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Re: [math-fun] The largest twin-primes known today...
by Bill Gosper 21 Sep '16

21 Sep '16

I think Allan means 3^2, not 3^12. This would have been an extremely easy factorization even for Lehmer's optical contraption <https://en.wikipedia.org/wiki/Lehmer_sieve>. Or Macsyma back when it trial-divided by consecutive odd numbers. Which is pretty much like GCDing with their product, now that we can store big numbers. I just wrote a tiny (and very untested) recursive program in a similar vein: In[832]:= Clear[dumfac]; dumfac@1 = {}; dumfac[n_Integer] := (dumfac@n = {n}; dumfac@n = Join[dumfac[#], dumfac[n/#]] &@ GCD[n, Binomial[#, Floor[#/2]] &@Floor[Sqrt[n]]]) In[833]:= dumfac[2996863034895] // tim During evaluation of In[833]:= 0.188517 sec, 5 Out[833]= {5, 3, 3, 18583, 3583757} In[834]:= PrimeQ /@ % Out[834]= {True, True, True, True, True} --rwg On 2016-09-20 16:05, Allan Wechsler wrote: > Factoris says the coefficient factors to 3^12.5.18583.3583757. > > On Tue, Sep 20, 2016 at 6:55 PM, Dan Asimov <asimov(a)msri.org> wrote: > >> P.S. I'm puzzled by this statement about these twin primes at that link: >> >> ----- >> They will enter Chris Caldwell's “The Largest Known Primes Database” >> (http://primes.utm.edu/primes) ranked 1st for twins, and each entered >> individually ranked 4180th overall. >> ----- >> >> Why do they have the same ranking overall? Does it not matter that >> one is bigger than the other? >> >> —Dan >> >> >> > On Sep 20, 2016, at 3:35 PM, Dan Asimov <asimov(a)msri.org> wrote: >> > >> > Is anything known about the factorization of that coefficient >> > >> > (other than its divisibility by 5 and 9)? >> > >> > Was it chosen as part of some algorithm that singled out relatively >> > likely candidates? Or was it just stumbled on at random from a >> > massive search? >> > >> > >> > Or maybe one of our factoring experts can factor it? (You know who you >> are.) >> > >> > —Dan >> > >> > >> >> On Sep 20, 2016, at 3:18 PM, Eric Angelini <Eric.Angelini(a)kntv.be> >> wrote: >> >> >> >> >> >> ... are: >> >> 2996863034895*2^1290000-1 >> >> and >> >> 2996863034895*2^1290000+1 >> >> >> >> http://www.primegrid.com/download/twin-1290000.pdf >>

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[math-fun] The largest twin-primes known today...
by Eric Angelini 20 Sep '16

20 Sep '16

... are: 2996863034895*2^1290000-1 and 2996863034895*2^1290000+1 http://www.primegrid.com/download/twin-1290000.pdf Best, É.

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[math-fun] Something's rotten about Common Core math
by Henry Baker 20 Sep '16

20 Sep '16

FYI -- Parts of this article are pretty funny! https://www.salon.com/2015/11/28/youre_wrong_about_common_core_math_sorry_p… Youre wrong about Common Core math: Sorry, parents, but it makes more sense than you think

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[math-fun] gyroelongated bifastigium
by Bill Gosper 17 Sep '16

17 Sep '16

On 2016-09-14 17:45, James Buddenhagen wrote: > Haha -- that is an endearing name :) . > Do you happen to have an off file for that? > I'm still trying to figure out what it is! > You mean like Graphics3D@Polygon@{{{-(1/2), -(1/2), -(1/(2 2^(1/4)))}, {-(1/2), 1/ 2, -(1/(2 2^(1/4)))}, {-(1/2), 0, 1/4 (-2^(3/4) - 2 Sqrt[3])}}, {{1/2, 0, 1/4 (-2^(3/4) - 2 Sqrt[3])}, {1/2, 1/2, -(1/(2 2^(1/4)))}, {1/ 2, -(1/2), -(1/(2 2^(1/4)))}}, {{-(1/2), 0, 1/4 (-2^(3/4) - 2 Sqrt[3])}, {-(1/2), 1/2, -(1/(2 2^(1/4)))}, {1/2, 1/2, -(1/(2 2^(1/4)))}, {1/2, 0, 1/4 (-2^(3/4) - 2 Sqrt[3])}}, {{-(1/2), -(1/2), -(1/( 2 2^(1/4)))}, {-(1/2), 0, 1/4 (-2^(3/4) - 2 Sqrt[3])}, {1/2, 0, 1/4 (-2^(3/4) - 2 Sqrt[3])}, {1/2, -(1/2), -(1/(2 2^(1/4)))}}, {{1/ 2, 1/2, -(1/(2 2^(1/4)))}, {0, 1/Sqrt[2], 1/(2 2^(1/4))}, {1/Sqrt[ 2], 0, 1/(2 2^(1/4))}}, {{-(1/2), 1/ 2, -(1/(2 2^(1/4)))}, {-(1/Sqrt[2]), 0, 1/(2 2^(1/4))}, {0, 1/Sqrt[ 2], 1/(2 2^(1/4))}}, {{-(1/2), -(1/2), -(1/(2 2^(1/4)))}, {0, -(1/ Sqrt[2]), 1/(2 2^(1/4))}, {-(1/Sqrt[2]), 0, 1/(2 2^(1/4))}}, {{1/ 2, -(1/2), -(1/(2 2^(1/4)))}, {1/Sqrt[2], 0, 1/( 2 2^(1/4))}, {0, -(1/Sqrt[2]), 1/(2 2^(1/4))}}, {{1/2, 1/ 2, -(1/(2 2^(1/4)))}, {-(1/2), 1/2, -(1/(2 2^(1/4)))}, {0, 1/Sqrt[ 2], 1/(2 2^(1/4))}}, {{-(1/2), 1/ 2, -(1/(2 2^(1/4)))}, {-(1/2), -(1/2), -(1/(2 2^(1/4)))}, {-(1/ Sqrt[2]), 0, 1/( 2 2^(1/4))}}, {{-(1/2), -(1/2), -(1/(2 2^(1/4)))}, {1/ 2, -(1/2), -(1/(2 2^(1/4)))}, {0, -(1/Sqrt[2]), 1/( 2 2^(1/4))}}, {{1/2, -(1/2), -(1/(2 2^(1/4)))}, {1/2, 1/ 2, -(1/(2 2^(1/4)))}, {1/Sqrt[2], 0, 1/( 2 2^(1/4))}}, {{-(1/(2 Sqrt[2])), -(1/(2 Sqrt[2])), 1/4 (2^(3/4) + 2 Sqrt[3])}, {-(1/Sqrt[2]), 0, 1/( 2 2^(1/4))}, {0, -(1/Sqrt[2]), 1/(2 2^(1/4))}}, {{1/Sqrt[2], 0, 1/( 2 2^(1/4))}, {0, 1/Sqrt[2], 1/(2 2^(1/4))}, {1/(2 Sqrt[2]), 1/( 2 Sqrt[2]), 1/4 (2^(3/4) + 2 Sqrt[3])}}, {{1/(2 Sqrt[2]), 1/( 2 Sqrt[2]), 1/4 (2^(3/4) + 2 Sqrt[3])}, {0, 1/Sqrt[2], 1/( 2 2^(1/4))}, {-(1/Sqrt[2]), 0, 1/( 2 2^(1/4))}, {-(1/(2 Sqrt[2])), -(1/(2 Sqrt[2])), 1/4 (2^(3/4) + 2 Sqrt[3])}}, {{1/Sqrt[2], 0, 1/(2 2^(1/4))}, {1/( 2 Sqrt[2]), 1/(2 Sqrt[2]), 1/4 (2^(3/4) + 2 Sqrt[3])}, {-(1/(2 Sqrt[2])), -(1/(2 Sqrt[2])), 1/4 (2^(3/4) + 2 Sqrt[3])}, {0, -(1/Sqrt[2]), 1/(2 2^(1/4))}}} ? A fastigium is apparently just a triangular prism with square sides. This is two of them endcapping a square antiprism. --rwg Johnson had to eschew nonconvex solids because they're infinitudinous, narrowly excluding such gems as bilunagyrobicupola. > On Wed, Sep 14, 2016 at 4:10 AM, Bill Gosper <billgosper(a)gmail.com> wrote: >> is nonconvex, but the name is irresistible. >> gosper.org/gyroelongatedbifastigium.png >> Resistince is futile. --rwg

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Re: [math-fun] A powerful Zero Torque Square (Ed Pegg Jr)
by Walter Trump 16 Sep '16

16 Sep '16

Hi Ed, your square is a candidate for the most interesting magic square of order 4. It additionally has the longest Anderson Graph (a closed path from entry 1 to 2 to 3 to ... to 16 to 1) of all classical magic 4x4 squares (together with the square Frenicle # 361.) The length of the graph is 43.942968 units. For general orders we can say that all magic and semi-magic squares are balanced. (Obvious) And all centrally symmetric magic squares remain balanced if their entries were squared. (Not difficult to prove) Question: Are there non-symmetric magic squares of orders greater than 4 with this property? In this context Peter Lolys work should be mentioned. He showed that the moment of inertia is equal for all classical magic squares of the same order. See: http://home.cc.umanitoba.ca/~loly/MathGaz.pdf And: https://oeis.org/A126275 Walter

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[math-fun] An enigma solved on magic squares
by Christian Boyer 16 Sep '16

16 Sep '16

In 2010, twelve enigmas were launched: www.multimagie.com/English/MagicSquaresEnigmasE.pdf <http://www.multimagie.com/English/MagicSquaresEnigmasE.pdf> Three of them were solved from 2010 to 2015. I am pleased to announce that a fourth enigma (#6b) is now solved! Here is the first known 7x7 additive-multiplicative magic square, constructed by Sébastien Miquel. The 7 rows, 7 columns and 2 diagonals have the same sum. The 7 rows, 7 columns and 2 diagonals have the same product. 126 66 50 90 48 1 84 20 70 16 54 189 110 6 100 2 22 98 36 72 135 96 60 81 4 10 49 165 3 63 30 176 120 45 28 99 180 14 25 7 108 32 21 24 252 18 55 80 15 More details will be given at www.multimagie.com <http://www.multimagie.com> in the coming weeks. Before this square, 8x8 was the size of smallest known add-mult magic squares. 5x5 and 6x6 are still unknown (enigmas #6 and #6a), but 3x3 and 4x4 are proved impossible. Now, there remain eight unsolved enigmas for winning €6,500 (~$7,300) and eight bottles of champagne! Christian Boyer.

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Re: [math-fun] Moore curve drawn with epicycles
by Bill Gosper 15 Sep '16

15 Sep '16

Jörg nailed it. This is similar to http://gosper.org/TDrag3c.mp4 (plays in Safari but not Firefox). Gawd, I can't believe E. H. Moore would perpetrate such an inelegant kludge! Gluing four Hilbert arcs onto the sides of a degenerate rhombus apparently for the mere purpose of creating a closed squarefilling curve. Whose quadrants are not Moore curves! Better would have been filling a domino with two Hilberts (back to back) on the sides of a digon. gosper.org/fst.pdf explains how to get the Fourier series of a curve to repeat on the sides of a regular n-gon, indented for negative n. http://gosper.org/TDrag3c.mp4 is three triadic dragons on the sides of an equilateral triangle. Actually, for Fourier purposes, the curve need not even close. It can just snap back after each period, interpolating just one point halfway through the snap. Better yet, why didn't "algoritmic" draw a https://en.wikipedia.org/wiki/Sierpiński_curve, which is closed and legitimately four copies of itself. Apparently the "disks" are to emphasize that the rotors (harmonics) retain fixed amplitudes. But they don't assure the skeptical viewer that their relative frequencies and phases remain fixed. I wonder if "algoritmic" had an analytic formula for the nth Hilbert harmonic. Given some such formula describing an arc, I'll bet there's a neat formula for arranging them on the sides of an arbitrary rhombus. I'm not surprised there seem to be excess rotors in the video. Spacefilling Fourier series converge very slowly, You typically need to double the number of harmonics for each additional level of detail of the spacefiller. And, it would help if "algoritmic" started and ended with zero angular velocity, like http://gosper.org/TDrag3c.mp4 . --rwg On 2016-09-08 16:30, Joerg Arndt wrote: > * James Propp <jamespropp(a)gmail.com> [Sep 08. 2016 17:59]: >> Can Bill Gosper or anyone else explain what's going on with >> https://twitter.com/algoritmic/status/772699702064254976 >> ("Moore curve drawn with epicycles")? >> >> Jim Propp >> _______________________________________________ >> math-fun mailing list >> math-fun(a)mailman.xmission.com >> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > Unless I am very mistaken this is more and more terms of the Fourier > series (in polar coordinates). The disks seem to indicate the > magnitude of the terms of the series (but there seem to be too many > disks for my feeling after the first go-around is finished). > > One of the many many cases where people really should indicate > what they are doing when putting pictures/movies online. > > Best regards, jj >

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[math-fun] A powerful Zero Torque Square
by Ed Pegg Jr 15 Sep '16

15 Sep '16

Consider one of the 880 order 4 magic squares. .6, 12, .9, .7, 15, .1, .4, 14, .3, 13, 16, .2, 10, .8, .5, 11 If these weights are placed on the odd-odd vertices from (-3,-3) to (3,3), then this will balance perfectly on the center point (0,0). Square each number, and it will still remain perfectly balanced. There are 48 4x4 magic squares with this property. .36, 144, .81, .49, 225, ..1, .16, 196, ..9, 169, 256, ..4, 100, .64, .25, 121 Cube each number, and this magic square is still perfectly balanced. And the same when the numbers are raised to the 4th powers. (But not the 5th or 6th powers) This is the only magic square that remains balanced at powers 3 and 4. .216, 1728, .729, .343, 3375, ...1, ..64, 2744, ..27, 2197, 4096, ...8, 1000, .512, .125, 1331 --Ed Pegg Jr

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[math-fun] thermodynamic question
by Henry Baker 15 Sep '16

15 Sep '16

[This is a thermo question, not a climate troll.] California just passed energy efficiency requirements for computers. 1. If I have an inefficient computer that requires twice as much power to run a particular computation as another, "efficient" computer, then almost certainly my inefficient computer is "worse for the environment" than an efficient computer. 2. What if, on the other hand, I power my "inefficient" computer using solar power ? To avoid grid issues, I'll power my inefficient computer directly from a solar panel so that it isn't connected to the grid at all. The sunlight is going to be eventually converted to heat whether my computer is there or not; so what difference does it make?

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[math-fun] Draft of my September 2016 blog post
by James Propp 15 Sep '16

15 Sep '16

I started writing a new draft titled "Going Negative" and would love to get your feedback. I plan on publishing it on the 17th and will continue to tinker with it between now and the weekend. Is it too long? If so, what passages would you suggest I compress, or cut? I'm not an historian. Do I get my math history wrong, either blatantly (with mis-statements of fact) or subtly (by misplacement of emphasis or other forms of distortion)? I'm still confused about the differences between Frend's position and De Morgan's (and I'm sure the difference is an important one). I'm not a pre-college teacher. Do I misunderstand the pedagogical issues posed by negative numbers at the pre-college level? Suggestions for references, and comments of all kinds, are welcome. I appreciate candid criticism from people who are sympathetic to my aims but think I've fallen short of them. My prose style is designed to make the material accessible, but my breeziness should not be interpreted as indicating indifference to scholarly correctness. Please leave your feedback at https://mathenchant.wordpress.com?p=1196&shareadraft=57d777dd7094f keeping in mind that the comments of EVERYONE on math-fun will get funneled through the same email conduit; if you want me to know who you are, please sign your comments! If you sign your comments I'll assume (unless you indicate otherwise) that you don't mind my acknowledging your contribution. Title: Going Negative Beginning: Minus times minus equals plus / The reason for this we will not discuss. --- W. H. Auden, recalling a popular verse from his school days Ever tried mixing together your two least favorite foods? I suspect you haven't. Nobody mixes two noxious ingredients and expects the results to be tasty... Read more: https://mathenchant.wordpress.com?p=1196&shareadraft=57d777d d7094f Thanks, Jim Propp

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