News
Archive: December 1999
Sol'n Puzzle 76, q.3  Chris Nash has also solved (21/12/99) the question 3 of the puzzle 76  Posted on Friday, December 31, 1999  
Solution of question 1 of the Puzzle 76  Chris Nash has solved (20/12/99) the question 1 of the puzzle 76 and consequently and in certain unexpected manner (applying the Möbius function to each divisor of n  see the equation 7 ) the question 2 also... I must confess that I'm completely astonished for the beauty of this reasoning and in particular for the unknown (for me) trick of the so called "Möbius inversion formula"....phew!!!
 Posted on Thursday, December 30, 1999  
Solution of Puzzle 72  Felice Russo (20/12/99) "Item 2. Puzzle 72, No solution for rank 7/10 has been found up to 10^11."
 Posted on Thursday, December 30, 1999  
See Problem 5  Jo Yeong Uk (16/12/99) has factored c100 from W542. See Problem 5.  Posted on Thursday, December 30, 1999  
The smallest prime with 200 digits  Chris Nash found the smallest prime with 2000 digits and digit sum 2000. Here is his email sent at 29/11/99, solving completely the 4th claim of the Puzzle 75. Chris Nash has also found smaller primes of the form k*2^n+/1, k<2^n, such that SOD=2000:  Posted on Thursday, December 30, 1999  
Record to the Puzzle 54  Warut Roonguthai (28/11/99) improved his own record for the largest pair of primes of the form (p, 4*p^2+1, Puzzle 54) getting now: p=591279151*2^7000 + 1 (2116 digits) and 4*p^2+1 has 4233 digits".  Posted on Thursday, December 30, 1999  
See Conjecture 15  Warut Roonguthai thinks that maybe it's easier to probe the primality of (2^1048573+1)/3, than getting a small factor of it. See Conjecture 15.  Posted on Thursday, December 30, 1999  
Several results to Puzzle 72  Felice Russo sent (26/11/99) several results for item 4. of the Puzzle 72.  Posted on Thursday, December 30, 1999  
Remarkable extension  Jaime Ayala & Carlos Rivera got a remarkable extension of one conspicuous Ramanujan's equation
 Posted on Thursday, December 30, 1999  
Confirmed the result for the Puzzle 74  Landon Curt Noll and  independently  Jim Howell confirmed the Enoch's results for the Puzzle 74. Howell also has calculated "SOD adding by separate the digits in odd position and the digits in even position" as was asked in the hint 2.  Posted on Thursday, December 30, 1999  
See Puzzle 74  Enoch Haga has calculated that SOD(269725931) = 9440671 . How? See Puzzle 74.  Posted on Thursday, December 30, 1999  
Solution of Puzzle 54  Chris Nash sent the following chain of 5 primes of the type asked in the Puzzle 54, starting with the prime 1333168253 (10 digits), beating the before record...
 Posted on Thursday, December 30, 1999  
A surprising result of Puzzle 54  A surprising result has been obtained for the question b) of the Puzzle 54, by Chris Nash: no chain larger than 5 is possible!!.
 Posted on Thursday, December 30, 1999  
Solution if the Gordon Lee Puzzle 1  This last October 31, Wilfred Whiteside improved his better solution for the 8x8 matrix of the Gordon Lee Puzzle. Now he got a solution with 382 primes inside. By his side James Bonfield started tackling the 4x4x4 version of this puzzle and the November 1, he found several (7) solutions with 233 primes inside.
 Posted on Thursday, December 30, 1999  
See Puzzle 54  Warut Roonguthai produced a higher pair (p, 4p^2+1) whose p = 140873041*2^4000+1 (1213 digits). See Puzzle 54.  Posted on Thursday, December 30, 1999  
Earliest CC1stK of L=14  Paul Jobling sent (28/10/99) the earliest CC1stK of L=14, and also the earliest CC2ndK for L= 14 and L=15, see Problem 26.
 Posted on Thursday, December 30, 1999  
Solution to Problem 5  Jo Yeong Uk (8/10/99) has factored c101 from W404, Problem 5.  Posted on Thursday, December 30, 1999  
Chris Nash has probably found ......  Chris Nash has probably found the following smallest contiguous different three primes asked in the Problem 18. One of them is an Eulerprobableprime consisting of 3057 digits...
 Posted on Thursday, December 30, 1999  
Solution to Puzzle 67  Jack Brennen has solved completely the Puzzle 67.
 Posted on Thursday, December 30, 1999  
Solution for Puzzle 70  Eric Weisstein has completed the table base 10 for the Puzzle 70.
 Posted on Thursday, December 30, 1999  
Surfing....  Surfing through the very organized and complete pages of Mutsumi Suzuki I have found a smaller and older matrix than the 9x9 magic square of Alen W. Johnson Jr. (see Puzzle 68). This older one is composed of nothing more but 81 consecutive matrix (from 37 to 479), and was discovered by Akio Suzuki... in 1957!  Posted on Thursday, December 30, 1999  
Contributions to the Puzzle 50  Paul Leyland has sent (25/9/99) two very interesting contributions to the Puzzle 50 that  in principle  permit to get approximations to pi with any desired degree of accuraccy using only a fixed number of prime numbers, producing concomitantly any desired Rank value.  Posted on Thursday, December 30, 1999  
Result for the Puzzle 50  Jean Brette has improved the Jud McCranie's result for the Puzzle 50, obtaining an approximation for the pi value of Rank = 200%  Posted on Thursday, December 30, 1999  
Contributions to Puzzle 66  Jud McCranie and Enoch Haga have sent some contributios to Puzzle 66  Posted on Thursday, December 30, 1999  
A pentagradeprimerelation for the Puzzle 65  T.W.A. Baumann found (31/08/99) a pentagradeprimerelation and two heptagrade prime relations for the Puzzle 65  Posted on Thursday, December 30, 1999  
Solution of Problem 22  Wolfgang Creyaufmüller and independently Jim Howell have factored the "c97" from Problem 22 (term 1131 in the Aliqout Sequence).  Posted on Thursday, December 30, 1999  
A higher matrix for Puzzle 1  Wilfred Whiteside has gotten a higher 8x8 matrix (379 prime) than the Hernández one (373), for the Gordon Lee, puzzle (Puzzle #1).  Posted on Thursday, December 30, 1999  
Similar solution of Problem 21  TWA Baumann & Enoch Haga sent similar solutions to part a) of Problem 21.  Posted on Thursday, December 30, 1999  
Solution to Puzzle 1  Alberto Hernández Narváez from México sent a record matrix 8x8 for the Gordon Lee Puzzle #1.  Posted on Thursday, December 30, 1999  
Contributions to Problem 20  Jud McCranie has sent (20/07/99) some contributions to Problem 20.  Posted on Thursday, December 30, 1999  
Solutions of Problem 19  Jud McCranie, T.W.A. Baunmann & Enoch Haga, solved the part a) of the Problem 19. See also their contributions to the part b) and my comments about this.  Posted on Thursday, December 30, 1999  
Details for n=4, Puzzle 63  Jim R. Howell sent (10/07/99) the details for n = 4, Puzzle 63.
 Posted on Thursday, December 30, 1999  
Contributions to Puzzle 39  Felice Russo sent (June 99) some contibutions to Puzzle 39.
 Posted on Thursday, December 30, 1999  
Contribution to Puzzle 3  Aale de Winkel sent (30/06/99) a contribution to Puzzle 3  Posted on Thursday, December 30, 1999  
Contributions to Puzzle 8  Felice Russo sent (28/06/99) some contibutions to Puzzle 8.  Posted on Thursday, December 30, 1999  
Solution of Puzzle 62  Jud McCranie has solved the question 1 of Puzzle 62. He also has found the solution to the question 2...  Posted on Thursday, December 30, 1999  
Factored C97 of W368  Jo Yeong Uk (22/6/99) has factored C97 of W368 (See Problem 5). He spent about 3 months, using the code GMPECM 3, by P. Zimmermann and a 167 Mhz PC.  Posted on Thursday, December 30, 1999  
A new triplet of pimes  Warut Roonguthai obtained a new triplet of primes in A.P. beating his own previous record (See Puzzle 34).  Posted on Thursday, December 30, 1999  
A great jump!!!!  A great jump has been done by a new puzzler, T.W.A. Baumann, from Germany: an 11x11 solution for the Puzzle 4!!!  Posted on Thursday, December 30, 1999  
Solution of Puzzle 60  Carlos Rivera found (15/06/99) a 'Generalized Cunningham Chain' of first order and k = 10 members starting with the prime P1 = 228698251, for the Puzzle 60.  Posted on Thursday, December 30, 1999  
Explanation to Puzzle 59  Jim R. Howell sent (14/06/99) an explanation to Puzzle 59. Maybe you'll find interesting/educative to read  below the Howell's solution  "The story behind this puzzle" written for Jud McCranie.
 Posted on Thursday, December 30, 1999  
Solution of Puzzle 57  It was again Jim R. Howell who solved (12/06/99) the part a) of the Puzzle 57 with an argument that I would say that it is absolutely simple not without being at the same time complete & clever.  Posted on Thursday, December 30, 1999  
Two solutions to Puzzle 47  Warut Roonguthai sent (10/6/99) two solutions to Puzzle 47, previously reported in the Eric Weisstein's "Treasure Troves of Science".  Posted on Thursday, December 30, 1999  
Solutions to Puzzle 57  Jim R. Howell has found (10/06/99) some solutions to Puzzle 57, part b)  Posted on Thursday, December 30, 1999  
Formula for Puzzle 55  Yves Gallot found (5/6/99) a formula to calculate the Last Odd Term sequence of the Patrick De Geest's Puzzle No. 55, extending the search for primes up the 1000th generation, finding other 12 probable primes.  Posted on Thursday, December 30, 1999  
Solutions to Puzzle 32  Felice Russo has produced (4/6/99) several solutions to Puzzle 32, (and maybe a method to produce larger and larger solutions...)  Posted on Thursday, December 30, 1999  
Solution of Puzzle 56  Jud McCranie solved (1/6/99) part a) of Puzzle 56.  Posted on Thursday, December 30, 1999  
Another sequence of Problem 17  Jud McCranie has gotten  at last, 27/05/99  a sequence of 11 terms: 1477271183 through 1477271387, solving the Problem 17. One day after he got a 12 terms sequence, from 9387802769 to 9387803033  Posted on Thursday, December 30, 1999  
Another solution of Puzzle 54  Rudy Ruiz and Jud McCranie solved the same day (24/05/99) and independently the part a) of Puzzle 54. Jim R. Howell produced (24/05/99) two higher pairs p, 4p^2+1, for the same puzzle and Felice Russo produced still two higher pairs.  Posted on Thursday, December 30, 1999  
One more sequence for Problem 17  Jud McCranie sent (May 22, 1999) one more 10 members sequence of consecutive reversible and non palindromic primes, 9 digits each, for the Problem 17.  Posted on Thursday, December 30, 1999  
Another solution to Puzzle 31  Jack Brennen has obtained (21/05/99) another solution to Puzzle 31.  Posted on Thursday, December 30, 1999  
Another sequence of Problem 17  Felice Russo has obtained (May 21, 1999) another sequence of 10 consecutive reversible non palindromic primes, 8 digits each. See Problem 17.  Posted on Thursday, December 30, 1999  
Largest sequences  Jack Brennen has improved (May 20) the sequences of consecutive primes types 4k+1 and 4k+3. See my The Largest sequences of primes page.  Posted on Thursday, December 30, 1999  
Solutions for Puzzle 4  Wilfred Whiteside has produced (1415/05/99) all the solutions for the 4x4 and 5x5 dimensions of the Puzzle No. 4 (and some 'exotic' ones of the 6x6)  Posted on Thursday, December 30, 1999  
Contribution to Puzzle 48  Felice Russo has sent (1011/05/99) other contributions to Puzzle 48 and Puzzle 52.  Posted on Thursday, December 30, 1999  
Solution of Puzzle 45  Wilfred Whiteside has solved absolutely (9/5/99) the Puzzle No. 45.
 Posted on Thursday, December 30, 1999  
Current solution to Puzzle 1 is unique  Eric W. Weisstein has probed completely by exhaustive enumeration (8/5/99) that the current solution to Puzzle No. 1 of the matrix 3x3 (30 primes) is unique and maximal.  Posted on Thursday, December 30, 1999  
Solution for the case K=2 of Puzzle 52  Jud McCranie has obtained (5/5/99) other 29 solutions for the case K=2, Puzzle 52, for primes < 2^32, and no one solution for K=>3...  Posted on Thursday, December 30, 1999  
Solution of Puzzle 48  Felice Russo has found (4/5/99) a solution to b) of Puzzle 48  Posted on Thursday, December 30, 1999  
Take a look  You need to take a look of the very smart solutions of Jud McCranie (to Puzzle No. 50, Rank = 130.4%!!!) and Wilfred Whiteside (to Puzzle 1 & Puzzle 37)  Posted on Wednesday, December 29, 1999  
100% Ranking approximation  Felice Russo has sent (28/04/99) a 100% Ranking approximation to Pi, Puzzle No. 50!!!.... Congratulations, Felice. Then the real current challenge now is to beat that 100% limit, don't you think so?  Posted on Wednesday, December 29, 1999  
Another Solution to Puzzle 50  Carlos Rivera has obtained (23/04/99) another solution to Puzzle No. 50, approximating Pi wth 553 digits for primes, producing 547 correct digits, for a rank of 98.91%.  Posted on Wednesday, December 29, 1999  
