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Palindrome |
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.
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 101234567 - 20342924302 · 10617278 - 1 1234567 p423 Sep 2021 Palindrome 2 10490000 + 3 · (107383 - 1)/9 · 10241309 + 1 490001 p413 Aug 2021 Palindrome 3 10474500 + 999 · 10237249 + 1 474501 p363 Nov 2014 Palindrome 4 10400000 + 4 · (10102381 - 1)/9 · 10148810 + 1 400001 p413 Jul 2021 Palindrome 5 10390636 + 999 · 10195317 + 1 390637 p363 Nov 2014 Palindrome 6 10362600 + 666 · 10181299 + 1 362601 p363 Nov 2014 Palindrome 7 Phi(3, 10160118) + (137 · 10160119 + 731 · 10159275) · (10843 - 1)/999 320237 p44 Mar 2014 Palindrome 8 Phi(3, 10160048) + (137 · 10160049 + 731 · 10157453) · (102595 - 1)/999 320097 p44 Mar 2014 Palindrome 9 10314727 - 8 · 10157363 - 1 314727 p235 Jan 2013 Near - repdigit, palindrome 10 10300000 + 5 · (1048153 - 1)/9 · 10125924 + 1 300001 p413 Jun 2021 Palindrome 11 10290253 - 2 · 10145126 - 1 290253 p235 Apr 2012 Near - repdigit, Palindrome 12 10283355 - 737 · 10141676 - 1 283355 p399 May 2020 Palindrome 13 Phi(3, 10137747) + (137 · 10137748 + 731 · 10129293) · (108454 - 1)/999 275495 p44 Jan 2012 Palindrome 14 10269479 - 7 · 10134739 - 1 269479 p235 Feb 2012 Near - repdigit, Palindrome 15 10262144 + 7 · (105193 - 1)/9 · 10128476 + 1 262145 p413 Jun 2021 Palindrome 16 10223663 - 454 · 10111830 - 1 223663 p363 Jan 2016 Palindrome 17 10220285 - 949 · 10110141 - 1 220285 p363 Jan 2016 Palindrome 18 10219113 - 535 · 10109555 - 1 219113 p363 Jan 2016 Palindrome 19 10216091 - 7 · (1037627 - 1)/9 · 1089232 - 1 216091 p413 Oct 2020 Palindrome 20 10214575 - 20002 · 10107285 - 1 214575 p363 Jan 2016 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.
- 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, 1995. New York, NY, 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.]