For centuries prime numbers, though among simplest numbers to define, have behavior thought to be enigmatic and seemingly random. The difficult nature of identifying large primes (primes that are hundreds of digits in length) has served as the basis of commonly used methods for encrypting information on the internet in order to keep it secure.

Mathematicians in coding theory and in number theory may need to re-think these cyber-security measures. Recently, two mathematicians discovered a property of prime numbers which could unravel encryption/decryption algorithms based on the difficulty of decomposing numbers whose only factors are very large primes.

In simple terms the property is this: among the first billion or so primes, prime numbers seem to repel other prime numbers which end in the same digit. For example, prime number 59 is preceded by primes 31, 37, 41, 43, 47, 53, and followed by primes 61, 67, 71, 73. The prime numbers on either end of this list are 29 and 79 – making 59 relatively far removed from any other prime ending with the digit 9. But the property isn’t restricted to primes ending in 9; readers will also note that among the other primes in this short list, no pair of consecutive primes end in the same digit.

Fortunately the discoverers of this property have no intention of using the information to break any security codes, but you can be certain their discovery has coding theorists hard at work looking for new ways to keep internet communication secure.

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From QUANTA Magazine - illminating science, Sunday, March 13, 2016. See https://www.quantamagazine.org/20160313-mathematicians-discover-prime-conspiracy/