There is a pattern in the binary expansion of this number. The request was sent by B.J. Mares on Sun Dec 3 15:20:18 PST 1995 The email address is: bjmares@teleport.com ------------------------------------------------------- The request was sent by Joe Keane on Sun Sep 10 05:02:26 PDT 1995 The email address is: jgk@netcom.com The number to be tested is: 1.38432969165678691636600070469187275993602894672280031682863878069088210808356345 The number of correct digits in the number: 79 The hints given by the user: It's log((3+sqrt(7))/sqrt(2)) or 1/2*arccosh(8). -------------------------------------------------------- The request was sent by (Mr.) B.J. Mares on Sat Dec 9 19:10:27 PST 1995 The email address is: bjmares@teleport.com The number to be tested is: .86224012586805457155779028324939457856576474276829909451607121455730674059051645804203844143861813$ 451257229030330958513908111490904372705631904836799517334609935566864203581911199877725969528883243$ Another binary pattern. --------------------------------------------------------- The request was sent by Jon Borwein on Sun Nov 5 06:09:28 GMT 1995 The email address is: jborwein@cecm.sfu.ca The number to be tested is: .01118680003287710787004681 The number of correct digits in the number: 20 The test(s) to be performed on the number: algebraic -------------------------------------------------------- 1.456791031046907 The number of correct digits in the number: 16 The test(s) to be performed on the number: algebraic gamma_multiplicative gamma_additve zeta_multiplicative zeta_additive psi_digamma linear_dependence_salvage The hints given by the user: p(0)=1 q(0)=2 p(i+1)=sqrt(p(i)*q(i)) i = 0,1,2,.. q(i+1)=(p(i) + q(i))/2 i = 0,1,2,.. x = lim p(i) = lim q(i) i->+inf i->+inf -------------------------------------------------------- The request was sent by Olivier Gerard on Mon Jan 29 18:48:42 PST 1996 The email address is: quadrature@onco.techlink.fr The number to be tested is: 1.062550805496255938 This number arises in the study of generalized Zeta functions on non associative sets. -------------------------------------------------------- The request was sent by Michael Mossinghoff on Fri Feb 9 14:40:28 PST 1996 The email address is: mjm@math.appstate.edu The number to be tested is: 1.296210659593309 (see below for 2500 digits of it). As I mentioned in the original note, it would be interesting to see if this number satisfies a simple polynomial of degree > 34. The simplest polynomial I know of that it satisfies is x^38-x^36-x^34-x^29+x^28-x^24-x^14+x^10-x^9-x^4-x^2+1 I found this during a search for polynomials with height 1, degree 38, and Mahler measure < 1.3. I also have a second new Salem number that would be interesting to try. Thanks for running this! Best regards, Mike Mossinghoff mjm@math.appstate.edu