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devlux [soylentnews.org] writes:

I was browsing nature today and came across this article I thought I would share.

Peculiar pattern found in ‘random’ prime numbers
http://www.nature.com/news/peculiar-pattern-found-in-random-prime-numbers-1.19550 [nature.com] [this article may be paywalled]

The original preprint is available in arxiv
http://arxiv.org/abs/1603.03720 [arxiv.org]

The crux is that prime numbers near to eachother tend to avoid repeating their last digits.

If 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.

Now the original authors claim that this has no impact that they are aware of on cryptography. Any crypto experts care to chime in?

Original Submission