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The record Palindromic Primes

[ Submitted October 18, 2021 ]The newest palindromic prime record is from Propper and Batalov 10 ^{1888529} – 10^{944264} – 1(1888529 digits) Written out, it's 944264 nines, an eight, and 944264 more nines and is therefore a PWP or a Palindromic Wing Prime. Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=132851 Top Twenty Record Palindromic Primes |

[ Submitted September 15, 2021 ]This palindromic prime is from Propper and Batalov 10 ^{1234567} – 20342924302 * 10^{617278} – 1(1234567 digits) Source (The PrimePages, NMBRTHRY, ...) https://primes.utm.edu/primes/page.php?id=132715 |

[ Submitted September 29, 2021 ]This palindromic prime is from Propper and Batalov 10 ^{1234567} – 3626840486263 * 10^{617277} – 1(1234567 digits) Source (The PrimePages, NMBRTHRY, ...) https://primes.utm.edu/primes/page.php?id=132766 |

[ Submitted September 29, 2021 ]This palindromic prime is from Propper and Batalov 10 ^{1234567} – 4708229228074 * 10^{617277} – 1(1234567 digits) Source (The PrimePages, NMBRTHRY, ...) https://primes.utm.edu/primes/page.php?id=132767 |

[ Submitted August 6, 2021 ]This palindromic prime is from Makoto Morimoto 10 ^{490000} + 3 * (10^{7383} – 1)/9 * 10^{241309} + 1(490001 digits) Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=132591 Nieuw (voorlopig) grootste palindroom-priemgetal ontdekt https://www.mersenneforum.org/showthread.php?p=579376 |

[ Submitted November 16, 2014 ]This palindromic prime is from Serge Batalov 10 ^{474500} + 999 * 10^{237249} + 1(474501 digits) Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=118775 http://groups.yahoo.com/group/primeform/message/11538 |

[ Submitted July 27, 2021 ]This palindromic prime is from Makoto Morimoto 10 ^{400000} + 4 * (10^{102381} – 1)/9 * 10^{148810} + 1(400001 digits) Source (The PrimePages, NMBRTHRY, ...) https://primes.utm.edu/primes/page.php?id=132557 |

[ Submitted November 16, 2014 ]This palindromic prime is from Serge Batalov 10 ^{390636} + 999 * 10^{195317} + 1(390637 digits) Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=118773 http://groups.yahoo.com/group/primeform/message/11536 |

[ Submitted November 15, 2014 ]This palindromic prime is from Serge Batalov 10 ^{362600} + 666 * 10^{181299} + 1(362601 digits) Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=118770 http://groups.yahoo.com/group/primeform/message/11535 |

[ Submitted March 5, 2014 ]This palindromic prime is from David Broadhurst Phi(3, 10 ^{160118}) +(137 * 10 ^{160119} + 731 * 10^{159275}) * (10^{843} – 1)/999(320237 digits) Written out it looks like this : 1_(0)
Source (The PrimePages, NMBRTHRY, ...) _{159274}_(137)_{281}_1_(731)_{281}_(0)_{159274}_1http://primes.utm.edu/primes/page.php?id=117373 Message 11475 Big Palindrome + Reply Message 11476 |
The function Phi used here in the first part stands for Pfgw's 'Cyclotomic Number' It provides us the left, the middle and the right digit 1 in the decimal expansion. Pfgw64 -f0 -od -q"Phi(3,10^2)" = 10101 Pfgw64 -f0 -od -q"Phi(3,10^3)" = 1001001 Pfgw64 -f0 -od -q"Phi(3,10^4)" = 100010001 Pfgw64 -f0 -od -q"Phi(3,10^160118)" = 100.. ..00100.. ..001 Change the first parameter into e.g. 5 and you get Pfgw64 -f0 -od -q"Phi(5,10^4)" = 10001000100010001 This cyclotomic number seems to be related to Euler's phi (totient) function ? Pfgw64 Phi(10^4): 4000 Pari/gp (16:59) gp > eulerphi(10^4) %1 = 4000 What is the role of the first parameter in pfgw64's Phi ? |

[ Submitted March 8, 2014 ]This palindromic prime is from David Broadhurst Phi(3, 10 ^{160048}) +(137 * 10 ^{160049} + 731 * 10^{157453}) * (10^{2595} – 1)/999(320097 digits) Written out it looks like this :
1_(0)
Source (The PrimePages, NMBRTHRY, ...) _{157452}_(137)_{865}_1_(731)_{865}_(0)_{157452}_1http://primes.utm.edu/primes/page.php?id=117386 |
Analyse of the second part of the equation It provides us the left and the right string of digits around the central digit 1 in the expansion. Pfgw64 -f0 -od -q"(137*10^11+731*10^7)*(10^3-1)/999" 13707310000000 Pfgw64 -f0 -od -q"(137*10^15+731*10^8)*(10^6-1)/999" 137137073173100000000 Notice the zero between the 137 and 731 string where the middle digit '1' of the Phi function will be added to. General formula is (137*10^K+731*10^L)*(10^A-1)/999 (10^A-1)/999 is the repeater; with A multiple of 3 (137 and 731 are each three digits long). L is the number of trailing zeros you want implemented (The last zero will change to a '1' when the right digit '1' of the Phi function is added). K = L + A + 1 |

[ Submitted January 7, 2013 ]This palindromic prime is from Darren Bedwell 10 ^{314727} – 8 * 10^{157363} – 1(314727 digits) Written out, it's 157363 nines, a one, and 157363 more nines and is therefore a PWP or a Palindromic Wing Prime. Source (The PrimePages, NMBRTHRY, ...) https://primes.utm.edu/primes/page.php?id=110658 http://zerosink.blogspot.com/2013/01/ http://groups.yahoo.com/group/primeform/message/11343 |

[ Submitted June 17, 2021 ]This palindromic prime is from Makoto Morimoto 10 ^{300000} + 5 * (10^{48153} – 1)/9 * 10^{125924} + 1(300001 digits) Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=132404 |

[ Submitted April 11, 2012 ]This palindromic prime is from Darren Bedwell 10 ^{290253} – 2 * 10^{145126} – 1(290253 digits) Written out, it's 145126 nines, a seven, and 145126 more nines and is therefore a PWP or a Palindromic Wing Prime. Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=106219 http://zerosink.blogspot.com/2012/04/ http://groups.yahoo.com/group/primeform/message/11254 http://groups.yahoo.com/group/primeform/message/11280 |

[ Submitted May 19, 2020 ]This palindromic prime is from Mohamed Reda Kebbaj 10 ^{283355} – 737 * 10^{141676} – 1(283355 digits) Source (The PrimePages, NMBRTHRY, ...) https://primes.utm.edu/primes/page.php?id=130908 |

[ Submitted January 13, 2012 ]This palindromic prime is from David Broadhurst who devised the next beautiful formula Phi(3, 10 ^{137747}) +(137 * 10 ^{137748} + 731 * 10^{129293}) * (10^{8454} – 1)/999(275495 digits) Written in concatenated form we get
1_(0)
One can verify this with the following 64-bit PFGW commandline_{129292}_(137)_{2818}_1_(731)_{2818}_(0)_{129292}_1
C:\Pfgw64>pfgw64 -f0 -od -q"formula" >> palprim.txt Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=103926 http://tech.groups.yahoo.com/group/primeform/message/11203 (Reply Message 11204 ) |

[ Submitted February 29, 2012 ]This palindromic prime is from Darren Bedwell 10 ^{269479} – 7 * 10^{134739} – 1(269479 digits) Written out, it's 134739 nines, a two, and 134739 more nines and is therefore a PWP or a Palindromic Wing Prime. Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=105258 http://zerosink.blogspot.com/2012/04/ |

[ Submitted June 3, 2021 ]This palindromic prime is from Makoto Morimoto 10 ^{262144} + 7 * (10^{5193} – 1)/9 * 10^{128476} + 1(262144 digits) Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=132365 |

[ Submitted January 7, 2016 ]This palindromic prime is from Serge Batalov 10 ^{223663} – 454 * 10^{111830} – 1(223663 digits) Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=120863 |

[ Submitted January 5, 2016 ]This palindromic prime is from Serge Batalov 10 ^{220285} – 949 * 10^{110141} – 1(220285 digits) Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=120848 |

[ Submitted September 17, 2010 ]This palindromic prime is from Bernardo Boncompagni 10 ^{200000} + 47960506974 * 10^{99995} + 1(200001 digits) Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=94993 http://tech.groups.yahoo.com/group/primeform/message/10535 |

[ Submitted May 23, 2010 ]This palindromic prime is from Harvey Dubner 10 ^{190004} + 214757412 * 10^{94998} + 1(190005 digits) Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=92828 |

[ Submitted May 2, 2010 ]This palindromic prime is from Harvey Dubner 10 ^{185008} + 130525031 * 10^{92500} + 1(185009 digits) Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=92569 |

[ Submitted September 8, 2007 ]Darren Bedwell re-establishes a new world palindromic prime record 10 ^{180054} + 8*R(58567) * 10^{60744} + 1(180055 digits) It is also tetradic, dihedral and strobogrammatic. Darren discovered this particular number using PFGW with the -f flag and a simple ABC2 file, only varying the length of the center string of 8's. Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=89907 http://zerosink.blogspot.com/2009/09/ |

[ Submitted August 8, 2007 ]Harvey Dubner re-establishes a palindromic prime record 10 ^{180004} + 248797842 * 10^{89998} + 1(180005 digits) Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=81904 http://tech.groups.yahoo.com/group/primeform/message/9261 |

[ Submitted June 9, 2007 ]Harvey Dubner re-establishes a palindromic prime record 10 ^{175108} + 230767032 * 10^{87550} + 1(175109 digits) Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=80980 http://tech.groups.yahoo.com/group/primeform/message/8673 |

[ Submitted October 21, 2006 ]Harvey Dubner re-establishes a palindromic prime record 10 ^{170006} + 3880883 * 10^{85000} + 1(170007 digits) Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=78702 |

[ Submitted May 19, 2006 ]Harvey Dubner re-establishes a palindromic prime record 10 ^{160016} + 8231328 * 10^{80005} + 1(160017 digits) Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=77815 Number Theory List - Message of 1 Jun 2006 |

[ Submitted February 1, 2006 ]Harvey Dubner retakes the palindromic prime record 10 ^{150008} + 4798974 * 10^{75001} + 1(150009 digits) Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=76932 http://groups.yahoo.com/group/primeform/message/6888 |

[ Submitted December 26, 2005 ]Paul Jobling tops the list now with his palindromic prime record 10 ^{150006} + 7426247 * 10^{75000} + 1(150007 digits) Source (The PrimePages, NMBRTHRY, ...) http://primes.utm.edu/primes/page.php?id=76550 http://groups.yahoo.com/group/primeform/message/6757 (Reply Messages 6764, 6765, 6766, 6767, 6768, 6769) |

[ Submitted November 25, 2010 ]Darren Bedwell announced this NearRepDigit palindromic prime record 10 ^{134809} – 10^{67404} – 1(134809 digits) Source (The PrimePages, NMBRTHRY, ...) http://groups.yahoo.com/group/primeform/message/10769 |

[ Submitted October 31, 2010 ]Darren Bedwell sent in this former NearRepDigit palindromic prime record 10 ^{125877} – 7 * 10^{62938} – 1(125877 digits) Source (The PrimePages, NMBRTHRY, ...) https://primes.utm.edu/primes/page.php?id=95802 http://groups.yahoo.com/group/primeform/message/10743 |

[ Submitted September 4, 2010 ]Darren Bedwell sent in (rather late) this former palindromic prime record 10 ^{111725} – 4 * 10^{55862} – 1(111725 digits) Source (The PrimePages, NMBRTHRY, ...) https://primes.utm.edu/primes/page.php?id=94508 http://groups.yahoo.com/group/primeform/message/10535 |

Former Palindromic Prime Records computed by Harvey Dubner & ass.

Harvey Dubner (1928-2019 †) Picture borrowed from Ivars Peterson webpage Palindromic Primes |

[ Submitted December 6, 2005 ]Harvey Dubner re-establishes a personal palindromic prime record 10 ^{140008} + 4546454 * 10^{70001} + 1(140009 digits) Source (The PrimePages, NMBRTHRY, ...) https://primes.utm.edu/primes/page.php?id=76391 http://groups.yahoo.com/group/primeform/message/6719 |

[ Submitted November 8, 2004 ]Harvey Dubner establishes again a new palindromic prime record 10 ^{130022} + 3761673 * 10^{65008} + 1(130023 digits) Source (The PrimePages, NMBRTHRY, ...) https://primes.utm.edu/primes/page.php?id=72332 Number Theory List - Message from 19 Nov 2004 http://groups.yahoo.com/group/primeform/message/4999 |

[ Submitted April 5, 2004 ]Let us acclaim Harvey Dubner's latest palindromic prime record 10 ^{120016} + 1726271 * 10^{60005} + 1(120017 digits) Source (The PrimePages, NMBRTHRY, ...) https://primes.utm.edu/primes/page.php?id=69756 Number Theory List - Message from 12 Apr 2004 http://groups.yahoo.com/group/primeform/message/4273 |

[ Submitted April 2, 2004 ]Let us acclaim Harvey Dubner's latest palindromic prime record 10 ^{120002} + 1617161 * 10^{59998} + 1(120003 digits) Source (The PrimePages, NMBRTHRY, ...) https://primes.utm.edu/primes/page.php?id=69729 Number Theory List- Message from 12 Apr 2004 http://groups.yahoo.com/group/primeform/message/4269 |

[ Submitted May 3, 2004 ]The largest palindromic prime (from Andersen and Dubner) with a palindromic prime length is 10 ^{98689} – 429151924 * 10^{49340} – 1(98689 digits) A doubly palindromic prime ! Source (The PrimePages, NMBRTHRY, ...) https://primes.utm.edu/primes/page.php?id=70157 Number Theory List - Message from 18 May 2004 http://groups.yahoo.com/group/primeform/message/4320 |

[ Submitted February 15, 2004 ]Harvey Dubner announced via the NMBRTHRY bulletin board a new palindromic prime record. 10 ^{91018} + 126696621 * 10^{45505} + 1(91019 digits) A doubly palindromic prime ! Source (The PrimePages, NMBRTHRY, ...) Number Theory List - Message from 12 Apr 2004 https://primes.utm.edu/primes/page.php?id=68843 |

[ Submitted April 8, 2004 ]Harvey Dubner announced via the NMBRTHRY bulletin board a new palindromic prime record. 10 ^{51000} + R(4133) * 10^{23434} + 1(51001 digits) R(4133) is a repunit consisting of 4133 1's. This is a tetradic prime or a 4-way prime that reads the same left, right, up & down and rotated. (previous record had 30803 digits). Source (The PrimePages, NMBRTHRY, ...) Number Theory List - Message from 12 Apr 2004 https://primes.utm.edu/primes/page.php?id=69773 |

[ Submitted July 17, 2001 ]Harvey Dubner announced via the NMBRTHRY bulletin board a new palindromic prime record. 10 ^{39026} + 4538354 * 10^{19510} + 1(39027 digits) Despite having a length that is not a prime nor a palindrome this time, it still is quite an achievement. Well done, Harvey ! Source (The PrimePages, NMBRTHRY, ...) https://primes.utm.edu/primes/page.php?id=2507 Number Theory List - Message from 17 Jul 2001 |

[ Submitted November 14, 1999 ]Harvey Dubner announced via the NMBRTHRY bulletin board a new palindromic prime record. 10 ^{35352} + 2049402 * 10^{17673} + 1(35353 digits) The number of digits, 35353, is also a palindromic prime (no accident). Source (The PrimePages, NMBRTHRY, ...) https://primes.utm.edu/primes/page.php?id=2783 Number Theory List - Message from 14 Nov 1999 ▼ |

The |

[ Submitted April 28, 1999 ]Harvey Dubner announced via the NMBRTHRY bulletin board a new palindromic prime record. 10 ^{30802} + 1110111 * 10^{15398} + 1(30803 digits) The number of digits, 30803, is also a palindromic prime (no accident). It consists of only 1's and 0's (definitely an accident). Source (The PrimePages, NMBRTHRY, ...) Number Theory List - Message from 28 Apr 1999 ▼ |

The site "The largest known primes" [http://www.utm.edu/research/primes/ftp/short.txt] kept monthly updates also about palindromic primes. The |

[ Submitted February 23, 1999 ]Harvey Dubner announced via the NMBRTHRY bulletin board a new palindromic prime record. 10 ^{19390} + 4300034 * 10^{9692} + 1(19391 digits) The number of digits, 19391, is also a palindromic prime (no accident). Source (The PrimePages, NMBRTHRY, ...) Number Theory List - Message from 23 Feb 1999 |

[ Submitted February 2002 ]David Broadhurst and Harvey Dubner announced via the NMBRTHRY bulletin board a new palindromic prime N = (1808010808) _{1560}1(15601 digits) This is a tetratic (4-way) prime: it is a palindrome as well as the same upside down and mirror reflected. Source (The PrimePages, NMBRTHRY, ...) Number Theory List - Message from 16 Feb 2002 |

[ Submitted October 5, 2001 ]David Broadhurst and Harvey Dubner announced via the NMBRTHRY bulletin board a new palindromic prime N = (1989191989) _{1560}1(15601 digits) This is not a new record however this palindrome is of a more varied form and hence considerably more demanding to prove ! Source (The PrimePages, NMBRTHRY, ...) https://primes.utm.edu/primes/page.php?id=11776 Wonplate 126 Number Theory List - Message from 4 Oct 2001 ▼ |

We have found a Konyagin-Pomerance proof of primality of the 15601-digit base-10 palindrome N = (1989191989) |

[ Submitted January 29, 2000 ]Warut Roonguthai found using PrimeForm a new palindromic prime . 10 ^{11840} + 42924 * 10^{5918} + 1(11841 digits) Source (The PrimePages, NMBRTHRY, ...) |

[ |

[ Submitted February 13, 1997 ]Harvey Dubner announced via the NMBRTHRY bulletin board some new palindromic prime records.
All are of the form k * [ R(a*b) / R(b) ] * 10 + 1 Source (The PrimePages, NMBRTHRY, ...) Number Theory List - Message from 13 Feb 1997 |

Sources

Most of Harvey's record palindromic primes are on display.

The Top Ten by Rudolph Ondrejka

Be warned that your mind might boggle when trying to grasp the magnitude of the numbers involved.

Warut Roonguthai provided me the following link that displays the largest palindromic primes.

The current list of the largest known palindromic primes

http://primes.utm.edu/top20/page.php?id=53

Read also this interesting article about Palindromic Primes by Ivars Peterson (email).

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