The Top Twenty--a Prime Page Collection

Palindrome

This page : Definition(s) | Records | References | Related Pages | RSS 2.0 Feed
  View this page in:   language help
The Prime Pages keeps a list of the 5000 largest known primes, plus a few each of certain selected archivable forms and classes. These forms are defined in this collection's home page. This page is about one of those forms. Comments and suggestions requested.

(up) Definitions and Notes

A palindrome (from the Greek palindromos "running back again") is a word, verse, sentence, or integer that reads the same forward or backward. For example, "Able was I ere I saw Elba" or 333313333. Here is a little longer one by Peter Hilton (a code-breaker on the British team that cracked the German Enigma):
Doc, note. I dissent. A fast never prevents a fatness. I diet on cod.

Sotades the obscene of Maronea (3rd century BC) is credited with inventing the palindrome. Though today only eleven lines of his works still remain, he is thought to have recast the entire Illiad as palindromic verse. Sotades also wrote lines which when read backwards had the opposite meaning, now sometimes called Sotadic verses. Sotades attacked many with his unrestrained toungue, and eventually was jailed by Ptolemy II. Sotades eventually escaped, but Ptolemy's admiral Patroclus caught him, sealed him in a leaden chest and tossed him into the sea.

Though palindromic numbers have no significant role in modern mathematics, the survival of the old mysticism so often attached to numbers (perfect numbers, amicable numbers, abundant numbers...) insures the palindromes a secure place in the heart of the amateur numerologists.

(up) Record Primes of this Type

rankprime digitswhowhencomment
110314727 - 8 · 10157363 - 1 314727 p235 Jan 2013 Near - repdigit, palindrome
210290253 - 2 · 10145126 - 1 290253 p235 Apr 2012 Near - repdigit, Palindrome
3Phi(3, 10137747) + (137 · 10137748 + 731 · 10129293) · (108454 - 1)/999 275495 p44 Jan 2012 Palindrome
410269479 - 7 · 10134739 - 1 269479 p235 Feb 2012 Near - repdigit, Palindrome
510205030 + 7047407 · 10102512 + 1 205031 D Nov 2011 Palindrome
610200000 + 47960506974 · 1099995 + 1 200001 p288 Sep 2010 Palindrome
710190004 + 214757412 · 1094998 + 1 190005 D May 2010 Palindrome
810185008 + 130525031 · 1092500 + 1 185009 D May 2010 Palindrome
910180054 + 8 · R(58567) · 1060744 + 1 180055 p235 Sep 2009 Tetradic palindrome
1010180004 + 248797842 · 1089998 + 1 180005 D Aug 2007 Palindrome
1110175108 + 230767032 · 1087550 + 1 175109 D Jun 2007 Palindrome
1210170006 + 3880883 · 1085000 + 1 170007 D Oct 2006 Palindrome
1310160016 + 8231328 · 1080005 + 1 160017 D May 2006 Palindrome
1410150008 + 4798974 · 1075001 + 1 150009 D Feb 2006 Palindrome
1510150006 + 7426247 · 1075000 + 1 150007 p5 Dec 2005 Palindrome
1610140008 + 4546454 · 1070001 + 1 140009 D Dec 2005 Palindrome
1710134809 - 1067404 - 1 134809 p235 Nov 2010 Near - repdigit, palindrome
1810130048 + (9 · 1037077 - 2)/11 · 1046486 + 1 130049 p235 Sep 2008 Tetradic palindrome
1910130036 + 116010611 · 1065014 + 1 130037 D Dec 2004 Palindrome
2010130022 + 3761673 · 1065008 + 1 130023 D Nov 2004 Palindrome

(up) Related Pages

(up) References

DO94
H. Dubner and R. Ondrejka, "A PRIMEr on palindromes," J. Recreational Math., 26:4 (1994) 256--267.
GC1969
H. Gabai and D. Coogan, "On palindromes and palindromic primes," Math. Mag., 42 (1969) 252--254.  MR0253979
HC2000
G. L. Honaker, Jr. and C. Caldwell, "Palindromic prime pyramids," J. Recreational Math., 30:3 (1999-2000) 169--176. (Annotation available)
Iseki1988
Iséki, Kiyoshi, "Palindromic prime numbers from experimental number theory," Math. Japon., 33:5 (1988) 715--720.  MR 972382
Iseki1988b
Iséki, Kiyoshi, "Palindromic prime numbers," Math. Japon., 33:6 (1988) 861--862.  MR 975864
Iseki1988c
Iséki, Kiyoshi, "Palindromic prime numbers from experimental number theory. II," Math. Japon., 33:6 (1988) 863--872.  MR 975865
McDaniel87b
W. McDaniel, "Palindromic Smith numbers," J. Recreational Math., 19:1 (1987) 34--37.
Ribenboim95
P. Ribenboim, The new book of prime number records, 3rd edition, Springer-Verlag, New York, NY, 1995.  pp. xxiv+541, ISBN 0-387-94457-5. MR 96k:11112 [An excellent resource for those with some college mathematics. Basically a Guinness Book of World Records for primes with much of the relevant mathematics. The extensive bibliography is seventy-five pages.]
Chris K. Caldwell © 1996-2013 (all rights reserved)