Astounding Revelation of the Nature of Prime Numbers: What Does it Mean? Bob Zimmerman,

Mar 18, 2016, 05:11 AM

03-17-2016 (Photo: What is a Prime Number?) Twitter: @BatchelorShow Astounding Revelation of the Nature of Prime Numbers: What Does it Mean? Bob Zimmerman, “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….”

“Two mathematicians have found a strange pattern in prime numbers — showing that the numbers are not distributed as randomly as theorists often assume. “Every single person we’ve told this ends up writing their own computer program to check it for themselves,” says Kannan Soundararajan, a mathematician at Stanford University in California, who reported the discovery with his colleague Robert Lemke Oliver in a paper submitted to the arXiv preprint server on 11 March1. “It is really a surprise,” he says. “Prime numbers near to each other tend to avoid repeating their last digits, the mathematicians say: that is, a prime that ends in 1 is less likely to be followed by another ending in 1 than one might expect from a random sequence. “As soon as I saw the numbers, I could see it was true,” says mathematician James Maynard of the University of Oxford, UK. “It’s a really nice result.” “Although prime numbers are used in a number of applications, such as cryptography, this ‘anti-sameness’ bias has no practical use or even any wider implication for number theory, as far as Soundararajan and Lemke Oliver know. But, for mathematicians, it’s both strange and fascinating..."