Szathmáry László honlapja @ DEIK | Nim2 / The largest prime number found so far

On October 21, 2024, it was announced (https://www.mersenne.org) that the largest prime number ever found had been discovered! The number is 2^136,279,841-1, which consists of 41,024,320 digits. The previous largest prime was discovered 6 years earlier and was 16 million digits shorter.

Task

Determine the value of 2^136,279,841-1, and write its digits to a text file (e.g. prime.txt) such that each line is 80 characters wide.

Fun fact

In Programming 1, we learned that the largest value that can be stored in an int variable (4 bytes) is 2_147_483_647, which is approximately 2.1 billion.

This value is also a Mersenne prime! Namely:

2³¹ - 1 = 2,147,483,647

This was proven by the famous Swiss mathematician Leonhard Euler in 1772 (link).

Task: verify that 2,147,483,647 is indeed a Mersenne prime.