Patroon in priemgetallen?

[Professor Puntje]

Er lijkt een nieuw patroon in de verdeling van priemgetallen te zijn gevonden:
 
https://www.quantamagazine.org/20160313-mathematicians-discover-prime-conspiracy/
 
Klopt dit, en zo ja is het wel zo nieuw. Over dat laatste lezen we in het artikel:
 

The primes’ preferences about the final digits of the primes that follow them can be explained, Soundararajan and Lemke Oliver found, using a much more refined model of randomness in primes, something called the prime k-tuples conjecture. Originally stated by mathematicians G. H. Hardy and J. E. Littlewood in 1923, the conjecture provides precise estimates of how often every possible constellation of primes with a given spacing pattern will appear. A wealth of numerical evidence supports the conjecture, but so far a proof has eluded mathematicians.
The prime k-tuples conjecture subsumes many of the most central open problems in prime numbers, such as the twin primes conjecture, which posits that there are infinitely many pairs of primes — such as 17 and 19 — that are only two apart. Most mathematicians believe the twin primes conjecture not so much because they keep finding more twin primes, Maynard said, but because the number of twin primes they’ve found fits so neatly with what the prime k-tuples conjecture predicts.
In a similar way, Soundararajan and Lemke Oliver have found that the biases they uncovered in consecutive primes come very close to what the prime k-tuples conjecture predicts. In other words, the most sophisticated conjecture mathematicians have about randomness in primes forces the primes to display strong biases. “I have to rethink how I teach my class in analytic number theory now,” Ono said.

[tempelier]

Het hoeft geen eigenschap van Priemen te zijn.
 
Het kan aan het talstelsel gebonden zijn net zoals het al of niet repeteren van een breuk.

[Professor Puntje]

Ook dan zou het nog een eigenschap van de priemgetallen zijn (in die zin dat het iets over de priemgetallen zegt), maar ik zal nog even zoeken want ik meen te hebben gelezen dat een dergelijk effect ook voor andere talstelsels werd aangetroffen. Gevonden:
 

Lemke Oliver and Soundararajan discovered that this sort of bias in the final digits of consecutive primes holds not just in base 3, but also in base 10 and several other bases; they conjecture that it’s true in every base. The biases that they found appear to even out, little by little, as you go farther along the number line — but they do so at a snail’s pace. “It’s the rate at which they even out which is surprising to me,” said James Maynard, a number theorist at the University of Oxford. When Soundararajan first told Maynard what the pair had discovered, “I only half believed him,” Maynard said. “As soon as I went back to my office, I ran a numerical experiment to check this myself.”

 
Bron: https://www.quantamagazine.org/20160313-mathematicians-discover-prime-conspiracy/