A new prime number, 23 million digits long

An online pubic program designed to allow ordinary people to use their computers to identify previously unknown prime numbers has found the largest so far, 23 million digits long.

It was discovered on December 26, 2017 by electrical engineer Jonathan Pace, and it initially took six days of non-stop number crunching to show that it was indeed a prime number. Pace was using a consumer-level PC running an Intel i5-6600 processor, and after it was identified it was then independently verified by other users, with a range of other programs and hardware setups.

Mathematicians discover pattern in prime numbers

The uncertainty of science: Mathematicians have discovered that, among the first billion prime numbers, there is a peculiar uneven distribution that is not random to the last digit of each prime.

[I]f the sequence were truly random, then a prime with 1 as its last digit should be followed by another prime ending in 1 one-quarter of the time. That’s because after the number 5, there are only four possibilities — 1, 3, 7 and 9 — for prime last digits. And these are, on average, equally represented among all primes, according to a theorem proved around the end of the nineteenth century, one of the results that underpin much of our understanding of the distribution of prime numbers. (Another is the prime number theorem, which quantifies how much rarer the primes become as numbers get larger.)

Instead, Lemke Oliver and Soundararajan saw that in the first billion primes, a 1 is followed by a 1 about 18% of the time, by a 3 or a 7 each 30% of the time, and by a 9 22% of the time. They found similar results when they started with primes that ended in 3, 7 or 9: variation, but with repeated last digits the least common. The bias persists but slowly decreases as numbers get larger.

As the article notes, this pattern does not appear to have any practical use, though it definitely fascinates everyone who hears about.