The Top Twenty--a Prime Page Collection

Palindrome

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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
110180054+8 · R(58567) · 1060744+1 180055 p235 Sep 2009 Tetradic palindrome
210180004+248797842 · 1089998+1 180005 D Aug 2007 Palindrome
310175108+230767032 · 1087550+1 175109 D Jun 2007 Palindrome
410170006+3880883 · 1085000+1 170007 D Oct 2006 Palindrome
510160016+8231328 · 1080005+1 160017 D May 2006 Palindrome
610150008+4798974 · 1075001+1 150009 D Feb 2006 Palindrome
710150006+7426247 · 1075000+1 150007 p5 Dec 2005 Palindrome
810140008+4546454 · 1070001+1 140009 D Dec 2005 Palindrome
910130048+(9 · 1037077-2)/11 · 1046486+1 130049 p235 Sep 2008 Tetradic palindrome
1010130036+116010611 · 1065014+1 130037 D Dec 2004 Palindrome
1110130022+3761673 · 1065008+1 130023 D Nov 2004 Palindrome
1210127590+1042297 · (9 · 1042997-2)/11+1 127591 x40 Sep 2009 Tetradic palindrome
1310127576+1081101080188810801011801 · 1063776+1 127577 p185 Jan 2006 Tetradic, palindrome
1410120016+1726271 · 1060005+1 120017 D Apr 2004 Palindrome
1510120002+1617161 · 1059998+1 120003 D Apr 2004 Palindrome
1610105022+523111325 · 1052507+1 105023 D Feb 2008 Palindrome
1710105018+920383029 · 1052505+1 105019 D May 2008 Palindrome
1810105016+318939813 · 1052504+1 105017 D Jan 2008 Palindrome
1910105014+682787286 · 1052503+1 105015 D Apr 2008 Palindrome
2010105014+424787424 · 1052503+1 105015 D Feb 2008 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)
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.]
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