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Tuesday, March 15, 2016

Story of the Week! (and it's only Tuesday)


Like a good magician, prime numbers never quite reveal everything held up their sleeves.
As most have likely heard already the momentous story of the week (perhaps the month) for many of us, doesn't include Donald Trump, but rather a new 'pattern' or bit of non-randomness noted for prime numbers.

Of course primes aren't truly random to begin with (in their distribution throughout the number system), but this finding indicates that even their final individual digits appear for some reason skewed away from randomness, with a given prime being followed by another prime who's final digit differs from the first with greater-than-expected probability. As articles have mentioned, it is remarkable it's taken this long for anyone to notice. Like the magician who's sleight-of-hand distracts us from seeing what's right in front of our eyes. Whether this finding will have any practical application is difficult to see; for now it simply sits baldly and boldly in the rarefied domain of number theory awaiting further explication.

Significantly (I would think) it may open up a Pandora's Box of other questions to be looked at regarding individual digits of primes and their relationships in placement, order, succession... and will any variances from 'randomness' discovered be mere mathy statistical glitches or 'accidents', or do they hold some rich, deeper meaning not yet understood? I suspect most believe the latter.

Anyway, the story started in the popular press (so far as I'm aware) with Quanta Magazine and this fantastic piece by Erica Klarreich:
https://www.quantamagazine.org/20160313-mathematicians-discover-prime-conspiracy/

Evelyn Lamb covered the subject for Nature:
http://tinyurl.com/zzj2yd6

ADDENDUM:  Dr. Lamb now also has this fascinating followup post at her "Roots of Unity" blog
http://blogs.scientificamerican.com/roots-of-unity/two-plausible-facts-that-cannot-both-be-true/

John Baez offers good coverage here:
https://golem.ph.utexas.edu/category/2016/03/unexpected_biases_in_the_distr.html#more

And more technically, Terry Tao here:
https://terrytao.wordpress.com/2016/03/14/biases-between-consecutive-primes/

(there are many other articles, but these give a great run-down)


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