[math-fun] New Mersenne Prime confirmed
Tony Reix reported this morning on the NMBRTHRY list that the Mersenne prime 2 ^ 25964951 - 1 is confirmed. A triple check is expected to finsh tomorrow. George Woltman has requested that the exponent be kept off "the web" until his press release is posted, and the discoverer's local newspaper has a chance to report it. This is probably M42. It is the largest known Mersenne prime. The next smaller MP exponent known is 24036583, giving modest support to the cluster theory. The GIMPS project is burning at about 16Tflops. Every prime exponent < 15 million has been tested at least once. There are still lots of untested numbers < 25 million, so there's a chance of another, smaller, MP being found. Rich rcs@cs.arizona.edu
I recently did a column on approximations. http://www.maa.org/editorial/mathgames/mathgames_02_14_05.html I've gotten a lot of results, including an article on class polynomials: http://www.geocities.com/titus_piezas/Approximations.htm The following is a TeX document that includes all of the best approximations I've received. I plan to split off the Class numbers into their own table, as I did with the approximations using Sin/Cos. I plan to exclude Sin/Cos in the next version of the rules. I did a little contest on my site -- whoever sends me the approximation with the highest keenness, on or before 15 March, wins $50 from me. It's looking like Derek Ross and Titus Piezas will be winning it, at the moment. --Ed Pegg Jr \documentclass{amsart} \usepackage{graphicx} \begin{document} \begin{tabular}{|c|c|c|c|l|} \hline Keenness & Com & Dscv & Result & Function\\ \hline $2.202$ & 13 & CH & $163 + 2.321 \times 10^{-29}$ & $ ( {\log(640320^3+744) / \pi} )^2$\\ $2.115$ & 22 & CH & $\pi - 9.303 \times 10^{-47}$ & ${\log((640320^3+744)^2-393768)\over\sqrt{652}}$\\ $2.020$ & 6 & CH & $640320^3 + 744 - 7.5003 \times10^{-13}$ & $ e^{\sqrt{163} \pi } $\\ $1.732$ & 7 & TP & $640320^3 + 744 - 7.4888 \times10^{-13}$ & $ (x^3-6x^2+4x-2)_1^{24}-24$\\ $1.846$ & 4 & DR & 5.999999958593812545675 $ & $ \pi - F_{\alpha} + 6^{- \gamma}$\\ $1.716$ & 4 & DR & $45.0000001373108134890 $ & $ \frac{1}{4}+3^{\pi + 1/ \pi }$\\ $1.679$ & 3 & RS & $e + 0.0000091665339017 $ & $ 2^{.4^{-.4}}$\\ $1.575$ & 4 & MH & $G-4.2542 \times 10^{-7}$ & $ \sqrt[52]{\frac{1}{96}} $\\ $1.546$ & 4 & DR & $12.0000006524114304506 $ & $ ( 1/ \gamma + 3 \gamma )^2$\\ $1.512$ & 4 & DR & $49.9999991061598799437 $ & $ 7^{\phi^{e^{K^{-1}}}}$\\ $1.506$ & 5 & DR & $2.99999997062451090800 $ & $ \frac{1+5 \sqrt[5]{6}}{e}$\\ $1.501$ & 5 & DR & $14212169.0000000311917 $ & $ (\phi +\pi ) 12^6 $\\ $1.499$ & 4 & DR & $1.00000101156823755142 $ & $ \frac{1}{8}+\sqrt[7]{\frac{\pi}{8}}$\\ $1.484$ & 5 & DR & $110.999999961886583322 $ & $ \sqrt[e]{9!+\frac{\pi }{3}} $\\ $1.471$ & 5 & DC & $5.99999995619189332962 $ & $ \log \left(\pi ^4+\pi ^5\right) $\\ $1.468$ & 4 & DR & $2.00000134678219335309 $ & $ (4+1 / \phi )^{e/6}$\\ $1.449$ & 5 & DR & $9112774.00000005695228 $ & $ \left(52+\frac{8}{e}\right)^4 $\\ $1.443$ & 6 & DR & $45.9999999978124612031 $ & $ 3^{(20+\gamma)/6}+e$\\ $1.414$ & 5 & DR & $4.99999991507443309454 $ & $ \sqrt[6]{e} \sqrt[\pi ]{93}$\\ $1.413$ & 6 & MH & $\gamma - 3.3307 \times 10^{-9}$ & $ \frac{1}{\sqrt{3}}-\frac{1}{7429}$\\ $1.412$ & 5 & EP & $e + 8.6631 \times 10^{-8} $ & $ 3-\sqrt{5/(7\times9)} $\\ $1.390$ & 4 & SR & $2143.00000274805361920 $ & $ 22 \pi ^4$\\ \hline \end{tabular} \bigskip \begin{tabular}{|cccl|} \hline Pi & $\pi$ & A000796 & $3.14159265358979323846264338327950288419$\\ e & $e$ & A001113 & $2.71828182845904523536028747135266249775$\\ Golden Ratio & $\phi$ & A001622 & $1.61803398874989484820458683436563811772$\\ Euler's Constant & $\gamma$ & A001620 & $0.57721566490153286060651209008240243104$\\ Feigenbaum alpha & $F_{\alpha}$& A006891 & $-2.502907875095892822283902873218215786$\\ Khinchin constant & $K$ & A002210 & $2.68545200106530644530971483548179569382$\\ Catalan constant & $G$ & A006752 & $0.91596559417721901505460351493238411077$\\ \hline \end{tabular} \bigskip \begin{tabular}{|c|c|c|c|l|} \hline Keenness & Com & Dscv & Result & Function\\ \hline $2.781$ & 7 & MS & $-0.99999999999999999996$ & $ \sin (80.68\times2^.2)$\\ $2.381$ & 7 & MT & $-0.9999999999999999785 $ & $ \sin \left(2017 \sqrt[5]{2}\right) $\\ $2.336$ & 4 & x & $-0.9999999995456589801 $ & $ \cos (355) $\\ $2.280$ & 4 & JC & $-0.9999999992436801330 $ & $ \Re\left((20+\pi )^i\right) $\\ $2.120$ & 6 & OR & $ 0.9999999999998081724 $ & $ \sin (54^{6/53})$\\ $2.023$ & 6 & EF & $-0.9999999999992758284 $ & $ \cos (\sqrt[7]{52} + \sqrt[6]{7} )$\\ $1.923$ & 10 & DT & $-1 + 5.84709 \times 10^{-20}$ & $ \cos \left(\log \left(\frac{10691}{462}\right)\right)$\\ $1.669$ & 3 & x & $-0.9999902065507034570 $ & $ \sin (11) $\\ $1.442$ & 6 & OR & $-0.9999999977723618905 $ & $ \cos ( \log (44^{44}) ) $\\ \hline \end{tabular} \bigskip \begin{tabular}{|rcl|} \hline CH & is & Charles Hermite \\ DC & is & Dario Castellanos \\ DR & is & Derek Ross \\ DT & is & David Terr \\ EF & is & Erich Friedman \\ EP & is & Ed Pegg Jr \\ JC & is & John H. Conway \\ MH & is & Mark Hudson \\ MS & is & Mike Shafer \\ OR & is & Oliver Runge \\ RS & is & Richard Sabey \\ SR & is & Srinivasa Ramanujan \\ TP & is & Titus Piezas III \\ \hline \end{tabular} \end{document}
participants (2)
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ed pegg -
Schroeppel, Richard