A pair of mathematicians have discovered a prime number conspiracy
A prime is a number that is divisible only by 1 and itself, like 2, 3, 5, 7, and 11. A number like 6 is not prime, because 6 is divisible by 2 and 3.
Prime numbers are one of the major objects of interest of the mathematical subfield of number theory. One favourite obsession of number theorists is the distribution of prime numbers among all the whole numbers.
One of the main intuitive ideas about the distribution of the primes that mathematicians have traditionally held is that they are distributed somewhat "randomly." That is, there aren't particular patterns to be found in the prime numbers.
But now Prof. Kannan Soundararajan and Dr. Robert Lemke Oliver from Stanford University believe they have found such a pattern.
Speaking with Quanta Magazine, the two said they had uncovered that primes that end in a particular digit were less likely to be followed by another prime that also ends in that digit. Prime numbers larger than 5 have to end in a 1, 3, 7, or 9: Numbers that end with an even digit are divisible by 2 and therefore not prime, and numbers with a final digit of 5 are divisible by 5.
Under the idea that the primes are randomly distributed, then, the odds of a prime ending in 1 being followed by another prime ending in 1 would be 25%: Final digits should be evenly distributed among the four possibilities mentioned above.
But Soundararajan and Oliver's research, available on the science and math preprint site arXiv, showed the actual odds were closer to 18%.
Oliver puts it quite simply: "Primes really hate to repeat themselves."
A prime ending in 1 actually has a greatly increased chance of being followed by a figure ending in 3 or 7 (about 30%) and a 22% chance of the figure ending with a 9.
That nonrandom behavior is very surprising and challenges mathematicians' assumptions about prime numbers. Number theorist Andrew Granville told the New Scientist: "We've been studying primes for a long time, and no one spotted this before. It's crazy."