And you thought I was all about dick jokes...

The largest known prime number (as of August 2019) is 282,589,933 − 1, a number which has 24,862,048 digits when written in base 10. It was found by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018.

I want to discuss another facet of Prime Numbers Porn called Mersenne Primes, named after:

a 17th-century French friar who studied the numbers that bear his name. Mersenne numbers are 1 less than a power of 2. Mersenne primes, logically enough, are Mersenne numbers that are also prime. The number 3 is a Mersenne prime because it’s one less than 22, which is 4. The next few Mersenne primes are 7, 31, and 127.

M74207281 is the 49th known Mersenne prime. The next largest known prime, 257,885,161-1, is also a Mersenne prime. So is the one after that. And the next one. And the next one. All in all, the 11 largest known primes are Mersenne.


That last paragraph is now outdated by the discovery of two larger primes:

Although primes are infinite, they become rarer as you go up the number line.

We don’t know the exact answer, but the prime number theorem gets us close enough. It makes sense that primes get less common as we stroll out on the number line. Fully 40 percent of one-digit numbers are prime, 22 percent of two-digit numbers are prime, and only 16 percent of three-digit numbers are. The prime number theorem, first proved in the late 1800s, quantifies that decline.


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