In October 2024, as part of the GIMPS project, Luke Durant broke the record for the largest known prime number.
It is a Mersenne number, equal to 2136 279 841 – 1.
This integer, which we shall denote by M, is incredibly large compared with the numbers we use in everyday life. We shall obviously not ask here how to verify that it really is prime, but instead tackle the simpler question of how many digits are needed to write down such a monster.
Recall that the number of digits in a number N is the smallest value n such that N < 10 *n*. Logarithms are an excellent tool for answering this kind of question.
Logarithms turn multiplication into addition. Here we use natural (or Napierian) logarithms, denoted by ln; the key relation is ln(ab) = ln(a) + ln(b).
