{"id":7297,"date":"2016-03-26T02:25:45","date_gmt":"2016-03-26T09:25:45","guid":{"rendered":"http:\/\/BigJimIndustries.com\/wordpress\/?p=7297"},"modified":"2016-03-24T03:39:28","modified_gmt":"2016-03-24T10:39:28","slug":"patternizing-primes-or-re-defining-random","status":"publish","type":"post","link":"https:\/\/bigjimindustries.com\/wordpress\/2016\/03\/26\/patternizing-primes-or-re-defining-random\/","title":{"rendered":"Patternizing Primes (or, Re-defining Random)"},"content":{"rendered":"

from Quanta Magazine<\/a><\/em><\/p>\n

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Mathematicians Discover Prime Conspiracy<\/h1>\n

A previously unnoticed property of prime numbers seems to violate a longstanding assumption about how they behave.<\/em><\/p>\n

By Erica Klarreich<\/a><\/strong><\/p>\n

\"\"Zim + Teemo<\/a> for Quanta Magazine<\/em><\/p>\n

Two mathematicians have uncovered a simple, previously unnoticed property of prime numbers \u2014 those numbers that are divisible only by 1 and themselves. Prime numbers, it seems, have decided preferences about the final digits of the primes that immediately follow them.<\/p>\n

Among the first billion prime numbers, for instance, a prime ending in 9 is almost 65 percent more likely to be followed by a prime ending in 1 than another prime ending in 9. In a paper posted online today<\/a>, Kannan Soundararajan<\/a> and Robert Lemke Oliver<\/a> of Stanford University present both numerical and theoretical evidence that prime numbers repel other would-be primes that end in the same digit, and have varied predilections for being followed by primes ending in the other possible final digits.<\/p>\n

\u201cWe\u2019ve been studying primes for a long time, and no one spotted this before,\u201d said Andrew Granville<\/a>, a number theorist at the University of Montreal and University College London. \u201cIt\u2019s crazy.\u201d<\/p>\n

The discovery is the exact opposite of what most mathematicians would have predicted, said Ken Ono<\/a>, a number theorist at Emory University in Atlanta. \u00a0When he first heard the news, he said, \u201cI was floored. I thought, \u2018For sure, your program\u2019s not working.\u2019\u201d<\/p>\n

This conspiracy among prime numbers seems, at first glance, to violate a longstanding assumption in number theory: that prime numbers behave much like random numbers. Most mathematicians would have assumed, Granville and Ono agreed, that a prime should have an equal chance of being followed by a prime ending in 1, 3, 7 or 9 (the four possible endings for all prime numbers except 2 and 5).<\/p>\n

\u201cI can\u2019t believe anyone in the world would have guessed this,\u201d Granville said. Even after having seen Lemke Oliver and Soundararajan\u2019s analysis of their phenomenon, he said, \u201cit still seems like a strange thing.\u201d<\/p>\n

Yet the pair\u2019s work doesn\u2019t upend the notion that primes behave randomly so much as point to how subtle their particular mix of randomness and order is. \u201cCan we redefine what \u2018random\u2019 means in this context so that once again, [this phenomenon] looks like it might be random?\u201d Soundararajan said. \u201cThat\u2019s what we think we\u2019ve done.\u201d<\/p>\n

[ click to continue reading at Quanta<\/a> ]<\/p>\n<\/header>\n<\/header>\n","protected":false},"excerpt":{"rendered":"

from Quanta Magazine Mathematicians Discover Prime Conspiracy A previously unnoticed property of prime numbers seems to violate a longstanding assumption about how they behave. By Erica Klarreich Zim + Teemo for Quanta Magazine Two mathematicians have uncovered a simple, previously unnoticed property of prime numbers \u2014 those numbers that are divisible only by 1 and […]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[3],"tags":[],"class_list":["post-7297","post","type-post","status-publish","format-standard","hentry","category-culture-art"],"_links":{"self":[{"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/posts\/7297","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/users\/26"}],"replies":[{"embeddable":true,"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/comments?post=7297"}],"version-history":[{"count":0,"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/posts\/7297\/revisions"}],"wp:attachment":[{"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/media?parent=7297"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/categories?post=7297"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/tags?post=7297"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}