Mathematicians stunned at discovery that prime numbers really do have a pattern

Prime numbers are divisible only by themselves and 1, and, except for 2 and 5, they all end in 1, 3, 7 or 9. Every other number can be created by multiplying prime numbers together, making them the building blocks of the entire number line. Until now it was thought that the occurrence of primes was random across all numbers, but mathematicians have recently made the stunning discovery that primes actually do have a pattern.

Stanford researchers Robert Lemke Oliver and Kannan Soundararajan ran a program that checks the randomness of the first 100 million primes and found a pattern that mathematicians have been overlooking for many years. Included in a number of their findings was the discovery that prime numbers ending in 1 are followed by another prime that ends in 1 only 18.5 percent of the time. If the pattern was truly random that figure should have been 25 percent.

The highest probability was in the chance of a prime number that ends in 1 being followed by a prime that ends in 3 or 7. That occurrence was 30 percent. However, for 9 to follow 1 it was only 22 percent. The researchers wanted to know why prime numbers ending in 1 seem to prefer being followed by 3 or 7. Even when they expanded the program to include 1 trillion prime numbers the pattern persisted.

Oliver and Soundararajan came up with a theory, which is that primes are forced to display the strong preferences they identified because of the k-tuple conjecture. This conjecture, which is well-established but unproven, deals with how often pairs, triples and larger sets of primes make their appearance, and how closely the sets should occur.

They also found that the larger the prime numbers that were examined, the less the patterns held true, tending more toward the random distribution typically expected.

Andrew Granville is a number theorist at the University of Montreal, and was not involved in the study. He said, “we’ve been studying primes for a long time, and no one spotted this before. It’s crazy.” He added, “you could wonder, what else have we missed about the primes.”