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Monday, March 21, 2016

The March of Primes

               ...1     ...3     ...7      ...9

Last week when an article reported looking at 'patterns' in the last digits of consecutive primes, I mentioned I thought it swung the door wide open to a plethora of prime digit data exploration one might do. Mike Lawler gets that ball rolling in this post (and I suspect others out there are looking at a variety of possibilities):


(specifically, -- Mike looks at final digits of prime triples, but one can imagine plenty of other possibilities -- having said that, it's also possible that the sheer act of looking over loads of data, now so easy to generate, will result in occasional pattern-like findings emerging... that may lack any real meaning, beyond "chance").
Anyway, could all make for a very interesting year ahead in primes and number theory....

1 comment:

Evelyn said...

Just to clarify, something that was kind of glossed over in the articles about it is that Lemke Oliver's and Soundararajan's work has results (provable assuming the Hardy-Littlewood k-tuple conjecture) about prime tuples of all sizes, so it's unlikely that anyone will discover something new about those this year. (It's still fun to play with for yourself, though.) If you dig into the paper (http://arxiv.org/abs/1603.03720), it's in conjectue 1.1. The bold a is actually not just one number, it's a tuple of any length.