What is the highest prime factor?

Answer 1

As of 2013, the largest known Prime number is 257,885,161 − 1. It is 17,425,170 digits long.

There is no largest prime, there is only the largest number that has been shown to be prime. There has been a mathematical proof that no number can be the largest prime since the time of Euclid.

No matter how large a prime number is discovered, a larger one exists. The problem is that the larger the primes get, the rarer they get. Just picking a number at random with 20 million digits will almost certainly produce a nonprime number. That is why there are various formulas to give good guesses for prime numbers.

The formula for Mersenne numbers Mn=2n − 1. Not all Mersenne numbes are prime, but they have been shown to be good guesses.

257,885,161 − 1 is the 48th Mersenne prime discovered.

A Mersenne prime is named after the French monk Marin Mersenne who studied prime numbers in the 17th century.This Mersenne prime and the previous 9 record primes were discovered by the "Great internet Mersenne Prime Search" (GIMPS), a distributed computing project on the Internet operated just for the purpose of finding Mersenne prime.

Answer 2

As of February 2013, the largest known prime number is 2^57,885,161 − 1, a number with 17,425,170 digits.

Answer 3

As of October 2015, the largest known prime number is 2^57,885,161 − 1, a number with 17,425,170 digits.