2^(43112609) − 1, the infinitude of primes

2^(43112609) − 1 is currently largest prime number known to mathematicians, totaling over 12,978,189 digits. In 300 BC Euclid, the Greek mathematician, proved that there are infinitely many prime numbers; 2^(43112609) − 1 is thus only special for the moment and accordingly this blog post.

Prime numbers are simple: they are natural numbers divisible by only 1 and themselves.  Prime numbers can’t be broken down into smaller pieces. They are stand-alone, non-communal, sporadic, random, difficult to find and too far in between.  It’s quite melancholic that a number with nearly 13 million digits should be so solitary.  Mathematicians are now searching for a prime number with over a billion digits. They’ll eventually find one. It’s quite revealing. A billion digits and yet only divisible by 1 and yourself.

The infinitude of primes… the inevitably of solitariness. Quite telling.