NEWS: Pattern Behind the Primes?

Although I had another blog post planned for today (also about primes surprisingly!), I read about an exciting new discovery on prime numbers in the news, and thought I’d write a quick blog post about it.

Kannan Soundararajan and Robert Lemke Oliver of Stanford University in the US have discovered a surprising pattern in the final digit of prime numbers. Apart from 2 and 5, all prime numbers have to end in 1, 3, 7 or 9 to prevent them from being divisible by 2 or 5. You would expect then that each of these 4 numbers have an equal probability (25%) of being the final digit of the next prime number, if the sequence of prime numbers is truly random.

However, the mathematicians made a discovery while performing a randomness check on the first 400 billion primes: prime numbers tend to avoid having the same number as their predecessor. In fact, it was found that:

  • a prime ending in 1 is followed by another ending in 1 just 18.5% of the time (considerably lower than 25%);
  • primes ending in 3 were more likely followed by primes ending in 9, rather than 1 or 7.

Although this isn’t necessarily a pattern, it does hint at the fact that the sequence of prime numbers isn’t completely random, something that mathematicians have taken to be true for many years. Ken Ono told Quanta Magazine:

“I was floored. I have to rethink how I teach my class in analytic number theory now.”

The two mathematicians suggest that the pattern they’ve discovered could be explained by the k-tuple conjecture, which predicts how groupings of primes will appear. Although this may not help in other prime related problems such as the twin-prime conjecture or the Riemann hypothesis, and may in fact have no implications to maths or number theory, Andrew Granville told the New Scientist:

“It gives us more of an understanding, every little bit helps. If what you take for granted is wrong, that makes you rethink some other things you know.”

What do you think about the news? M x


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