tag:blogger.com,1999:blog-3722233.post4014480869116787596..comments2024-02-27T11:33:56.576-06:00Comments on Computational Complexity: What is the least boring number (NOT the usual paradox)Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-3722233.post-86837942677314023612009-08-24T16:37:23.735-05:002009-08-24T16:37:23.735-05:00It's worth mentioning that numbers that requir...It's worth mentioning that numbers that require four squares aren't just those congruent to 7 mod 8, but all those of the form 4^a (8b + 7).<br /><br />I happen to collect lists of uninteresting numbers on <a href="http://math.crg4.com/uninteresting.html" rel="nofollow">my website</a>, so I found this post particularly interesting.Unknownhttps://www.blogger.com/profile/00289914092399670337noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-41936478576009423192009-08-23T05:30:44.770-05:002009-08-23T05:30:44.770-05:00There's also this list...There's also <a href="http://primes.utm.edu/curios/page.php?short=11" rel="nofollow">this list</a>...Unknownhttps://www.blogger.com/profile/04752384695446260553noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-22220553998740563552009-08-19T05:24:50.453-05:002009-08-19T05:24:50.453-05:004 is the first composite number4 is the first composite numberAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-36452684676122037912009-08-18T16:31:08.379-05:002009-08-18T16:31:08.379-05:00Someone expands on Michael's idea and gets 116...<a href="http://www.nathanieljohnston.com/index.php/2009/06/11630-is-the-first-uninteresting-number/" rel="nofollow">Someone expands on Michael's idea and gets 11630</a>Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-3160063219519502732009-08-18T12:17:42.520-05:002009-08-18T12:17:42.520-05:00The integers -1,0,1 are extremely interesting beca...The integers -1,0,1 are extremely interesting because of their role in fields. The integer 2 is extremely interesting, especially in computer science, because it is the least prime and because (-1)^2 = 1. No other integers are anywhere near as interesting as {-1,0,1,2}, so I claim 3 is the least boring natural number.<br /><br />By the way it's silly to say that 2 is interesting because it is the only even prime. That is equivalent to saying that 2 is the only prime divisible by 2, which would be true if "2" were replaced by any other prime! The number 2 is so important that there are special words for numbers that are divisible by it, but that is a <i>consequence</i> of its being interesting, not the <i>reason</i>.Unknownhttps://www.blogger.com/profile/01106301822827737278noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-85578518684047532842009-08-18T12:02:24.274-05:002009-08-18T12:02:24.274-05:00In finite geometry, 9 is the order of the smallest...In finite geometry, 9 is the order of the smallest Non-Desarguesian projective plane, and also the first order for which the projective plane is non-unique.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-69760615778745902292009-08-18T11:30:29.452-05:002009-08-18T11:30:29.452-05:00Yes, that's an unusual paradox: "The leas...Yes, that's an unusual paradox: "The least boring number is boring"Rahulnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-38069375892779441252009-08-18T10:57:17.269-05:002009-08-18T10:57:17.269-05:00How many times do these numbers appear in Sloane&#...How many times do these numbers appear in Sloane's <i>Encyclopedia of Integer Sequences</i>?<br /><br />I searched for 1, 2, ..., 31. As you might expect there's a decreasing trend. But 9 is the first number to appear less often than its successor (9 appears 53266 times, 10 appears 57972 times). This doesn't necessarily mean 9 is uninteresting, though; it might just mean 10 is interesting. <br /><br />And of course there are flaws in this method. For example there are 10 hits for 196884 -- which occurs in the study of the Monster group -- but most of them are really "the same" as there are a lot of trivial variations on the same sequence, or sequences that don't include 196884 at all but include it in the explanatory text.Michael Lugohttps://www.blogger.com/profile/01950197848369071260noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-73111615153380201952009-08-18T10:27:02.923-05:002009-08-18T10:27:02.923-05:005 is interesting also because Z[\sqrt{-5}] isn'...5 is interesting also because Z[\sqrt{-5}] isn't a UFD; 5 is the smallest integer with this property.<br /><br />A_5 is the smallest nonabelian simple group.<br /><br />In group theory, 11 is related to the smallest Mathieu group (the smallest sporadic simple group) -- it's one of only four special cases of 4-transitive permutation groups.<br /><br />8 is extremely interesting (more or less because it divides 24, which is probably the MOST interesting number) -- the E_8 lattice is one example.<br /><br />My vote for the first boring number is 9, which doesn't have nearly as many interesting algebraic, geometric, etc. properties as the numbers around it.harrisonhttp://harrisonbrown.wordpress.comnoreply@blogger.com