May 8, 2009 |
Let us search for ever larger sporadic palindromes
of the form Ap + Bq (Sum Of Powers).
won178.htm (new) |
March 21, 2009 |
B.S. Rangaswamy presents some nice offshoots
after perusing the latest submission of Peter Kogel
i.e., pandigitals as products of two 5-digit palindromes.
won177.htm (new)
won175.htm (update) |
March 15, 2009 |
Shyam Sunder Gupta counted and announced on the
Number Theory List all the 21-digit palindromic primes.
palprim1.htm (update) |
January 13, 2009 |
Farideh Firoozbakht shows some intricate patterns.
leading to squares with only three distinct digits 0, 2 & 5.
threedigits.htm (update) |
November 24, 2008 |
Investigator Peter Kogel multiplies palindromes to
arrive at a beautiful wheel of pandigitals.
won175.htm (new) |
September 15, 2008 |
B.S. Rangaswamy shows some nice Hopping Numerals .
Is this a topic for further theorization ?
won174.htm (new) |
August 24, 2008 |
Justin Chan makes nice contributions to various topics
exosquar.htm (update)
circular.htm (update) |
July 28, 2008 |
Greg Childers factorized Rsm93.
revfact.htm (update) |
June 23, 2008 |
Programmer Daniel Fischer finishes the topic of finding
multipliers k such that n.k is palindromic. He did so by
writing some keen 'Haskell' code.
won36.htm (update)
won96.htm (update) |
May 27, 2008 |
Investigator Peter Kogel combines nine- & pandigitals by
using various operations. Some gems arose from his effort.
ninedig2.htm (update) |
May 25, 2008 |
Greg Childers sets a new milestone by factorizing Sm99.
factorlist.htm (update) |
March 31, 2008 |
B.S. Rangaswamy relates palindromes with
nine- & pandigitals
using straightforward multiplication by 9.
The offspring is a table of 34 nice equations !
won173.htm (new) |
February 16, 2008 |
Carlos Rivera's pandigital solutions to Mustonen's puzzle.
won172.htm (update) |
January 2, 2008 |
Feng Yuan sent in record Palindromic Squares
of odd lengths i.e., with 47, 49 & many more digits.
Palindromic Squares (update) |
December 11, 2007 |
Greg Childers factorized Sm94 and Rsm88.
factorlist.htm (update)
revfac.htm (update) |
June 17, 2007 |
A pandigital divertimento from Seppo Mustonen
won172.htm (new) |
May 23, 2007 |
Jean Claude Rosa presents the 43rd palindrome
expressible as the sum of the squares of two consecutives.
sumsquare.htm (update) |
May 21, 2007 |
Milton L. Brown makes a random walk around the
powers of ten and conjectures alongside.
won171.htm (new) |
February 25, 2007 |
Michael Bergman faces a ninedigital problem.
won170.htm (new) |
January 11, 2007 |
Farideh Firoozbakht adds two smallest base 2 pseudo-
primes of lengths 17 & 18 and comments her approach.
won125.htm (update) |
November 11, 2006 |
Farideh Firoozbakht found two nice consecutive primes
of tautonymic length 4949.
won169.htm (new) |
September 4, 2006 |
Carlos Rivera shows some remarkable pandigital curios.
won168.htm (new) |
June 12, 2006 |
Philippe Strohl factorized Sm98.
factorlist.htm (update) |
March 4, 2006 |
Greg's proof of this 15769-digit PDP combines
state-of-the-art factorization with three types of
primality testing and proving (BLS, CHG, ECPP).
This prime has only prime digits,
therefore it resides also at
won150.htm (update) |
February 25, 2006 |
Sean A. Irvine factorized Sm93.
factorlist.htm (update) |
February 18, 2006 |
Shyam Sunder Gupta counted and announced on the
Number Theory List the 19-digit palindromic primes.
palprim1.htm (update) |
February 2, 2006 |
Harvey Dubner retakes the palindromic prime record
10150008 + 4798974 * 1075001 + 1
Congratulations with this number of 150009 digits !
palprim2.htm (update) |
January 23, 2006 |
Sean A. Irvine factorized Sm92.
factorlist.htm (update) |
December 31, 2005 |
Paul Jobling and Harvey Dubner each established a new
palindromic prime record this month
10150006 + 7426247 * 1075000 + 1
10140008 + 4546454 * 1070001 + 1
Congratulations both for your amazing palindromes
of resp. 150007 and 140009 digits !
palprim2.htm (update) |
November 12, 2005 |
B.S. Rangaswamy's book "Wonders of Numerals"
inspired me to expand on some of the subjects, especially
when it deals with palindromes, pan- and/or ninedigitals.
won167.htm (new) |
October 25, 2005 |
Sean A. Irvine factorized Sm90 and Sm91.
factorlist.htm (update) |
October 24, 2005 |
A new property for palindrome 69696.
won26.htm (update) |
October 15, 2005 |
Beast's real mark devalued to '616'.
Reported by Enoch Haga.
won166.htm (new) |
September 12, 2005 |
Sean A. Irvine factorized Sm87, Sm88 and Sm89.
factorlist.htm (update) |
September 4, 2005 |
B.S. Rangaswamy from Bangalore, India generated 117
pandigitals from palindromes through Fibonacci iteration.
ninedig2.htm (new) |
August 28, 2005 |
Sean A. Irvine factorized the Sm83 up to Sm86
by using GNFS.
Philippe Strohl completed factorization of Rsm80
up to Rsm87
revfact.htm (major update) |
August 27, 2005 |
Robert Backstrom factorized the c131 of the 79th
Reversed Smarandache Concatenated Number by GGNFS.
Rsm78 = 3 * 17 * 47 * p14 * p62 * p69
revfact.htm (update) |
August 3, 2005 |
Sean A. Irvine factorized the c139 of the 78th
Concatenated Smarandache Number by using GNFS.
Sm78 = 2 * 3 * 31 * 185897 * p57 * p83
factorlist.htm (update) |
July 24, 2005 |
Peter Kogel investigated more nine digit powers.
Some notable results are highlighted at the start.
ninedig4.htm (update) |
June 28, 2005 |
Robert Backstrom factorized the c142 of the 76th
Reversed Smarandache Concatenated Number by GGNFS.
Rsm76 = 53 * p63 * p79
revfact.htm (update) |
May 30, 2005 |
What is the relation between 66 and a palindromic circle.
Giovanni Resta's amazing picture will show you!
won165.htm (new) |
May 18, 2005 |
Read Peter Kogel's addendum to Nine and Ten digit powers.
ninedig4.htm (update) |
March, 2005 |
TurkZeka.Com Aim : was established with a purpose of
helping puzzle fans improve their ability of imaging,
finding winding key, heading conclusion, finding out hidden
properties etc. and also having a nice and useful time.
Created by Yilmaz Ekici.
Turkzeka - Puzzle Competition |
March 24, 2005 |
Follow John Morse's explanation and discovers with him
why 3816547290 is such a unique pandigital number.
ninedig4.htm (update) |
March 20, 2005 |
Robert Hein discovers some important equations for
the construction of all infinite Pythagorean Triples.
won164.htm (new) |
March 8, 2005 |
Zakir Seidov puts palprimes between two ones
and collects statistical data from it.
palprim5.htm (update) |
February 27, 2005 |
Peter Kogel investigates nine and ten digit squares.
Along the way he discovered some fascinating specimen.
ninedig4.htm (update) |
February 20, 2005 |
Jens Kruse Andersen contributes some gigantic (prp)
primes and lays the foundation for the smallest gigantic
semiprime.
WONplate 144 (update)
palprim1.htm (update) |
January 23, 2005 |
Zakir Seidov contributes a list of palindromic areas
of primitive Phytagorean triangles (PPTs).
WONplate 163 (new) |
January 16, 2005 |
Enjoy Hugo Sanchez' latest presentation of
Sumas Palindromizadas con Factores de Corrección.
Naturales del 1 al 100.
WONplate 162 (new) |
January 10, 2005 |
Nearest (probable) primes bordering powers of ten
situated at equal distances... (by pdg)
and all three with palindromic displacements so far!
WONplate 161 (new) |
January, 2005 |
PuzzleUp is a new weekly problem and games website that
is set to launch on January 2nd 2005 and which will consist
of 50 individual problems over a one year basis.
Created by Emrehan Halici.
puzzleup - weekly puzzle competition |
December 16, 2004 |
Jean Claude Rosa explains why there are no 18-digit
palindromic products of two ninedigitals.
twonine.htm (update) |
December 15, 2004 |
David Broadhurst found a nice addendum to
Nelson Mandela's prison number 46664
in the form of a palindromic (probable) prime.
won154.htm (update) |
November 24, 2004 |
Harvey Dubner establishes again a new palindromic prime
record 10130022 + 3761673 * 1065008 + 1
Congratulations with this number of 130023 digits !
palprim2.htm (update) |
November 18, 2004 |
Sean A. Irvine factorized the c133 of the 75th
Concatenated Smarandache Number by GNFS.
Sm75 = 3 * 5^2 * 193283 * p47 * p87
factorlist.htm (update) |
November 5-12, 2004 |
New Palindromic Subsets of Concatenated Prime
Sequences were found by G. Resta, J. K. Andersen
and F. Firoozbakht in Carlos Rivera's Puzzle 289.
palconca.htm (update) |
October 18, 2004 |
Two Prime Numbers starting from 18 and 19 lead us
to the list of Concatenated Smarandache Numbers
that are Probable Primes (by Farideh Firoozbakht)
won160.htm (new) |
September 20, 2004 |
Andrei Cucuianu (from Romania) demonstrates two
properties of numbers and their reversals.
Another 9/11 story...
won159.htm (new) |
September 2, 2004 |
Extracting palindromes from Pi (e.g. 7446447 &
110000011). A puzzle/question by the late Klaas Craye.
won158.htm (new) |
August 15, 2004 |
Find larger and larger palindromic primes
dividing numbers of the form k.bn ± 1.
won157.htm (new) |
August 7, 2004 |
A palindromic formula by Paul Oliverio. Check it out !
won156.htm (new) |
June 28, 2004 |
A 3*3 antimagic square composed of primes with
sums in a prime arithmetical progression cannot exist.
WONplate 132 (update) |
April 6, 2004 |
Let's acclaim Harvey Dubner's latest palindromic prime
record 10120016 + 1726271 * 1060005 + 1
Congratulations with this number of 120017 digits !
palprim2.htm (update) |
March 23, 2004 |
Philippe Strohl completed the factorization of the 73th
Concatenated Smarandache Number by GMP-ECM.
Sm73 = 37907 * p46 * p87
factorlist.htm (update) |
January 3, 2004 |
Alexander Kruppa and Paul Leyland need to give up !
They have done 5500 curves at B1=11M, and 9000 curves
at B1=44M, but have been unable to find a factor of
the c204 of HP49(100).
Home Primes (update) |
December 30, 2003 |
Philippe Strohl completely factorized Rsm_67 !
The next "unknown factorization" for reversed
smarandache concatenated numbers is now Rsm_76.
revfact.htm (update) |
December 26, 2003 |
David Broadhurst announced once again a record
palindromic prime (36401 digits) composed solely
of prime digits.
WONplate 150 (update) |
December 1, 2003 |
not merely a date...
46664, not merely a palindrome...
December 1st is worldAIDSday...
46664 is a vital campaign... |
|
November 25, 2003 |
Dw discovers more palindromes in the concatenated
string of consecutive prime numbers.
palconca.htm (update) |
November 3, 2003 |
Enjoy Hugo Sanchez' presentation of
Patrones Palindrómicos con
Multiples Operaciones Aritméticas.
WONplate 153 (new) |
October 20, 2003 |
Ninedigital expressions
Fourteen # variations have been statistically analyzed.
Can you discover additional curiosities ?
ninedig3.htm (update) |
October 13, 2003 |
Tautonymic numbers
Introducing a new class of recreational numbers.
WONplate 152 (new) |
September 1, 2003 |
Allan Jenks presents his intriguing problem
Recurring last digit multiplication numbers.
WONplate 151 (new) |
August 5, 2003 |
David Broadhurst
announced via the Number Theory List
a record palindromic prime (30913 digits)
composed solely of prime digits.
Details via WONplate 150 (new) |
August 2, 2003 |
Patrick prime proved a 3037-digit PDP using Primo 2.1.1
3(2)30353 or 2*(103037-1)/9 + (103036+1)
taking him ~171 hours on a 3000 MHz Intel Pentium 4 cpu. |
July 24, 2003 |
Philippe Strohl found all the factors of rsm65
Reversed Smarandache Concatenated Numbers (update) |
July 21, 2003 |
Hisanori Mishima revised his page
Chapter 2. Squares consisted of 3 different digits
The search range has now been extended from 1017 to 1020
There are 70 new sporadic solutions added to the list.
Entries 013 and 678 still remain without solutions.
Squares containing at most three distinct digits (update) |
July 16, 2003 |
Alex Kruppa & Paul Leyland
completed a few more stages of the search for HP49.
They successfully factored HP49(97).c151
into p55 * p96 after intelligent teamwork.
Method & prime factors can be found at the
Home Primes page.
HP49(98) and HP49(99) factored easily under ECM.
The 100th step, however, appears to be not so easy!
HP49(100) 3 * 37 * 2789 * c204
Paul and Alex think this 100th step will mark the end of the
HP49 sequence expansion for a long time to come... |
July 11, 2003 |
Hans Rosenthal found (prime proved) a new 6959-digit
Smoothly Undulating Palindromic Prime (SUPP for short)
3(23)3479 = (32*106959-23)/99
It took Hans around 18 months (!) to finish the proof.
He thereby also established a new Primo ECPP world record
See http://www.ellipsa.eu/primo/record.html |
June 21, 2003 |
Jeff prime proved a 5867-digit PWP using Primo 2
Rank 2nd at that moment !
(1)29337(1)2933 or (105867-1)/9 + 6*102933
taking him ~3406 hours on a 1.33GHz Athlon box. |
June 17, 2003 |
Dw found again a new record binary decimal palindrome !
A milestone, as he passed the magic 100 digit length.
10 1010110011 0000010011_
1100000010 0001000111 1010010111 1010010111_
1000100001 0000001111 0010000011 0011010101
3390741646331381831336461470933
The binary palindrome contains 102 digits !
The decimal string contains 31 digits !
nobase10.htm |
May 21, 2003 |
Dw found a new record binary decimal palindrome
1 0100110010_
1111101111 1100001110 1100100000 0010001000_
0000100110 1110000111 1110111110 1001100101
1609061098335005338901609061
The binary palindrome contains 91 digits !
The decimal string contains 28 digits !
nobase10.htm |
May 4, 2003 |
Two primes for a square please.
A simple search puzzle... with hard to find solutions !
WONplate 148 |
April 27, 2003 |
181, 313 & 545 are the only PDP's equal to
(plateau and depression primes)
the sum of the squares of two consecutive integers.
(181 = 92 + 102)
(313 = 122 + 132)
(545 = 162 + 172)
WONplate 147 (new) by Jean Claude Rosa |
April 13, 2003 |
Dw found a new record binary decimal palindrome
1010010001 1101011100 1110010101_
0010100001 0100000010 1000010100_
1010100111 0011101011 1000100101
795280629691202196926082597
The binary palindrome contains 90 digits !
The decimal string contains 27 digits !
nobase10.htm |
February 16, 2003 |
A threefold (probable) PRIME search.
WONplate 146 (new) |
January 27, 2003 |
Daniel Heuer announced a new PWP world record (#3033).
10104281-1052140-1 has over 100000 digits...
the largest ever base-10 palindromic prime !
ps. exponent 104281 is itself prime.
Palindromic Wing Primes (update) |
January 26, 2003 |
Plateau & Depression Primes
(or PDP's for short) are numbers that are primes,
palindromic in base 10, and consisting of an internal
repdigit sandwiched by a pair of identical digits
different of course from the repdigit itself.
Plateau and Depression Primes
Everyone is invited to work on or to extend this new
collection that forms the third part of a palindromic
prime TRILOGY (SUPP - PWP - PDP). |
January 20, 2003 |
Alex Kruppa & Paul Leyland
completed two more stages of the search for HP49.
They successfully factored HP49(95).c153
into p68 * p85 after months of work.
Method description & prime factors can be found at
Home Primes (update)
I'm still wondering if they may have to go
beyond 100 steps... |
January 14, 2003 |
1.241 trillion digits of computed by Prof. Y. Kanada.
WONplate 40 (update) |
January 2, 2003 |
Jeff prime proved a 4769-digit PWP using Primo.
(3)23841(3)2384 or (104769-1)/3 - 2*102384 while
Daniel got a worldrecord 95019-digit PWP
(9)475098(9)47509 or (1095019-1) - 1047509
using PrimeForm.
The (palindromic) wings are really taking off... |