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Palindromic Wing Primes (PWP's)
(near-repdigit palindromes)
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313717919727929
131737141747949
151353757959161
767171373979181
383787989191797


Palindromic Wing Primes

Palindromic Wing Primes (or PWP's for short) are numbers that
are primes, palindromic in base 10, and consisting of one central digit
surrounded by two wings having an equal amount of identical digits and
different from the central one. E.g.

101
99999199999
333333313333333
7777777777772777777777777
11111111111111111111111111111111411111111111111111111111111111111

While setting up this collection of palprimes I realised that perhaps
this kind of integers was already considered under another description.
And so it turned out!
Near-repunit palindromes
Near-repdigit palindromes
are the names used in the sources where I found more PWP's ¬
The Complete List of the Largest Known Primes by Chris Caldwell
The Top Ten Prime Numbers by Rudolf Ondrejka
Palindrome prime number patterns by Harvey Heinz
Liczby pierwsze o szczególnym rozmieszczeniu cyfr by Andrzej Nowicki
    Translated in Dutch "Priemgetallen met een speciale rangschikking van cijfers"
    Translated in English "Prime numbers with a special arrangement of digits"
In case one should discover more sources I will be most happy
to add them to the list. Just let me know.

PWP's sorted by length

[ October 3, 2002 ]
Harvey Dubner (email) informed me that he co-authored an article :

" I think your idea to collect PWP's is a great and worthwhile project.
Most of the work I did on this subject was included in a paper that Chris Caldwell
and I wrote that was published in the
“Journal of Recreational Mathematics”, Volume 28, No. 1, 1996-97, pp. 1-9.
With the new hardware and software that is now available it would be easy to extend
these results. You really do good work. Please keep it up."

[ October 4, 2002 ]
Daniel Heuer (email) started to search at the beginning of 2001 :

" You have a very good initiative. I have studied numbers of the form
p(k,n) = 10^(2n+1)–k*10^n–1 from n = 1 to 38500 and 0 < k < 10.
if k = 3, 6 or 9 p(k,n)%3 = = 0
result for other value of k is:
k = 1, n = 26, 378, 1246, 1798, 2917, 23034
k = 2, n = 118
k = 4, n = 88, 112, 198, 622, 4228, 10052
k = 5, n = 14, 22, 36, 104, 1136, 17864, 25448
k = 7, n = 1, 8, 9, 352, 530, 697, 1315, 1918, 2874, 5876, 6768
k = 8, n = 1, 5, 13, 43, 169, 181, 1579, 18077, 22652
and I am still continuing..."

[ December 28, 2002 ]
Jeff Heleen prime proved a record PWP with Primo.
His prime (104769–1)/3 – 2*102384 consists of 4769 digits.

" Here is the prime cert for (3)2384_1_(3)2384.
It finished on Christmas day.
I send in 3 parts: Primo116A, Primo116B and Primo116C.
Happy Holidays.
jeff "
Jeff positioned himself at Rank 4 in Marcel Martin's
'primo top-20' with this feat !

[ January 2, 2003 ]
Daniel Heuer made a new PWP world record for the new year...

"1095019–1047509–1 is prime.
Have a good year.
Daniel "

[ January 14, 2003 ]
Daniel Heuer just finished scanning the provable PWP's
of the form 102n+1–k*10n–1 up to n = 50,000 (100,001 digits).
And he is continuing...
Ranges of this form are
(9)w1(9)w
(9)w2(9)w
(9)w4(9)w
(9)w5(9)w
(9)w7(9)w
(9)w8(9)w

[ January 27, 2003 ]
Daniel Heuer found a new PWP.

(9)521408(9)52140    or    (10104281-1) - 1052140
" 10104281 – 1052140 –1
is the first PWP with over 100,000 digits."

Some nontrivial combinations can never produce primes since
these generate infinite patterns of products of two factors.

(1)w0(1)w = (10w+1 + 1)(10w - 1)/9
101 x 1 = 101 ( is the only possible prime case when w = 1 )
1001 x 11 = 11011
10001 x 111 = 1110111
...
general formula 1(0)k1 x 1(1)k-21 ; ( k >= 2 )
(1)w2(1)w = (10w+1 - 1)(10w + 1)/9
11 x 11 = 121
101 x 111 = 11211
1001 x 1111 = 1112111
...
general formula 1(0)k1 x 1(1)k1
(3)w2(3)w = (5.10w + 1)(2.10w - 1)/3
17 x 19 = 323
167 x 199 = 33233
1667 x 1999 = 3332333
...
general formula 1(6)k7 x 1(9)k+1
(3)w4(3)w = (5.10w - 1)(2.10w + 1)/3
7 x 49 = 343
67 x 499 = 33433
667 x 4999 = 3334333
...
general formula (6)k7 x 4(9)k+1


PWP Factorization Projects

( n = 2.w + 1 )

(3)w1(3)w = (10n-1)/3 - 2.10w Factorizations of 33...33133...33 (M. Kamada)
(7)w1(7)w = (7.10n-1)/9 - 6.10w Factorizations of 77...77177...77 (M. Kamada)
(9)w1(9)w = (10n-1) - 8.10w Factorizations of 99...99199...99 (M. Kamada)
(7)w2(7)w = (7.10n-1)/9 - 5.10w Factorizations of 77...77277...77 (M. Kamada)
(9)w2(9)w = (10n-1) - 7.10w Factorizations of 99...99299...99 (M. Kamada)
(1)w3(1)w = (10n-1)/9 + 2.10w Factorizations of 11...11311...11 (M. Kamada)
(7)w3(7)w = (7.10n-1)/9 - 4.10w Factorizations of 77...77377...77 (M. Kamada)
(1)w4(1)w = (10n-1)/9 + 3.10w Factorizations of 11...11411...11 (M. Kamada)
(7)w4(7)w = (7.10n-1)/9 - 3.10w Factorizations of 77...77477...77 (M. Kamada)
(9)w4(9)w = (10n-1) - 5.10w Factorizations of 99...99499...99 (M. Kamada)
(1)w5(1)w = (10n-1)/9 + 4.10w Factorizations of 11...11511...11 (M. Kamada)
(3)w5(3)w = (10n-1)/3 + 2.10w Factorizations of 33...33533...33 (M. Kamada)
(7)w5(7)w = (7.10n-1)/9 - 2.10w Factorizations of 77...77577...77 (M. Kamada)
(9)w5(9)w = (10n-1) - 4.10w Factorizations of 99...99599...99 (M. Kamada)
(1)w6(1)w = (10n-1)/9 + 5.10w Factorizations of 11...11611...11 (M. Kamada)
(7)w6(7)w = (7.10n-1)/9 - 10w Factorizations of 77...77677...77 (M. Kamada)
(1)w7(1)w = (10n-1)/9 + 6.10w Factorizations of 11...11711...11 (M. Kamada)
(3)w7(3)w = (10n-1)/3 + 4.10w Factorizations of 33...33733...33 (M. Kamada)
(9)w7(9)w = (10n-1) - 2.10w Factorizations of 99...99799...99 (M. Kamada)
(1)w8(1)w = (10n-1)/9 + 7.10w Factorizations of 11...11811...11 (M. Kamada)
(3)w8(3)w = (10n-1)/3 + 5.10w Factorizations of 33...33833...33 (M. Kamada)
(7)w8(7)w = (7.10n-1)/9 + 10w Factorizations of 77...77877...77 (M. Kamada)
(9)w8(9)w = (10n-1) - 10w Factorizations of 99...99899...99 (M. Kamada)
(1)w9(1)w = (10n-1)/9 + 8.10w Factorizations of 11...11911...11 (M. Kamada)
(7)w9(7)w = (7.10n-1)/9 + 2.10w Factorizations of 77...77977...77 (M. Kamada)


The Table


The reference table for
Palindromic Wing Primes
This collection is complete for
probable primes up to 40001
digits (by DH) and for proven
primes up to  3000  digits.
DB = Darren Bedwell
DH = Daniel Heuer
HD = Harvey Dubner
JH = Jeff Heleen
P&B = Propper & Batalov
PDG = Patrick De Geest
RP = Robert Price
PWPFormula
blue exp = # of digits		WhoWhenStatusOutput
Logs
 ¬ 
(1)10(1)1 (103-1)/9 - 101
IMPORTANT NOTE		 PDG Sep 23 2002 PRIME View
A077775 ¬
A183174 ¬		 
   [ n > 200000 ]
(3)11(3)1 (103-1)/3 - 2*101 PDG Sep 23 2002 PRIME View
(3)31(3)3 (107-1)/3 - 2*103 PDG Sep 23 2002 PRIME View
(3)71(3)7 (1015-1)/3 - 2*107 PDG Sep 23 2002 PRIME View
(3)611(3)61 (10123-1)/3 - 2*1061 PDG Sep 23 2002 PRIME View
(3)901(3)90 (10181-1)/3 - 2*1090 PDG Sep 23 2002 PRIME View
(3)921(3)92 (10185-1)/3 - 2*1092 PDG Sep 23 2002 PRIME View
(3)2691(3)269 (10539-1)/3 - 2*10269 PDG Sep 23 2002 PRIME View
(3)2981(3)298 (10597-1)/3 - 2*10298 PDG Sep 23 2002 PRIME View
(3)3211(3)321 (10643-1)/3 - 2*10321 PDG Sep 23 2002 PRIME View
(3)3711(3)371 (10743-1)/3 - 2*10371 PDG Sep 23 2002 PRIME View
(3)7761(3)776 (101553-1)/3 - 2*10776 JH Sep 28 2002 PRIME View
(3)15671(3)1567 (103135-1)/3 - 2*101567 JH Oct 25 2002 PRIME View
(3)23841(3)2384 (104769-1)/3 - 2*102384 JH Dec 25 2002 PRIME View
(3)25661(3)2566 (105133-1)/3 - 2*102566 PDG Sep 26 2002 PRIME View
(3)30881(3)3088 (106177-1)/3 - 2*103088 PDG Sep 26 2002 PRIME View
(3)58661(3)5866 (1011733-1)/3 - 2*105866 DH Oct 31 2002 PROBABLE
PRIME		 View
(3)80511(3)8051 (1016103-1)/3 - 2*108051 DH Oct 31 2002 PROBABLE
PRIME		 View
(3)94981(3)9498 (1018997-1)/3 - 2*109498 DH Nov 04 2002 PROBABLE
PRIME		 View
(3)126351(3)12635 (1025271-1)/3 - 2*1012635 DH Nov 07 2002 PROBABLE
PRIME		 View
(3)245121(3)24512 (1049025-1)/3 - 2*1024512 PDG Jul 05 2005 PROBABLE
PRIME		 View
(3)325211(3)32521 (1065043-1)/3 - 2*1032521 RP Jan 29 2016 PROBABLE
PRIME		 View
(3)439821(3)43982 (1087965-1)/3 - 2*1043982 RP Jan 29 2016 RECORD
PROBABLE
PRIME		 View
 ¬ 
   [ n > 200000 ] searched from july 2005 till january 2006 !
(7)1161(7)116 7*(10233-1)/9 - 6*10116 PDG Sep 23 2002 PRIME View
A077776 ¬
A183184 ¬		 
   [ n > 100000 ]
(9)11(9)1 (103-1) - 8*101 PDG Sep 23 2002 PRIME View
(9)51(9)5 (1011-1) - 8*105 PDG Sep 23 2002 PRIME View
(9)131(9)13 (1027-1) - 8*1013 PDG Sep 23 2002 PRIME View
(9)431(9)43 (1087-1) - 8*1043 PDG Sep 23 2002 PRIME View
(9)1691(9)169 (10339-1) - 8*10169 PDG Sep 23 2002 PRIME View
(9)1811(9)181 (10363-1) - 8*10181 PDG Sep 23 2002 PRIME View
(9)15791(9)1579 (103159-1) - 8*101579 PDG Sep 23 2002 PRIME View
(9)180771(9)18077 (1036155-1) - 8*1018077 DH Jul 21 2001 PRIME View
(9)226521(9)22652 (1045305-1) - 8*1022652 DH Sep 18 2001 PRIME View
(9)1573631(9)157363 (10314727-1) - 8*10157363 DB Jan 8 2013 PRIME View
A077777 ¬
A183178 ¬		 
(7)12(7)1 7*(103-1)/9 - 5*101 PDG Sep 23 2002 PRIME View
(7)32(7)3 7*(107-1)/9 - 5*103 PDG Sep 23 2002 PRIME View
(7)72(7)7 7*(1015-1)/9 - 5*107 PDG Sep 23 2002 PRIME View
(7)102(7)10 7*(1021-1)/9 - 5*1010 PDG Sep 23 2002 PRIME View
(7)122(7)12 7*(1025-1)/9 - 5*1012 PDG Sep 23 2002 PRIME View
(7)4802(7)480 7*(10961-1)/9 - 5*10480 PDG Sep 23 2002 PRIME View
(7)9492(7)949 7*(101899-1)/9 - 5*10949 JH Sep 30 2002 PRIME View
(7)19452(7)1945 7*(103891-1)/9 - 5*101945 PDG Sep 23 2002 PRIME View RC
(7)75482(7)7548 7*(1015097-1)/9 - 5*107548 DH Oct 31 2002 PROBABLE
PRIME		 View
(7)89232(7)8923 7*(1017847-1)/9 - 5*108923 DH Oct 31 2002 PROBABLE
PRIME		 View
A077778 ¬
A115073 ¬		 
(9)12(9)1 (103-1) - 7*101 PDG Sep 23 2002 PRIME View
(9)82(9)8 (1017-1) - 7*108 PDG Sep 23 2002 PRIME View
(9)92(9)9 (1019-1) - 7*109 PDG Sep 23 2002 PRIME View
(9)3522(9)352 (10705-1) - 7*10352 PDG Sep 23 2002 PRIME View
(9)5302(9)530 (101061-1) - 7*10530 JH Sep 28 2002 PRIME View
(9)6972(9)697 (101395-1) - 7*10697 JH Sep 28 2002 PRIME View
(9)13152(9)1315 (102631-1) - 7*101315 HD --- -- 1989 PRIME View
(9)19182(9)1918 (103837-1) - 7*101918 HD --- -- 1999 PRIME View
(9)28742(9)2874 (105749-1) - 7*102874 HD --- -- 1999 PRIME View
(9)58762(9)5876 (1011753-1) - 7*105876 HD --- -- 1999 PRIME View
(9)67682(9)6768 (1013537-1) - 7*106768 HD --- -- 1999 PRIME View
(9)629382(9)62938 (10125877-1) - 7*1062938 DB Oct 31 2010 PRIME View
(9)1347392(9)134739 (10269479-1) - 7*10134739 DB Feb 29 2012 PRIME View
A077779 ¬
A107123 ¬		 
(1)13(1)1 (103-1)/9 + 2*101 PDG Sep 23 2002 PRIME View
(1)23(1)2 (105-1)/9 + 2*102 PDG Sep 23 2002 PRIME View
(1)193(1)19 (1039-1)/9 + 2*1019 PDG Sep 23 2002 PRIME View
(1)973(1)97 (10195-1)/9 + 2*1097 PDG Sep 23 2002 PRIME View
(1)98183(1)9818 (1019637-1)/9 + 2*109818 DH Nov 04 2002 PROBABLE
PRIME		 View
 ¬ 
(7)23(7)2 7*(105-1)/9 - 4*102 PDG Sep 23 2002 PRIME View
A077780 ¬
A107124 ¬		 
(1)24(1)2 (105-1)/9 + 3*102 PDG Sep 23 2002 PRIME View
(1)34(1)3 (107-1)/9 + 3*103 PDG Sep 23 2002 PRIME View
(1)324(1)32 (1065-1)/9 + 3*1032 PDG Sep 23 2002 PRIME View
(1)454(1)45 (1091-1)/9 + 3*1045 PDG Sep 23 2002 PRIME View
(1)15444(1)1544 (103089-1)/9 + 3*101544 PDG Sep 23 2002 PRIME View DB
A077781 ¬
A183179 ¬		 
   [ n > 200000 ]
(7)24(7)2 7*(105-1)/9 - 3*102 PDG Sep 23 2002 PRIME View
(7)34(7)3 7*(107-1)/9 - 3*103 PDG Sep 23 2002 PRIME View
(7)64(7)6 7*(1013-1)/9 - 3*106 PDG Sep 23 2002 PRIME View
(7)234(7)23 7*(1047-1)/9 - 3*1023 PDG Sep 23 2002 PRIME View
(7)364(7)36 7*(1073-1)/9 - 3*1036 PDG Sep 23 2002 PRIME View
(7)694(7)69 7*(10139-1)/9 - 3*1069 PDG Sep 23 2002 PRIME View
(7)5614(7)561 7*(101123-1)/9 - 3*10561 JH Sep 28 2002 PRIME View
(7)7234(7)723 7*(101447-1)/9 - 3*10723 JH Oct 01 2002 PRIME View
(7)34384(7)3438 7*(106877-1)/9 - 3*103438 PDG Oct 10 2002 PRIME View
(7)41044(7)4104 7*(108209-1)/9 - 3*104104 PDG Oct 10 2002 PROBABLE
PRIME		 View
(7)90204(7)9020 7*(1018041-1)/9 - 3*109020 DH Nov 04 2002 PROBABLE
PRIME		 View
(7)139774(7)13977 7*(1027955-1)/9 - 3*1013977 DH Nov 13 2002 PROBABLE
PRIME		 View
(7)196554(7)19655 7*(1039311-1)/9 - 3*1019655 DH Nov 25 2002 PROBABLE
PRIME		 View
(7)324004(7)32400 7*(1064801-1)/9 - 3*1032400 RP Nov 23 2015 PROBABLE
PRIME		 View
A077782 ¬
A183185 ¬		 
(9)144(9)14 (1029-1) - 5*1014 PDG Sep 23 2002 PRIME View
(9)224(9)22 (1045-1) - 5*1022 PDG Sep 23 2002 PRIME View
(9)364(9)36 (1073-1) - 5*1036 PDG Sep 23 2002 PRIME View
(9)1044(9)104 (10209-1) - 5*10104 PDG Sep 23 2002 PRIME View
(9)11364(9)1136 (102273-1) - 5*101136 JH Oct 13 2002 PRIME View
(9)178644(9)17864 (1035729-1) - 5*1017864 DH Jul 02 2001 PRIME View
(9)254484(9)25448 (1050897-1) - 5*1025448 DH Oct 29 2001 PRIME View
A077783 ¬
A107125 ¬		 
(1)15(1)1 (103-1)/9 + 4*101 PDG Sep 23 2002 PRIME View
(1)75(1)7 (1015-1)/9 + 4*107 PDG Sep 23 2002 PRIME View
(1)455(1)45 (1091-1)/9 + 4*1045 PDG Sep 23 2002 PRIME View
(1)1155(1)115 (10231-1)/9 + 4*10115 PDG Sep 23 2002 PRIME View
(1)6815(1)681 (101363-1)/9 + 4*10681 JH Sep 29 2002 PRIME View
(1)12485(1)1248 (102497-1)/9 + 4*101248 JH Oct 09 2002 PRIME View
(1)24815(1)2481 (104963-1)/9 + 4*102481 PDG Sep 23 2002 PRIME View
(1)26895(1)2689 (105379-1)/9 + 4*102689 PDG Oct 11 2002 PRIME View
(1)61985(1)6198 (1012397-1)/9 + 4*106198 DH Oct 31 2002 PROBABLE
PRIME		 View
(1)131975(1)13197 (1026395-1)/9 + 4*1013197 DH Nov 06 2002 PROBABLE
PRIME		 View
A077784 ¬
A183175 ¬		 
(3)15(3)1 (103-1)/3 + 2*101 PDG Sep 23 2002 PRIME View
(3)25(3)2 (105-1)/3 + 2*102 PDG Sep 23 2002 PRIME View
(3)175(3)17 (1035-1)/3 + 2*1017 PDG Sep 23 2002 PRIME View
(3)795(3)79 (10159-1)/3 + 2*1079 PDG Sep 23 2002 PRIME View
(3)1185(3)118 (10237-1)/3 + 2*10118 PDG Sep 23 2002 PRIME View
(3)1625(3)162 (10325-1)/3 + 2*10162 PDG Sep 23 2002 PRIME View
(3)1775(3)177 (10355-1)/3 + 2*10177 PDG Sep 23 2002 PRIME View
(3)1855(3)185 (10371-1)/3 + 2*10185 PDG Sep 23 2002 PRIME View
(3)2405(3)240 (10481-1)/3 + 2*10240 PDG Sep 23 2002 PRIME View
(3)8245(3)824 (101649-1)/3 + 2*10824 JH Sep 29 2002 PRIME View
(3)18205(3)1820 (103641-1)/3 + 2*101820 PDG Sep 23 2002 PRIME View DB
(3)23545(3)2354 (104709-1)/3 + 2*102354 PDG Sep 23 2002 PRIME View RC
A077785 ¬
A183180 ¬		 
(7)15(7)1 7*(103-1)/9 - 2*101 PDG Sep 23 2002 PRIME View
(7)75(7)7 7*(1015-1)/9 - 2*107 PDG Sep 23 2002 PRIME View
(7)135(7)13 7*(1027-1)/9 - 2*1013 PDG Sep 23 2002 PRIME View
(7)585(7)58 7*(10117-1)/9 - 2*1058 PDG Sep 23 2002 PRIME View
(7)1295(7)129 7*(10259-1)/9 - 2*10129 PDG Sep 23 2002 PRIME View
(7)2535(7)253 7*(10507-1)/9 - 2*10253 PDG Sep 23 2002 PRIME View
(7)16575(7)1657 7*(103315-1)/9 - 2*101657 PDG Sep 23 2002 PRIME View DB
(7)22445(7)2244 7*(104489-1)/9 - 2*102244 PDG Sep 23 2002 PRIME View DB
(7)24375(7)2437 7*(104875-1)/9 - 2*102437 PDG Sep 23 2002 PRIME View
(7)79245(7)7924 7*(1015849-1)/9 - 2*107924 DH Oct 31 2002 PROBABLE
PRIME		 View
(7)99035(7)9903 7*(1019807-1)/9 - 2*109903 DH Nov 04 2002 PROBABLE
PRIME		 View
(7)118995(7)11899 7*(1023799-1)/9 - 2*1011899 DH Nov 05 2002 PROBABLE
PRIME		 View
(7)181575(7)18157 7*(1036315-1)/9 - 2*1018157 DH Nov 18 2002 PROBABLE
PRIME		 View
(7)189575(7)18957 7*(1037915-1)/9 - 2*1018957 DH Nov 20 2002 PROBABLE
PRIME		 View
(7)236655(7)23665 7*(1047331-1)/9 - 2*1023665 RP Jun 25 2017 PROBABLE
PRIME		 View
A077786 ¬
A183186 ¬		 
(9)885(9)88 (10177-1) - 4*1088 PDG Sep 23 2002 PRIME View
(9)1125(9)112 (10225-1) - 4*10112 PDG Sep 23 2002 PRIME View
(9)1985(9)198 (10397-1) - 4*10198 PDG Sep 23 2002 PRIME View
(9)6225(9)622 (101245-1) - 4*10622 JH Oct 02 2002 PRIME View
(9)42285(9)4228 (108457-1) - 4*104228 PDG Oct 04 2002 PRIME View
(9)100525(9)10052 (1020105-1) - 4*1010052 DH Mar 28 2001 PRIME View
(9)558625(9)55862 (10111725-1) - 4*1055862 DB Sep 19 2010 PRIME View
A077787 ¬
A107126 ¬		 
(1)106(1)10 (1021-1)/9 + 5*1010 PDG Sep 23 2002 PRIME View
(1)146(1)14 (1029-1)/9 + 5*1014 PDG Sep 23 2002 PRIME View
(1)406(1)40 (1081-1)/9 + 5*1040 PDG Sep 23 2002 PRIME View
(1)596(1)59 (10119-1)/9 + 5*1059 PDG Sep 23 2002 PRIME View
(1)1606(1)160 (10321-1)/9 + 5*10160 PDG Sep 23 2002 PRIME View
(1)4126(1)412 (10825-1)/9 + 5*10412 PDG Sep 23 2002 PRIME View
(1)5606(1)560 (101121-1)/9 + 5*10560 JH Oct 02 2002 PRIME View
(1)12896(1)1289 (102579-1)/9 + 5*101289 JH Oct 07 2002 PRIME View
(1)18466(1)1846 (103693-1)/9 + 5*101846 PDG Sep 23 2002 PRIME View DB
A077788 ¬
A183181 ¬		 
(7)46(7)4 7*(109-1)/9 - 104 PDG Sep 23 2002 PRIME View
(7)56(7)5 7*(1011-1)/9 - 105 PDG Sep 23 2002 PRIME View
(7)86(7)8 7*(1017-1)/9 - 108 PDG Sep 23 2002 PRIME View
(7)116(7)11 7*(1023-1)/9 - 1011 PDG Sep 23 2002 PRIME View
(7)12446(7)1244 7*(102489-1)/9 - 101244 JH Oct 16 2002 PRIME View
(7)16856(7)1685 7*(103371-1)/9 - 101685 PDG Sep 23 2002 PRIME View DB
(7)20096(7)2009 7*(104019-1)/9 - 102009 PDG Sep 23 2002 PRIME View DB
(7)146576(7)14657 7*(1029315-1)/9 - 1014657 DH Nov 13 2002 PROBABLE
PRIME		 View
(7)151186(7)15118 7*(1030237-1)/9 - 1015118 DH Nov 13 2002 PROBABLE
PRIME		 View
A077789 ¬
A107127 ¬		 
   [ n > 100000 ]
(1)37(1)3 (107-1)/9 + 6*103 PDG Sep 23 2002 PRIME View
(1)337(1)33 (1067-1)/9 + 6*1033 PDG Sep 23 2002 PRIME View
(1)3117(1)311 (10623-1)/9 + 6*10311 PDG Sep 23 2002 PRIME View
(1)29337(1)2933 (105867-1)/9 + 6*102933 JH Jun 21 2003 PRIME View
(1)222357(1)22235 (1044471-1)/9 + 6*1022235 RP Apr 30 2017 PROBABLE
PRIME		 View
(1)391657(1)39165 (1078331-1)/9 + 6*1039165 RP Apr 30 2017 PROBABLE
PRIME		 View
(1)415857(1)41585 (1083171-1)/9 + 6*1041585 RP Apr 30 2017 PROBABLE
PRIME		 View
A077790 ¬
A183176 ¬		 
(3)17(3)1 (103-1)/3 + 4*101 PDG Sep 23 2002 PRIME View
(3)37(3)3 (107-1)/3 + 4*103 PDG Sep 23 2002 PRIME View
(3)77(3)7 (1015-1)/3 + 4*107 PDG Sep 23 2002 PRIME View
(3)117(3)11 (1023-1)/3 + 4*1011 PDG Sep 23 2002 PRIME View
(3)137(3)13 (1027-1)/3 + 4*1013 PDG Sep 23 2002 PRIME View
(3)177(3)17 (1035-1)/3 + 4*1017 PDG Sep 23 2002 PRIME View
(3)297(3)29 (1059-1)/3 + 4*1029 PDG Sep 23 2002 PRIME View
(3)317(3)31 (1063-1)/3 + 4*1031 PDG Sep 23 2002 PRIME View
(3)337(3)33 (1067-1)/3 + 4*1033 PDG Sep 23 2002 PRIME View
(3)777(3)77 (10155-1)/3 + 4*1077 PDG Sep 23 2002 PRIME View
(3)9337(3)933 (101867-1)/3 + 4*10933 JH Oct 01 2002 PRIME View
(3)15557(3)1555 (103111-1)/3 + 4*101555 PDG Sep 23 2002 PRIME View DB
(3)117587(3)11758 (1023517-1)/3 + 4*1011758 DH Nov 13 2002 PROBABLE
PRIME		 View
 ¬ 
(9)1187(9)118 (10237-1) - 2*10118 PDG Sep 23 2002 PRIME View
(9)1451267(9)145126 (10290253-1) - 2*10145126 DB Apr 11 2012 PRIME View
A077791 ¬
A107648 ¬		 
(1)18(1)1 (103-1)/9 + 7*101 PDG Sep 23 2002 PRIME View
(1)48(1)4 (109-1)/9 + 7*104 PDG Sep 23 2002 PRIME View
(1)68(1)6 (1013-1)/9 + 7*106 PDG Sep 23 2002 PRIME View
(1)78(1)7 (1015-1)/9 + 7*107 PDG Sep 23 2002 PRIME View
(1)3848(1)384 (10769-1)/9 + 7*10384 PDG Sep 23 2002 PRIME View
(1)6668(1)666 (101333-1)/9 + 7*10666 JH Oct 02 2002 PRIME View
(1)6758(1)675 (101351-1)/9 + 7*10675 JH Oct 02 2002 PRIME View
(1)31658(1)3165 (106331-1)/9 + 7*103165 DH Oct 31 2002 PRIME View
A077792 ¬
A183177 ¬		 
   [ n > 100000 ]
(3)18(3)1 (103-1)/3 + 5*101 PDG Sep 23 2002 PRIME View
(3)78(3)7 (1015-1)/3 + 5*107 PDG Sep 23 2002 PRIME View
(3)858(3)85 (10171-1)/3 + 5*1085 PDG Sep 23 2002 PRIME View
(3)948(3)94 (10189-1)/3 + 5*1094 PDG Sep 23 2002 PRIME View
(3)2738(3)273 (10547-1)/3 + 5*10273 PDG Sep 23 2002 PRIME View
(3)3568(3)356 (10713-1)/3 + 5*10356 PDG Sep 23 2002 PRIME View
(3)10778(3)1077 (102155-1)/3 + 5*101077 JH Oct 11 2002 PRIME View
(3)17978(3)1797 (103595-1)/3 + 5*101797 PDG Sep 23 2002 PRIME View DB
(3)67588(3)6758 (1013517-1)/3 + 5*106758 DH Oct 31 2002 PROBABLE
PRIME		 View
(3)302328(3)30232 (1060465-1)/3 + 5*1030232 RP Apr 21 2016 PROBABLE
PRIME		 View
A077793 ¬
A183182 ¬		 
(7)18(7)1 7*(103-1)/9 + 101 PDG Sep 23 2002 PRIME View
(7)38(7)3 7*(107-1)/9 + 103 PDG Sep 23 2002 PRIME View
(7)398(7)39 7*(1079-1)/9 + 1039 PDG Sep 23 2002 PRIME View
(7)548(7)54 7*(10109-1)/9 + 1054 PDG Sep 23 2002 PRIME View
(7)1688(7)168 7*(10337-1)/9 + 10168 PDG Sep 23 2002 PRIME View
(7)2408(7)240 7*(10481-1)/9 + 10240 PDG Sep 23 2002 PRIME View
(7)53288(7)5328 7*(1010657-1)/9 + 105328 DH Oct 31 2002 PROBABLE
PRIME		 View
(7)61598(7)6159 7*(1012319-1)/9 + 106159 DH Oct 31 2002 PROBABLE
PRIME		 View
A077794 ¬
A183187 ¬		 
(9)268(9)26 (1053-1) - 1026 PDG Sep 23 2002 PRIME View
(9)3788(9)378 (10757-1) - 10378 PDG Sep 23 2002 PRIME View
(9)12468(9)1246 (102493-1) - 101246 HD --- -- 1989 PRIME View
(9)17988(9)1798 (103597-1) - 101798 PDG Sep 23 2002 PRIME View
(9)29178(9)2917 (105835-1) - 102917 PDG Oct 04 2002 PRIME View
(9)230348(9)23034 (1046069-1) - 1023034 DH Sep 22 2001 PRIME View
(9)475098(9)47509 (1095019-1) - 1047509 DH Jan 02 2003 PRIME View
(9)521408(9)52140 (10104281-1) - 1052140 DH Jan 27 2003 PRIME View
(9)674048(9)67404 (10134809-1) - 1067404 DB Nov 24 2010 PRIME View
(9)9442648(9)944264 (101888529-1) - 10944264 P&B Oct 18 2021 RECORD
PROVEN
PRIME		 View
A077795 ¬
A107649 ¬		 
(1)19(1)1 (103-1)/9 + 8*101 PDG Sep 23 2002 PRIME View
(1)49(1)4 (109-1)/9 + 8*104 PDG Sep 23 2002 PRIME View
(1)269(1)26 (1053-1)/9 + 8*1026 PDG Sep 23 2002 PRIME View
(1)1879(1)187 (10375-1)/9 + 8*10187 PDG Sep 23 2002 PRIME View
(1)2269(1)226 (10453-1)/9 + 8*10226 PDG Sep 23 2002 PRIME View
(1)8749(1)874 (101749-1)/9 + 8*10874 JH Oct 03 2002 PRIME View
(1)133099(1)13309 (1026619-1)/9 + 8*1013309 DH Nov 13 2002 PROBABLE
PRIME		 View
A077796 ¬
A183183 ¬		 
(7)19(7)1 7*(103-1)/9 + 2*101 PDG Sep 23 2002 PRIME View
(7)29(7)2 7*(105-1)/9 + 2*102 PDG Sep 23 2002 PRIME View
(7)89(7)8 7*(1017-1)/9 + 2*108 PDG Sep 23 2002 PRIME View
(7)199(7)19 7*(1039-1)/9 + 2*1019 PDG Sep 23 2002 PRIME View
(7)209(7)20 7*(1041-1)/9 + 2*1020 PDG Sep 23 2002 PRIME View
(7)2129(7)212 7*(10425-1)/9 + 2*10212 PDG Sep 23 2002 PRIME View
(7)2809(7)280 7*(10561-1)/9 + 2*10280 PDG Sep 23 2002 PRIME View
(7)8879(7)887 7*(101775-1)/9 + 2*10887 JH Oct 03 2002 PRIME View
(7)10219(7)1021 7*(102043-1)/9 + 2*101021 JH Oct 04 2002 PRIME View
(7)55159(7)5515 7*(1011031-1)/9 + 2*105515 DH Oct 31 2002 PROBABLE
PRIME		 View
(7)81169(7)8116 7*(1016233-1)/9 + 2*108116 DH Oct 31 2002 PROBABLE
PRIME		 View
(7)118529(7)11852 7*(1023705-1)/9 + 2*1011852 DH Nov 05 2002 PROBABLE
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 Wing numbers. Start is identical to sequence A046075
%N Palindromic wing primes. under A077798
%N Palindromic wing primes exist for digitlengths a(n). under A077797
Wing numbers otherwise ordered by its wing digit and not its central digit by Amarnath Murthy
%N a(1) = 11; for n > 1, palindromic primes in which a single digit is sandwiched between strings of '1's. A088281
%N a(1) = 11; for n > 1, palindromic primes in which a single digit is sandwiched between strings of '3's. A088282
%N a(1) = 11; for n > 1, palindromic primes in which a single digit is sandwiched between strings of '7's. A088283
%N a(1) = 11; for n > 1, palindromic primes in which a single digit is sandwiched between strings of '9's. A088284
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
101
131
151
181
191
313
353
373
383
727
757
787
797
919
929
11311
1114111
1115111
111181111
777767777
77777677777
99999199999
1111118111111
11111...5...11111 (91-digits)
77777...8...77777 (109-digits)
77777...2...77777 (961-digits)
99999...2...99999 (1061-digits)
99999...8...99999 (2493-digits)
99999...2...99999 (2631-digits)
99999...2...99999 (5749-digits)

All of Daniel Heuer's 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 : May 20, 2022.
Patrick De Geest - Belgium flag - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com