# Prime Numbers Are Not As Random As Previously Thought

An important discovery has rocked the mathematical world: Prime numbers are not really random. Excluding two and five, every prime number ends in either one, three, seven, or nine. If there was no pattern, then the probability of having two consecutive primes ending with either number should always be 25 percent, but that’s not always the case.

Kannan Soundararajan and Robert Lemke Oliver of Stanford University in California have discovered that in the first 100 million prime numbers, a prime ending in one is followed by another ending in one18.5 percent of the time, by three 29.7 percent, by seven 30 percent, and by nine 21.8 percent. In other words, the prime’s final number is most likely not to be repeated.

A very similar pattern is seen for primes ending in 3, 7, and 9, as the researchers show in a paper available online. Prime numbers are predetermined by the laws of mathematics, so theres nothing to suggest that they should care what their neighbors look like, but somehow they do.

It was very weird, Soundararajan told New Scientist. Its like some painting you are very familiar with, and then suddenly you realize there is a figure in the painting youve never seen before.

Prime numbers are numbers that are divisible only by themselves and one. They are of the uttermost importance in math because they are the building blocks of larger numbers, and they are the cornerstone of encryption in modern communication. Primes are not only present in our base-10 numbering system but also in other bases, and the phenomenon Soundararajan and Lemke Oliver have observed is found there as well.

Understanding where the phenomenon comes from could help us crack the mystery of prime numbers, namely that we don’t have a formula to predict them. Their explanation is based on the k-tuple conjecture, a mathematical supposition for the apparent grouping of prime numbers, indicating that at least some of them can be grouped in patterns.

Our initial thought was if there was an explanation to be found, we have to find it using the k-tuple conjecture, says Soundararajan. We felt that we would be able to understand it, but it was a real puzzle to figure out.

The findings wont help us solve any of the most important mysteries of prime numbers just yet, but they are telling us that something very interesting is going on.

[H/T: New Scientist]

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