Prime Numbers Just Got a Little Stranger

They repeat in patterns that aren't as random as thought
By John Johnson,  Newser Staff
Posted Mar 15, 2016 11:07 AM CDT
Prime Numbers Just Got a Little Stranger

Two Stanford mathematicians have managed to surprise others in their field with a previously undiscovered insight about prime numbers: They're not as random as believed. Or, more precisely, there seems to be some order in the way one prime number follows another, reports Quanta Magazine. Start with the basics: Except for 2 and 5, all primes—numbers divisible only by one or themselves—end in 1, 3, 7, or 9. Theoretically, there should be an equal chance of one prime being followed by another that ends in one of those four numbers. But Robert Lemke Oliver and Kannan Soundararajan found that's not the case, reports New Scientist. In looking at the first billion primes, they found that a number ending in 1 follows another ending in 1 about 18% of the time, with different percentages for the rest: 3 (30%), 7 (30%), and 9 (22%).

"It was very weird," says Soundararajan. "It’s like some painting you are very familiar with, and then suddenly you realize there is a figure in the painting you’ve never seen before." Others in the field agree. "We’ve been studying primes for a long time, and no one spotted this before," says a number theorist at the University of Montreal. "It’s crazy." The Stanford pair guess this anti-sameness bias is related to something called the "k tuple conjecture," which Gizmodo calls "an old idea about how often pairs, triples, and larger sets of primes make an appearance." (Dig in at Gizmodo or at Nature for more on that.) As for the practical implications of this new discovery, well, the Stanford scientists don't know of any just yet. But the Nature post calls it "both strange and fascinating" for mathematicians, and the University of Montreal professor sums up that sentiment: "You could wonder, what else have we missed about the primes?" (Behold the biggest prime number yet found.)

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