]

BLOWING ROCK, NC, October 21, 2024 -- The Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 2^136,279,841 - 1, having 41,024,320 decimal digits. Luke Durant, from San Jose, California, found the prime on October 12th.

Luke is currently GIMPS' most prolific contributor. He is joined by thousands of volunteers using free GIMPS software available at www.mersenne.org/download/.

The new prime number, also known as M136279841, is calculated by multiplying together 136,279,841 twos, and then subtracting 1. It is over 16 million digits larger than the previous record prime number, in a special class of extremely rare prime numbers known as Mersenne primes. It is only the 52nd known Mersenne prime ever discovered, each increasingly more difficult to find. Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. GIMPS, founded in 1996, has discovered the last 18 Mersenne primes. Volunteers download a free program to search for these primes, with a $3000 award offered to anyone lucky enough to find a new prime. Prof. Chris Caldwell founded an authoritative web site on the largest known primes which is now maintained by volunteers, and has an excellent history of Mersenne primes.

Further info: https://www.mersenne.org/primes/?press=M136279841

TFS