Apart from the single-digit prime numbers 2 and 5, all other prime numbers can only end in one of four digits: 1, 3, 7, or 9. (If a number ends in 2, 4, 6, 8 or 0, it will be divisible by 2. If it ends in 5, it will be divisible by 5.) Thus, if they were truly random, a prime number that ends in 1 should be followed by another prime number ending in 1 about 25% of the time. That is, this kind of pairing should occur at least one in four times.
But when Kannan Soundararajan and Robert Lemke Oliver checked the first billion prime numbers, they found that a prime number ending in 1 is followed by another also ending in 1 about 18% of the time. That is, this kind of pairing occurred only one in five times. Instead, that prime number was followed by a prime number ending in 3 or 7 about 30% of the time and by 9 about 22% of the time. This result holds true for prime numbers ending in 3, 7 or 9 too, but with slightly less bias.
Their study is yet to be checked by experts before it is accepted for publication in a peer-reviewed journal, but mathematicians are geeking out about the results already. “Every single person we’ve told this ends up writing their own computer program to check it for themselves,” Soundararajan told Nature.