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121141151171181
313323343353373
383717727747757
787919929949959
979989   


Palindromic Merlon Primes

Palindromic Merlon Primes (or PMP's for short) are numbers that
are (probable) primes, palindromic in base 10, and consisting of one central digit
(hereby named as a merlon_digit) surrounded by two symmetrical crennelations
with same digits different from the central merlon_digit and finally bordered left
and right by that same central merlon_digit. E.g.

3223223
31111111111111111311111111111111113

From these examples you will understand the naming of these kind of palindromic primes Visualising merlons

Some links where PMP's are discussed ¬
Liczby pierwsze o szczególnym rozmieszczeniu cyfr (Polish PostScript file) by Andrzej Nowicki
1221221 from the site 'Darkbyte'
3223223 from Prime Curios!

In case one should discover more sources I will be most happy
to add them to the list. Just let me know.


PMP's sorted by length






brown line

Some combinations can never produce primes since
these are always divisible by 3.
1(0)w1(0)w1
1(3)w1(3)w1
1(6)w1(6)w1
1(9)w1(9)w1
3(0)w3(0)w3
3(6)w3(6)w3
3(9)w3(9)w3
7(0)w7(0)w7
7(3)w7(3)w7
7(6)w7(6)w7
7(9)w7(9)w7
9(0)w9(0)w9
9(3)w9(3)w9
9(6)w9(6)w9



PMP Factorization Projects





The Table


The reference table for
Palindromic Merlon Primes
This collection is complete for
probable primes up to 20000
digits and for proven
primes up to  ????  digits.
PDG = Patrick De Geest
PMPFormula
blue exp = # of digits
WhoWhenStatusOutput
Logs
A?????? ¬   [ n > 35000 ]
1(2)21(2)21 2*(107-1)/9 - 106 - 103 - 1 PDG Nov 12 2011 PRIME View
1(2)41(2)41 2*(1011-1)/9 - 1010 - 105 - 1 PDG Nov 12 2011 PRIME View
1(2)111(2)111 2*(1025-1)/9 - 1024 - 1012 - 1 PDG Nov 12 2011 PRIME View
1(2)23921(2)23921 2*(104787-1)/9 - 104786 - 102393 - 1 PDG Nov 12 2011 PROBABLE
PRIME
View
A?????? ¬   [ n > 20000 ]
1(4)441(4)441 4*(1091-1)/9 - 3*1090 - 3*1045 - 3 PDG Nov 12 2011 PRIME View
1(4)641(4)641 4*(10131-1)/9 - 3*10130 - 3*1065 - 3 PDG Nov 12 2011 PRIME View
1(4)91491(4)91491 4*(1018301-1)/9 - 3*1018300 - 3*109150 - 3 PDG Nov 12 2011 PROBABLE
PRIME
View
A?????? ¬   [ n > 20000 ]
1(5)21(5)21 5*(107-1)/9 - 4*106 - 4*103 - 4 PDG Nov 12 2011 PRIME View
1(5)81(5)81 5*(1019-1)/9 - 4*1018 - 4*109 - 4 PDG Nov 12 2011 PRIME View
1(5)321(5)321 5*(1067-1)/9 - 4*1066 - 4*1033 - 4 PDG Nov 12 2011 PRIME View
1(5)1281(5)1281 5*(10259-1)/9 - 4*10258 - 4*10129 - 4 PDG Nov 12 2011 PRIME View
1(5)4941(5)4941 5*(10991-1)/9 - 4*10990 - 4*10495 - 4 PDG Nov 12 2011 PRIME View
1(5)42611(5)42611 5*(108525-1)/9 - 4*108524 - 4*104262 - 4 PDG Nov 12 2011 PROBABLE
PRIME
View
A?????? ¬   [ n > 20000 ]
1(7)41(7)41 7*(1011-1)/9 - 6*1010 - 6*105 - 6 PDG Nov 12 2011 PRIME View
1(7)221(7)221 7*(10>47-1)/9 - 6*1046 - 6*1023 - 6 PDG Nov 12 2011 PRIME View
1(7)3161(7)3161 7*(10635-1)/9 - 6*10634 - 6*10317 - 6 PDG Nov 12 2011 PRIME View
1(7)4421(7)4421 7*(10887-1)/9 - 6*10886 - 6*10443 - 6 PDG Nov 12 2011 PRIME View
A?????? ¬   [ n > 22000 ]
1(8)11(8)11 8*(105-1)/9 - 7*104 - 7*102 - 7 PDG Nov 12 2011 PRIME View
1(8)21(8)21 8*(107-1)/9 - 7*106 - 7*103 - 7 PDG Nov 12 2011 PRIME View
1(8)1451(8)1451 8*(10293-1)/9 - 7*10292 - 7*10146 - 7 PDG Nov 12 2011 PRIME View
1(8)2541(8)2541 8*(10511-1)/9 - 7*10510 - 7*10255 - 7 PDG Nov 12 2011 PRIME View
1(8)16271(8)16271 8*(103257-1)/9 - 7*103256 - 7*101628 - 7 PDG Nov 12 2011 PROBABLE
PRIME
View
1(8)18131(8)18131 8*(103629-1)/9 - 7*103628 - 7*101814 - 7 PDG Nov 12 2011 PROBABLE
PRIME
View
A?????? ¬   [ n > 20000 ]
3(1)163(1)163 (1035-1)/9 + 2*1034 + 2*1017 + 2 PDG Nov 12 2011 PRIME View
3(1)433(1)433 (1089-1)/9 + 2*1088 + 2*1044 + 2 PDG Nov 12 2011 PRIME View
3(1)863(1)863 (10175-1)/9 + 2*10174 + 2*1087 + 2 PDG Nov 12 2011 PRIME View
3(1)11533(1)11533 (102309-1)/9 + 2*102308 + 2*101154 + 2 PDG Nov 12 2011 PRIME View
A?????? ¬   [ n > 21000 ]
3(2)13(2)13 2*(105-1)/9 + 104 + 102 + 1 PDG Nov 12 2011 PRIME View
3(2)23(2)23 2*(107-1)/9 + 106 + 103 + 1 PDG Nov 12 2011 PRIME View
3(2)53(2)53 2*(1013-1)/9 + 1012 + 106 + 1 PDG Nov 12 2011 PRIME View
3(2)19033(2)19033 2*(103809-1)/9 + 103808 + 101904 + 1 PDG Nov 12 2011 PROBABLE
PRIME
View
3(2)29533(2)29533 2*(105909-1)/9 + 105908 + 102954 + 1 PDG Nov 12 2011 PROBABLE
PRIME
View
3(2)34133(2)34133 2*(106829-1)/9 + 106828 + 103414 + 1 PDG Nov 12 2011 PROBABLE
PRIME
View
A?????? ¬   [ n > 21000 ]
3(4)43(4)43 4*(1011-1)/9 - 1010 - 105 - 1 PDG Nov 12 2011 PRIME View
3(4)73(4)73 4*(1017-1)/9 - 1016 - 108 - 1 PDG Nov 12 2011 PRIME View
3(4)223(4)223 4*(1047-1)/9 - 1046 - 1023 - 1 PDG Nov 12 2011 PRIME View
3(4)263(4)263 4*(1055-1)/9 - 1054 - 1027 - 1 PDG Nov 12 2011 PRIME View
3(4)1823(4)1823 4*(10367-1)/9 - 10366 - 10183 - 1 PDG Nov 12 2011 PRIME View
3(4)2053(4)2053 4*(10413-1)/9 - 10412 - 10206 - 1 PDG Nov 12 2011 PRIME View
3(4)4763(4)4763 4*(10955-1)/9 - 10954 - 10477 - 1 PDG Nov 12 2011 PRIME View
3(4)13193(4)13193 4*(102641-1)/9 - 102640 - 101320 - 1 PDG Nov 12 2011 PROBABLE
PRIME
View
A?????? ¬   [ n > 20000 ]
3(5)13(5)13 5*(105-1)/9 - 2*104 - 2*102 - 2 PDG Nov 12 2011 PRIME View
3(5)23(5)23 5*(107-1)/9 - 2*106 - 2*103 - 2 PDG Nov 12 2011 PRIME View
3(5)173(5)173 5*(1037-1)/9 - 2*1036 - 2*1018 - 2 PDG Nov 12 2011 PRIME View
3(5)203(5)203 5*(1043-1)/9 - 2*1042 - 2*1021 - 2 PDG Nov 12 2011 PRIME View
3(5)263(5)263 5*(1055-1)/9 - 2*1054 - 2*1027 - 2 PDG Nov 12 2011 PRIME View
3(5)1573(5)1573 5*(10317-1)/9 - 2*10316 - 2*10158 - 2 PDG Nov 12 2011 PRIME View
3(5)6143(5)6143 5*(101231-1)/9 - 2*101230 - 2*10615 - 2 PDG Nov 12 2011 PROBABLE
PRIME
View
3(5)8333(5)8333 5*(101669-1)/9 - 2*101668 - 2*10834 - 2 PDG Nov 12 2011 PROBABLE
PRIME
View
3(5)33613(5)33613 5*(106725-1)/9 - 2*106724 - 2*103362 - 2 PDG Nov 12 2011 PROBABLE
PRIME
View
3(5)36313(5)36313 5*(107265-1)/9 - 2*107264 - 2*103632 - 2 PDG Nov 12 2011 PROBABLE
PRIME
View
3(5)38443(5)38443 5*(107691-1)/9 - 2*107690 - 2*103845 - 2 PDG Nov 12 2011 PROBABLE
PRIME
View
A?????? ¬   [ n > 30000 ]
3(7)23(7)23 7*(107-1)/9 - 4*106 - 4*103 - 4 PDG Nov 12 2011 PRIME View
3(7)43(7)43 7*(1011-1)/9 - 4*1010 - 4*105 - 4 PDG Nov 12 2011 PRIME View
3(7)473(7)473 7*(1097-1)/9 - 4*1096 - 4*1048 - 4 PDG Nov 12 2011 PRIME View
3(7)593(7)593 7*(10121-1)/9 - 4*10120 - 4*1060 - 4 PDG Nov 12 2011 PRIME View
3(7)703(7)703 7*(10143-1)/9 - 4*10142 - 4*1071 - 4 PDG Nov 12 2011 PRIME View
3(7)1223(7)1223 7*(10247-1)/9 - 4*10246 - 4*10123 - 4 PDG Nov 12 2011 PRIME View
3(7)1283(7)1283 7*(10259-1)/9 - 4*10258 - 4*10129 - 4 PDG Nov 12 2011 PRIME View
3(7)56443(7)56443 7*(1012191-1)/9 - 4*1012190 - 4*105645 - 4 PDG Dec 4 2011 PROBABLE
PRIME
View
3(7)85243(7)85243 7*(1017051-1)/9 - 4*1017050 - 4*108525 - 4 PDG Dec 4 2011 PROBABLE
PRIME
View
A?????? ¬   [ n > 22000 ]
3(8)83(8)83 8*(1019-1)/9 - 5*1018 - 5*109 - 5 PDG Nov 12 2011 PRIME View
3(8)103(8)103 8*(1023-1)/9 - 5*1022 - 5*1011 - 5 PDG Nov 12 2011 PRIME View
3(8)143(8)143 8*(1031-1)/9 - 5*1030 - 5*1015 - 5 PDG Nov 12 2011 PRIME View
3(8)673(8)673 8*(10137-1)/9 - 5*10136 - 5*1068 - 5 PDG Nov 12 2011 PRIME View
3(8)3643(8)3643 8*(10731-1)/9 - 5*10730 - 5*10365 - 5 PDG Nov 12 2011 PRIME View
3(8)5783(8)5783 8*(101159-1)/9 - 5*101158 - 5*10579 - 5 PDG Nov 12 2011 PRIME View
3(8)8483(8)8483 8*(101699-1)/9 - 5*101698 - 5*10849 - 5 PDG Nov 12 2011 PROBABLE
PRIME
View
3(8)30763(8)30763 8*(106155-1)/9 - 5*106154 - 5*103077 - 5 PDG Nov 12 2011 PROBABLE
PRIME
View
3(8)78403(8)78403 8*(1015683-1)/9 - 5*1015682 - 5*107841 - 5 PDG Dec 5 2011 PROBABLE
PRIME
View
A?????? ¬   [ n > 35000 ]
7(1)557(1)557 (10113-1)/9 + 6*10112 + 6*1056 + 6 PDG Nov 12 2011 PRIME View
A?????? ¬   [ n > 20000 ]
7(2)17(2)17 2*(105-1)/9 + 5*104 + 5*102 + 5 PDG Nov 12 2011 PRIME View
7(2)47(2)47 2*(1011-1)/9 + 5*1010 + 5*105 + 5 PDG Nov 12 2011 PRIME View
7(2)77(2)77 2*(1017-1)/9 + 5*1016 + 5*108 + 5 PDG Nov 12 2011 PRIME View
7(2)227(2)227 2*(1047-1)/9 + 5*1046 + 5*1023 + 5 PDG Nov 12 2011 PRIME View
7(2)297(2)297 2*(1061-1)/9 + 5*1060 + 5*1030 + 5 PDG Nov 12 2011 PRIME View
7(2)497(2)497 2*(10101-1)/9 + 5*10100 + 5*1050 + 5 PDG Nov 12 2011 PRIME View
7(2)737(2)737 2*(10149-1)/9 + 5*10148 + 5*1074 + 5 PDG Nov 12 2011 PRIME View
7(2)837(2)837 2*(10169-1)/9 + 5*10168 + 5*1084 + 5 PDG Nov 12 2011 PRIME View
7(2)1187(2)1187 2*(10239-1)/9 + 5*10238 + 5*10119 + 5 PDG Nov 12 2011 PRIME View
7(2)2417(2)2417 2*(10485-1)/9 + 5*10484 + 5*10242 + 5 PDG Nov 12 2011 PRIME View
A?????? ¬   [ n > 31000 ]
7(4)17(4)17 4*(105-1)/9 + 3*104 + 3*102 + 3 PDG Nov 12 2011 PRIME View
7(4)1217(4)1217 4*(10245-1)/9 + 3*10244 + 3*10122 + 3 PDG Nov 12 2011 PRIME View
7(4)5207(4)5207 4*(101043-1)/9 + 3*101042 + 3*10521 + 3 PDG Nov 12 2011 PROBABLE
PRIME
View
7(4)12647(4)12647 4*(102531-1)/9 + 3*102530 + 3*101265 + 3 PDG Nov 12 2011 PROBABLE
PRIME
View
7(4)17807(4)17807 4*(103563-1)/9 + 3*103562 + 3*101781 + 3 PDG Nov 12 2011 PROBABLE
PRIME
View
A?????? ¬   [ n > 56255 ]
7(5)262727(5)262727 5*(1052547-1)/9 + 2*1052546 + 2*1026273 + 2 PDG Nov 12 2011 PROBABLE
PRIME
View
A?????? ¬   [ n > 24000 ]
7(8)17(8)17 8*(105-1)/9 - 104 - 102 - 1 PDG Nov 12 2011 PRIME View
7(8)47(8)47 8*(1011-1)/9 - 1010 - 105 - 1 PDG Nov 12 2011 PRIME View
7(8)1277(8)1277 8*(10257-1)/9 - 10256 - 10128 - 1 PDG Nov 12 2011 PRIME View
7(8)3297(8)3297 8*(10661-1)/9 - 10660 - 10330 - 1 PDG Nov 12 2011 PRIME View
7(8)8037(8)8037 8*(101609-1)/9 - 101608 - 10804 - 1 PDG Nov 12 2011 PROBABLE
PRIME
View
7(8)18407(8)18407 8*(103683-1)/9 - 103682 - 101841 - 1 PDG Nov 12 2011 PROBABLE
PRIME
View
A?????? ¬   [ n > 20000 ]
9(1)49(1)49 (1011-1)/9 + 8*1010 + 8*105 + 8 PDG Nov 12 2011 PRIME View
9(1)79(1)79 (1017-1)/9 + 8*1016 + 8*108 + 8 PDG Nov 12 2011 PRIME View
9(1)299(1)299 (1061-1)/9 + 8*1060 + 8*1030 + 8 PDG Nov 12 2011 PRIME View
9(1)469(1)469 (1095-1)/9 + 8*1094 + 8*1047 + 8 PDG Nov 12 2011 PRIME View
9(1)589(1)589 (10119-1)/9 + 8*10118 + 8*1059 + 8 PDG Nov 12 2011 PRIME View
9(1)689(1)689 (10139-1)/9 + 8*10138 + 8*1069 + 8 PDG Nov 12 2011 PRIME View
9(1)839(1)839 (10169-1)/9 + 8*10168 + 8*1084 + 8 PDG Nov 12 2011 PRIME View
9(1)9559(1)9559 (101913-1)/9 + 8*101912 + 8*10956 + 8 PDG Nov 12 2011 PROBABLE
PRIME
View
9(1)11609(1)11609 (102323-1)/9 + 8*102322 + 8*101161 + 8 PDG Nov 12 2011 PROBABLE
PRIME
View
9(1)55049(1)55049 (1011011-1)/9 + 8*1011010 + 8*105505 + 8 PDG Nov 12 2011 PROBABLE
PRIME
View
9(1)62689(1)62689 (1012539-1)/9 + 8*1012538 + 8*106269 + 8 PDG Nov 12 2011 PROBABLE
PRIME
View
9(1)92909(1)92909 (1018583-1)/9 + 8*1018582 + 8*109291 + 8 PDG Nov 12 2011 PROBABLE
PRIME
View
A?????? ¬   [ n > 20000 ]
9(2)49(2)49 2*(1011-1)/9 + 7*1010 + 7*105 + 7 PDG Nov 12 2011 PRIME View
9(2)89(2)89 2*(1019-1)/9 + 7*1018 + 7*109 + 7 PDG Nov 12 2011 PRIME View
9(2)269(2)269 2*(1055-1)/9 + 7*1054 + 7*1027 + 7 PDG Nov 12 2011 PRIME View
9(2)2029(2)2029 2*(10407-1)/9 + 7*10406 + 7*10203 + 7 PDG Nov 12 2011 PRIME View
9(2)20689(2)20689 2*(104139-1)/9 + 7*104138 + 7*102069 + 7 PDG Nov 12 2011 PROBABLE
PRIME
View
9(2)63749(2)63749 2*(1012751-1)/9 + 7*1012750 + 7*106375 + 7 PDG Nov 12 2011 PROBABLE
PRIME
View
A?????? ¬   [ n > 20500 ]
9(4)19(4)19 4*(105-1)/9 + 5*104 + 5*102 + 5 PDG Nov 12 2011 PRIME View
9(4)49(4)49 4*(1011-1)/9 + 5*1010 + 5*105 + 5 PDG Nov 12 2011 PRIME View
9(4)79(4)79 4*(1017-1)/9 + 5*1016 + 5*108 + 5 PDG Nov 12 2011 PRIME View
9(4)209(4)209 4*(1043-1)/9 + 5*1042 + 5*1021 + 5 PDG Nov 12 2011 PRIME View
9(4)5099(4)5099 4*(101021-1)/9 + 5*101020 + 5*10510 + 5 PDG Nov 12 2011 PROBABLE
PRIME
View
A?????? ¬   [ n > 35000 ]
9(5)19(5)19 5*(105-1)/9 + 4*104 + 4*102 + 4 PDG Nov 12 2011 PRIME View
9(5)389(5)389 5*(1079-1)/9 + 4*1078 + 4*1039 + 4 PDG Nov 12 2011 PRIME View
9(5)1739(5)1739 5*(10349-1)/9 + 4*10348 + 4*10174 + 4 PDG Nov 12 2011 PRIME View
9(5)14939(5)14939 5*(102989-1)/9 + 4*102988 + 4*101494 + 4 PDG Nov 12 2011 PROBABLE
PRIME
View
A?????? ¬   [ n > 20000 ]
9(7)29(7)29 7*(107-1)/9 + 2*106 + 2*103 + 2 PDG Nov 12 2011 PRIME View
9(7)409(7)409 7*(1083-1)/9 + 2*1082 + 2*1041 + 2 PDG Nov 12 2011 PRIME View
9(7)2989(7)2989 7*(10599-1)/9 + 2*10598 + 2*10299 + 2 PDG Nov 12 2011 PRIME View
A?????? ¬   [ n > 20000 ]
9(8)29(8)29 8*(107-1)/9 + 106 + 103 + 1 PDG Nov 12 2011 PRIME View
9(8)49(8)49 8*(1011-1)/9 + 1010 + 105 + 1 PDG Nov 12 2011 PRIME View
9(8)149(8)149 8*(1031-1)/9 + 1030 + 1015 + 1 PDG Nov 12 2011 PRIME View
9(8)329(8)329 8*(1067-1)/9 + 1066 + 1033 + 1 PDG Nov 12 2011 PRIME View
9(8)569(8)569 8*(10115-1)/9 + 10114 + 1057 + 1 PDG Nov 12 2011 PRIME View
9(8)3829(8)3829 8*(10767-1)/9 + 10766 + 10383 + 1 PDG Nov 12 2011 PRIME View


Sources Revealed


Neil Sloane's "Integer Sequences" Encyclopedia can be consulted online :
Neil Sloane's Integer Sequences
Various numbers, primes and palindromic primes are categorised as follows :
%N Merlon numbers. Start is identical to sequence A??????
%N Palindromic merlon primes. under A??????
%N Palindromic merlon primes exist for digitlengths a(n). under A??????
Click here to view some of the author's [P. De Geest] entries to the table.
Click here to view some entries to the table about palindromes.


Prime Curios! - site maintained by G. L. Honaker Jr. and Chris Caldwell
3223223

All probable primes above 10000 digits are also
submitted to the PRP TOP records table maintained by Henri & Renaud Lifchitz.
See : http://www.primenumbers.net/prptop/prptop.php







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( © All rights reserved ) - Last modified : September 25, 2015.
Patrick De Geest - Belgium flag - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com