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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 pseudoprimes
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 Childers certified a record (34*1015768—43)/9
Plateau and Depression Prime (or PDP's for short)

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.

ninedigits.htm (new)
August 28, 2005 Sean A. Irvine factorized the Sm83 up to Sm86
by using GNFS.

factorlist.htm (major update)
Philippe Strohl completed factorizations 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.
ninedigits.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.
ninedigits.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.
ninedigits.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.
ninedigits.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...

More at WONplate 154
November 25, 2003 Dw discovers more palindromes in the concatenated
string of consecutive prime numbers. flash
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 or interesting facts ?
ninedigits.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 De Geest completed the certification for a record
Plateau and Depression Prime (or PDP's for short)

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.net/primo/record.html
June 21, 2003 Jeff Heleen just completed the certification for a new
Palindromic Wing Primes (or PWP's for short)

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 binarydecimal palindrome !
A milestone, as he passed the magic 100 digit length.
10 1010110011 0000010011
11
00000010 0001000111 1010010111 1010010111
1
000100001 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 binarydecimal 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 binarydecimal 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 Pi computed by Prof. Y. Kanada.
WONplate 40 (update)
January 2, 2003 Jeff Heleen and Daniel Heuer each found
new Palindromic Wing Primes (or PWP's for short)

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...

Archive Whatsnew 2002
Archive Whatsnew 2001
Archive Whatsnew 2000
















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Patrick De Geest - Belgium - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com