American mathematicians have discovered a previously unknown property of prime numbers.

Two mathematicians from Stanford University, Kannan Soundarajan [Kannan Soundararajan] and Robert Lemke Oliver [Robert Lemke Oliver] ( pictured above ) discovered a previously unknown property of prime numbers . It turned out that the chances that a simple number ending in 9 will be followed by a number ending in 1 are 65% greater than the chances that it will be followed by a number ending in 9. This assumption has been numerically tested by computer methods for billions of known primes.

According to Ken Ono, a mathematician from Emory University in Atlanta, this assumption is essentially contrary to the expectations of most mathematicians. Previously it was believed that primes in the mass behave quite randomly. Most theorists would agree on the assumption that the chances of having one of the numbers possible for primes (1, 3, 7, 9) are approximately equal for all such numbers.
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Andrew Granville of the University of Montreal, stated that “we have been studying the primes for a very long time, and no one has noticed this before. This is some kind of madness. I can not believe that someone could guess this. It looks very strange. ”

Soundarajan said that he was prompted by the idea of ​​checking "randomness" in the world of prime numbers by a lecture by Japanese mathematician Tokied Tadashi [Tadashi Tokieda]. In it, he gave an example from probability theory. If Alice throws the coins until she gets a tail next to the eagle, and Bob does until she gets two tails in a row, then Alice will need an average of four coin shots, while Bob will take six. In this case, the probability of falling eagles and tails is the same.

Since Soundarajan was engaged in prime numbers, he turned to them in search of previously unknown distributions. He found that if you write down primes in the ternary system, in which about half of the primes end in 1, and half end in 2, then for primes less than 1000, the number ending in 1 is twice as likely follow the number ending in 2, than again in 1.

He shared an interesting discovery with another scientist, Lemke Oliver, who, marveling at this fact, wrote a program that checked how things are working with the distribution of numbers on the first 400 billion prime numbers. The results confirmed the assumption - as Oliver put it, prime numbers "hate repetition." The assumption was tested for decimal notation and for some other number systems.

It is not yet known whether this property is a separate phenomenon, or whether it is associated with deeper properties of primes that have not been discovered so far. As Granville said, “I wonder what else we could have overlooked in prime numbers.”