Palindrome
This page : Definition(s) | Records | References | Related Pages |
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PalindromeThis page : Definition(s) | Records | References | Related Pages |
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Definitions and NotesDoc, 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.
Record Primes of this Type
rank prime digits who when comment 1 10314727 - 8 · 10157363 - 1 314727 p235 Jan 2013 Near - repdigit, palindrome 2 10290253 - 2 · 10145126 - 1 290253 p235 Apr 2012 Near - repdigit, Palindrome 3 Phi(3, 10137747) + (137 · 10137748 + 731 · 10129293) · (108454 - 1)/999 275495 p44 Jan 2012 Palindrome 4 10269479 - 7 · 10134739 - 1 269479 p235 Feb 2012 Near - repdigit, Palindrome 5 10205030 + 7047407 · 10102512 + 1 205031 D Nov 2011 Palindrome 6 10200000 + 47960506974 · 1099995 + 1 200001 p288 Sep 2010 Palindrome 7 10190004 + 214757412 · 1094998 + 1 190005 D May 2010 Palindrome 8 10185008 + 130525031 · 1092500 + 1 185009 D May 2010 Palindrome 9 10180054 + 8 · R(58567) · 1060744 + 1 180055 p235 Sep 2009 Tetradic palindrome 10 10180004 + 248797842 · 1089998 + 1 180005 D Aug 2007 Palindrome 11 10175108 + 230767032 · 1087550 + 1 175109 D Jun 2007 Palindrome 12 10170006 + 3880883 · 1085000 + 1 170007 D Oct 2006 Palindrome 13 10160016 + 8231328 · 1080005 + 1 160017 D May 2006 Palindrome 14 10150008 + 4798974 · 1075001 + 1 150009 D Feb 2006 Palindrome 15 10150006 + 7426247 · 1075000 + 1 150007 p5 Dec 2005 Palindrome 16 10140008 + 4546454 · 1070001 + 1 140009 D Dec 2005 Palindrome 17 10134809 - 1067404 - 1 134809 p235 Nov 2010 Near - repdigit, palindrome 18 10130048 + (9 · 1037077 - 2)/11 · 1046486 + 1 130049 p235 Sep 2008 Tetradic palindrome 19 10130036 + 116010611 · 1065014 + 1 130037 D Dec 2004 Palindrome 20 10130022 + 3761673 · 1065008 + 1 130023 D Nov 2004 Palindrome
Related Pages
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.]