Palindromic Sums of Powers of Consecutive Primes

Palindromic Sums of Powers of Consecutive Primes

At the time of my search, the green entries were already noted in Patrick De Geest's World!Of Numbers web-page on this topic, providing me with the inspiration for this effort. The 'squares' part of the search was done in five parts: The initial run looked for up to 100 consecutives anchored in the first ten-million primes. Subsequent runs constrained larger numbers of consecutives with smaller ranges of anchor-points. Total computation (Mathematica 4, on a 400 MHz iMac) time was around 7 days. I like to think that the results are illustrative, not exhaustive. [17 August 2001]

I've decided to update this page somewhat with new results. In May of 2005, I created a large prime database with which I began a search for more squares solutions. These new finds (currently, only 6) will be shown below in blue. I want to point out, for the sake of completeness, that there exist also (trivially) the single primes whose power is a palindrome. For squares, these correspond to Sloane's A065378, and I refer you to the sequence there, rather than reproducing it here.

Cubes

7 {43, 47, 53, 59, 61, 67, 71}

1423241

25 {659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827}

10450805401

273 {2441, ..., 4691}

13547744774531

Squares

2 {1019, 1021}

2080802

2 {1051, 1061}

2230322

3 {751, 757, 761}

1716171

5 {3, 5, 7, 11, 13}

373

5 {7, 11, 13, 17, 19}

989

5 {8646863861, 8646863891, 8646863893, 8646863921, 8646863941}

373841276646672148373

7 {2, 3, 5, 7, 11, 13, 17}

666

7 {157999, 158003, 158009, 158017, 158029, 158047, 158071}

174803308471

9 {13473689, 13473721, 13473751, 13473787, 13473833, 13473841, 13473851, 13473853, 13473857}

1633889119883361

10 {4921673, 4921711, 4921717, 4921757, 4921759, 4921769, 4921771, 4921781, 4921783, 4921811}

242236545632242

11 {9324617, 9324641, 9324677, 9324691, 9324697, 9324739, 9324743, 9324751, 9324761, 9324787, 9324803}

956454191454659

14 {47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107}

89798

14 {80071, 80077, 80107, 80111, 80141, 80147, 80149, 80153, 80167, 80173, 80177, 80191, 80207, 80209}

89933133998

18 {643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757}

8796978

19 {3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71}

30003

20 {570569, 570587, 570601, 570613, 570637, 570643, 570649, 570659, 570667, 570671, 570677, 570683, 570697, 570719, 570733, 570737, 570743, 570781, 570821, 570827}

6513643463156

21 {22279, 22283, 22291, 22303, 22307, 22343, 22349, 22367, 22369, 22381, 22391, 22397, 22409, 22433, 22441, 22447, 22453, 22469, 22481, 22483, 22501}

10527072501

21 {399271, 399277, 399281, 399283, 399353, 399379, 399389, 399391, 399401, 399403, 399409, 399433, 399439, 399473, 399481, 399491, 399493, 399499, 399523, 399527, 399541}

3350196910533

22 {305741, 305743, 305749, 305759, 305761, 305771, 305783, 305803, 305821, 305839, 305849, 305857, 305861, 305867, 305873, 305917, 305927, 305933, 305947, 305971, 305999, 306011}

2058023208502

23 {503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647}

7824287

23 {177239, 177257, 177269, 177283, 177301, 177319, 177323, 177337, 177347, 177379, 177383, 177409, 177421, 177427, 177431, 177433, 177467, 177473, 177481, 177487, 177493, 177511, 177533}

723757757327

23 {4001527, 4001531, 4001549, 4001551, 4001561, 4001567, 4001593, 4001597, 4001603, 4001611, 4001617, 4001629, 4001639, 4001689, 4001713, 4001719, 4001741, 4001743, 4001771, 4001779, 4001791, 4001807, 4001827}

368305303503863

24 {7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103}

86568

25 {11149, 11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251, 11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329, 11351, 11353, 11369, 11383}

3170330713

28 {49077661, 49077667, 49077671, 49077673, 49077713, 49077719, 49077737, 49077811, 49077857, 49077863, 49077871, 49077877, 49077887, 49077901, 49077907, 49077913, 49077923, 49077937, 49077953, 49077979, 49078009, 49078049, 49078069, 49078079, 49078091, 49078123, 49078153, 49078157}

67441932423914476

33 {131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311}

1650561

33 {53437, 53441, 53453, 53479, 53503, 53507, 53527, 53549, 53551, 53569, 53591, 53593, 53597, 53609, 53611, 53617, 53623, 53629, 53633, 53639, 53653, 53657, 53681, 53693, 53699, 53717, 53719, 53731, 53759, 53773, 53777, 53783, 53791}

94892829849

35 {3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463}

386595683

36 {2460659, 2460673, 2460677, 2460707, 2460719, 2460721, 2460743, 2460781, 2460791, 2460797, 2460803, 2460817, 2460827, 2460859, 2460863, 2460877, 2460881, 2460883, 2460889, 2460901, 2460917, 2460919, 2460947, 2460959, 2460961, 2460973, 2460989, 2461001, 2461021, 2461031, 2461037, 2461091, 2461093, 2461099, 2461103, 2461139}

218015797510812

37 {500287, 500299, 500317, 500321, 500333, 500341, 500363, 500369, 500389, 500393, 500413, 500417, 500431, 500443, 500459, 500471, 500473, 500483, 500501, 500509, 500519, 500527, 500567, 500579, 500587, 500603, 500629, 500671, 500677, 500693, 500699, 500713, 500719, 500723, 500729, 500741, 500777}

9269175719629

40 {41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239}

869968

43 {3006397, 3006413, 3006439, 3006457, 3006461, 3006469, 3006511, 3006529, 3006533, 3006551, 3006599, 3006623, 3006631, 3006649, 3006667, 3006677, 3006701, 3006713, 3006719, 3006733, 3006737, 3006761, 3006763, 3006781, 3006791, 3006793, 3006821, 3006823, 3006827, 3006847, 3006851, 3006881, 3006901, 3006917, 3006937, 3006967, 3006973, 3006989, 3007001, 3007003, 3007009, 3007019, 3007049}

388741434147883

43 {46072589, 46072591, 46072597, 46072613, 46072633, 46072673, 46072711, 46072729, 46072753, 46072757, 46072759, 46072781, 46072783, 46072799, 46072811, 46072837, 46072843, 46072849, 46072877, 46072919, 46072921, 46072927, 46072937, 46072951, 46072987, 46072991, 46072993, 46073003, 46073011, 46073123, 46073143, 46073149, 46073171, 46073173, 46073189, 46073219, 46073231, 46073273, 46073297, 46073311, 46073323, 46073387, 46073389}

91276833133867219

49 {332419567, 332419643, 332419651, 332419691, 332419693, 332419697, 332419699, 332419733, 332419741, 332419757, 332419781, 332419783, 332419793, 332419817, 332419823, 332419849, 332419859, 332419891, 332419939, 332419949, 332419957, 332419981, 332419993, 332420021, 332420041, 332420059, 332420089, 332420111, 332420117, 332420131, 332420141, 332420149, 332420183, 332420191, 332420197, 332420201, 332420213, 332420233, 332420267, 332420269, 332420273, 332420279, 332420281, 332420323, 332420351, 332420381, 332420383, 332420393, 332420419}

5414650417140564145

57 {29569, 29573, 29581, 29587, 29599, 29611, 29629, 29633, 29641, 29663, 29669, 29671, 29683, 29717, 29723, 29741, 29753, 29759, 29761, 29789, 29803, 29819, 29833, 29837, 29851, 29863, 29867, 29873, 29879, 29881, 29917, 29921, 29927, 29947, 29959, 29983, 29989, 30011, 30013, 30029, 30047, 30059, 30071, 30089, 30091, 30097, 30103, 30109, 30113, 30119, 30133, 30137, 30139, 30161, 30169, 30181, 30187}

50916361905

58 {380427833, 380427847, 380427851, 380427857, 380427863, 380427871, 380427911, 380427959, 380427973, 380427979, 380427991, 380427997, 380428031, 380428049, 380428067, 380428123, 380428129, 380428157, 380428183, 380428189, 380428201, 380428207, 380428289, 380428291, 380428297, 380428309, 380428327, 380428357, 380428403, 380428417, 380428423, 380428429, 380428493, 380428511, 380428547, 380428553, 380428571, 380428597, 380428649, 380428661, 380428663, 380428679, 380428681, 380428733, 380428751, 380428777, 380428787, 380428799, 380428801, 380428817, 380428831, 380428843, 380428871, 380428889, 380428927, 380428933, 380428949, 380428957}

8394094425244904938

59 {14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939, 14947, 14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073, 15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161, 15173, 15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259, 15263, 15269, 15271, 15277, 15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331, 15349, 15359, 15361, 15373, 15377, 15383}

13516661531

70 {350004439, 350004463, 350004467, 350004469, 350004481, 350004503, 350004533, 350004631, 350004637, 350004647, 350004667, 350004671, 350004679, 350004689, 350004737, 350004751, 350004769, 350004797, 350004803, 350004827, 350004829, 350004841, 350004881, 350004887, 350004899, 350004913, 350004917, 350004943, 350004953, 350004979, 350004983, 350004989, 350005001, 350005009, 350005013, 350005037, 350005039, 350005043, 350005067, 350005081, 350005093, 350005111, 350005133, 350005141, 350005153, 350005157, 350005181, 350005189, 350005211, 350005217, 350005219, 350005241, 350005247, 350005261, 350005267, 350005291, 350005297, 350005303, 350005319, 350005339, 350005343, 350005351, 350005361, 350005427, 350005457, 350005493, 350005511, 350005541, 350005543, 350005547}

8575245637365425758

71 {847681, 847687, 847697, 847703, 847727, 847729, 847741, 847787, 847789, 847813, 847817, 847853, 847871, 847883, 847901, 847919, 847933, 847937, 847949, 847967, 847969, 847991, 847993, 847997, 848017, 848051, 848087, 848101, 848119, 848123, 848131, 848143, 848149, 848173, 848201, 848203, 848213, 848227, 848251, 848269, 848273, 848297, 848321, 848359, 848363, 848383, 848387, 848399, 848417, 848423, 848429, 848443, 848461, 848467, 848473, 848489, 848531, 848537, 848557, 848567, 848579, 848591, 848593, 848599, 848611, 848629, 848633, 848647, 848651, 848671, 848681}

51080566508015

72 {179899, 179903, 179909, 179917, 179923, 179939, 179947, 179951, 179953, 179957, 179969, 179981, 179989, 179999, 180001, 180007, 180023, 180043, 180053, 180071, 180073, 180077, 180097, 180137, 180161, 180179, 180181, 180211, 180221, 180233, 180239, 180241, 180247, 180259, 180263, 180281, 180287, 180289, 180307, 180311, 180317, 180331, 180337, 180347, 180361, 180371, 180379, 180391, 180413, 180419, 180437, 180463, 180473, 180491, 180497, 180503, 180511, 180533, 180539, 180541, 180547, 180563, 180569, 180617, 180623, 180629, 180647, 180667, 180679, 180701, 180731, 180749}

2340047400432

73 {1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759}

165808561

76 {336121, 336143, 336151, 336157, 336163, 336181, 336199, 336211, 336221, 336223, 336227, 336239, 336247, 336251, 336253, 336263, 336307, 336317, 336353, 336361, 336373, 336397, 336403, 336419, 336437, 336463, 336491, 336499, 336503, 336521, 336527, 336529, 336533, 336551, 336563, 336571, 336577, 336587, 336593, 336599, 336613, 336631, 336643, 336649, 336653, 336667, 336671, 336683, 336689, 336703, 336727, 336757, 336761, 336767, 336769, 336773, 336793, 336799, 336803, 336823, 336827, 336829, 336857, 336863, 336871, 336887, 336899, 336901, 336911, 336929, 336961, 336977, 336983, 336989, 336997, 337013}

8609554559068

79 {2649992887, 2649992897, 2649992899, 2649992959, 2649992971, 2649993007, 2649993013, 2649993053, 2649993077, 2649993103, 2649993107, 2649993187, 2649993191, 2649993197, 2649993211, 2649993223, 2649993253, 2649993271, 2649993347, 2649993377, 2649993419, 2649993427, 2649993431, 2649993443, 2649993449, 2649993457, 2649993487, 2649993497, 2649993547, 2649993559, 2649993571, 2649993583, 2649993589, 2649993611, 2649993653, 2649993679, 2649993683, 2649993719, 2649993727, 2649993733, 2649993743, 2649993751, 2649993767, 2649993769, 2649993817, 2649993833, 2649993839, 2649993851, 2649993869, 2649993883, 2649993887, 2649993889, 2649993901, 2649993911, 2649993919, 2649993947, 2649993953, 2649994003, 2649994007, 2649994021, 2649994063, 2649994069, 2649994093, 2649994129, 2649994133, 2649994169, 2649994181, 2649994211, 2649994229, 2649994231, 2649994241, 2649994261, 2649994309, 2649994337, 2649994349, 2649994351, 2649994363, 2649994423, 2649994433}

554774858636858477455

92 {6612798721, 6612798743, 6612798761, 6612798769, 6612798823, 6612798847, 6612798851, 6612798853, 6612798901, 6612798917, 6612798919, 6612798947, 6612798953, 6612799003, 6612799019, 6612799087, 6612799093, 6612799129, 6612799147, 6612799163, 6612799181, 6612799187, 6612799189, 6612799217, 6612799231, 6612799283, 6612799289, 6612799309, 6612799331, 6612799363, 6612799393, 6612799447, 6612799469, 6612799471, 6612799477, 6612799499, 6612799537, 6612799549, 6612799573, 6612799601, 6612799603, 6612799643, 6612799673, 6612799693, 6612799727, 6612799783, 6612799789, 6612799799, 6612799801, 6612799807, 6612799811, 6612799819, 6612799829, 6612799847, 6612799861, 6612799871, 6612799913, 6612799979, 6612800003, 6612800009, 6612800011, 6612800053, 6612800083, 6612800101, 6612800111, 6612800177, 6612800189, 6612800203, 6612800213, 6612800231, 6612800239, 6612800263, 6612800269, 6612800291, 6612800297, 6612800323, 6612800347, 6612800353, 6612800377, 6612800393, 6612800423, 6612800477, 6612800521, 6612800561, 6612800581, 6612800591, 6612800599, 6612800611, 6612800647, 6612800683, 6612800693, 6612800707}

4023079051001509703204 = 22 digits, the largest palindrome on this page

95 {42839, 42841, 42853, 42859, 42863, 42899, 42901, 42923, 42929, 42937, 42943, 42953, 42961, 42967, 42979, 42989, 43003, 43013, 43019, 43037, 43049, 43051, 43063, 43067, 43093, 43103, 43117, 43133, 43151, 43159, 43177, 43189, 43201, 43207, 43223, 43237, 43261, 43271, 43283, 43291, 43313, 43319, 43321, 43331, 43391, 43397, 43399, 43403, 43411, 43427, 43441, 43451, 43457, 43481, 43487, 43499, 43517, 43541, 43543, 43573, 43577, 43579, 43591, 43597, 43607, 43609, 43613, 43627, 43633, 43649, 43651, 43661, 43669, 43691, 43711, 43717, 43721, 43753, 43759, 43777, 43781, 43783, 43787, 43789, 43793, 43801, 43853, 43867, 43889, 43891, 43913, 43933, 43943, 43951, 43961}

178849948871

95 {73326733, 73326769, 73326787, 73326791, 73326839, 73326853, 73326863, 73326917, 73326919, 73326949, 73326961, 73326989, 73327019, 73327027, 73327043, 73327073, 73327127, 73327139, 73327153, 73327159, 73327187, 73327211, 73327217, 73327223, 73327237, 73327253, 73327271, 73327277, 73327291, 73327297, 73327333, 73327337, 73327349, 73327357, 73327363, 73327417, 73327459, 73327481, 73327483, 73327531, 73327543, 73327559, 73327561, 73327571, 73327577, 73327591, 73327601, 73327603, 73327627, 73327637, 73327649, 73327651, 73327687, 73327691, 73327711, 73327729, 73327733, 73327739, 73327753, 73327757, 73327759, 73327763, 73327769, 73327777, 73327781, 73327789, 73327799, 73327801, 73327823, 73327853, 73327867, 73327889, 73327909, 73327951, 73327957, 73327963, 73327981, 73327997, 73327999, 73328009, 73328027, 73328033, 73328053, 73328119, 73328141, 73328159, 73328179, 73328219, 73328221, 73328243, 73328251, 73328279, 73328317, 73328329, 73328341}

510808567765808015

105 {21911, ..., 22961}

52811511825

106 {1657, ..., 2467}

459373954

114 {6113, ..., 7103}

4976116794

119 {1649917, ..., 1651571}

324260040062423

121 {275813, ..., 277261}

9252211122529

137 {5701, ..., 6899}

5452002545

141 {2642149, ..., 2644171}

985113696311589

145 {14153, ..., 15497}

31991319913

158 {23021, ..., 24571}

89384148398

162 {5424611, ..., 5427017}

4769250000529674

171 {20549, ..., 22193}

78369696387

187 {1193, ..., 2633}

701474107

214 {8861, ..., 10837}

20739493702

218 {322757, ..., 325477}

22908100180922

327 {4567, ..., 7459}

11930203911

353 {5340893, ..., 5346137}

10079478287497001

435 {1663, ..., 5231}

5514004155

447 {1699, ..., 5399}

5980550895

500 {91291, ..., 96893}

4426966696244

513 {3623, ..., 8101}

18273637281

539 {21179, ..., 26627}

308032230803

595 {12824807, ..., 12834331}

97935644044653979

605 {2884201, ..., 2893211}

5048205445028405

678 {56681, ..., 64123}

2472726272742

679 {115637, ..., 123491}

9708705078079

717 {1847, ..., 7907}

18708380781

717 {6959, ..., 13613}

77817671877

719 {12469549, ..., 12480997}

111900016610009111

755 {8410813, ..., 8422649}

53484847074848435

768 {4007, ..., 10859}

44764146744

810 {54799, ..., 63671}

2844434344482

882 {3191, ..., 10979}

47622322674

901 {7481, ..., 15823}

126872278621

902 {48787, ..., 58441}

2602300032062

972 {529709, ..., 542687}

279460808064972

1016 {75793, ..., 87383}

6770536350776

1025 {90071, ..., 101797}

9441818181449

1033 {3547, ..., 12823}

75055855057

1076 {196139, ..., 209311}

44253677635244

1303 {472937, ..., 489913}

301979606979103

1305 {41813, ..., 55921}

3134032304313

1318 {32057, ..., 45943}

2013667663102

1325 {855307, ..., 873139}

989547242745989

1780 {177337, ..., 198829}

63014033041036

1887 {7079, ..., 25343}

537252252735

1945 {277099, ..., 301927}

163121777121361

1966 {25943, ..., 46643}

2643402043462

1967 {2411, ..., 20611}

301654456103

2058 {21961, ..., 43291}

2258152518522

2097 {14699, ..., 35923}

1403954593041

2104 {25867, ..., 48029}

2938760678392

2283 {462409, ..., 491867}

519732414237915

2331 {269, ..., 21227}

329904409923

2514 {552301, ..., 585653}

814298080892418

2560 {14831, ..., 41051}

2112487842112

2620 {293941, ..., 326737}

252686090686252

2791 {491339, ..., 527749}

725080737080527

2878 {272477, ..., 309037}

243714838417342

2943 {430147, ..., 468613}

594276363672495

2947 {17737, ..., 48437}

3403613163043

3053 {471217, ..., 511169}

736743494347637

3287 {320387, ..., 362303}

383241242142383

3353 {22807, ..., 58237}

5813252523185

3409 {28571, ..., 65203}

7792387832977

3485 {365587, ..., 410789}

525818616818525

3546 {21377, ..., 58741}

6033521253306

3677 {10861, ..., 48571}

3587323237853

3741 {424147, ..., 472859}

753086656680357

3799 {18233, ..., 58151}

5966802086695

3867 {36847, ..., 79319}

13513922931531

4072 {226621, ..., 277231}

259254010452952

4511 {1285169, ..., 1348939}

7825744664475287

4690 {5501, ..., 53087}

4708008008074

5152 {7159, ..., 60101}

6791524251976

5311 {206447, ..., 272183}

305789282987503

5755 {316717, ..., 390263}

720428666824027

5904 {223963, ..., 297893}

403864454468304

5961 {354023, ..., 431203}

921869515968129

6136 {82619, ..., 154277}

88415422451488

6347 {1039607, ..., 1127881}

7459645995469547

6560 {918829, ..., 1009417}

6103211551123016

6903 {293413, ..., 381301}

788703030307887

7044 {137183, ..., 222461}

231490121094132

7229 {26497, ..., 106357}

35009622690053

7430 {120247, ..., 209371}

205915999519502

7691 {35327, ..., 121697}

51339255293315

7729 {207301, ..., 303691}

509046898640905

8179 {43049, ..., 136139}

70549700794507

8849 {737629, ..., 857963}

5642017337102465

9231 {261427, ..., 378463}

953064393460359

9461 {952481, ..., 1083809}

9819915445199189

11586 {4397, ..., 130267}

64380300308346

12295 {21433, ..., 160169}

117262989262711

13474 {59083, ..., 218069}

282025545520282

14133 {63793, ..., 231079}

335022939220533

14232 {52553, ..., 219799}

291113878311192

15999 {86951, ..., 280129}

579943787349975

17603 {24071, ..., 228251}

329430707034923

18473 {78697, ..., 302459}

733228474822337

18865 {9829, ..., 225637}

319418090814913

19270 {29347, ..., 255191}

456502929205654

20403 {77419, ..., 325009}

912738858837219

20766 {16829, ..., 258389}

473599838995374

20959 {26371, ..., 272563}

554124808421455

21090 {14369, ..., 259169}

478081424180874

24315 {103001, ..., 404191}

1715603113065171

32594 {61471, ..., 464251}

2610327777230162

32664 {78341, ..., 484489}

2958241221428592

50944 {14369, ..., 647401}

6925150440515296

52777 {63487, ..., 734807}

10031249994213001

56993 {30133, ..., 750157}

10651212221215601

77169 {99907, ..., 1114049}

33896836463869833

80631 {103291, ..., 1166323}

38771678587617783

83329 {80407, ..., 1176089}

39743366066334793

99227 {19501, ..., 1320091}

55720203530202755

116122 {683, ..., 1529513}

85827712521772858

Twin Primes

{3, 347, 2111, 3167, 21011, 22271, 30557, 33587, 34847, 202751, 211661, 240041, 2025251, 2037851, 2039351, 2129261, 2217671, 2303531, 2328281, 2404541, 2422241, 2431841, 2434841, 2442941, 3080807, 3087857, 3185867, 3263627, 3270227, 3289877, 3296477, 3375287, 3450047, 20161151, 20283251, 20461451, 21422411, 22005521, 22366871, 23194181, 23222231, 23477981, 23494481, 24227741, 24483491, 30600107, 30661157, 30677657, 32522027, 32972477, 33600137, 33633137, 34711247, 34894397, 200323001, 200828051, 201484601, 201499601, 201575651, 202232201, 202439201, 202944251, 204974951, 210348011, 210893561, 211232111, 211641161, 212419211, 213863861, 214202411, 220287521, 220626071, 221252621, 222348221, 222505271, 222560771, 223025321, 223651871, 224636471, 224979971, 230308031, 230702081, 230732081, 231671681, 232176731, 232383731, 233227331, 233404331, 233565881, 240616091, 241095641, 241272641, 241515191, 241545191, 242242241, 242510291, 243015341, 243196841, 243373841, 244409441, 305595557, 306333107, 306646157, 306742157, 306863657, 307095707, 307287707, 307666757, 307762757, 308297807, 308540357, 309444407, 309646457, 316353617, 316479617, 316792667, 316944167, 317813267, 318181817, 318535367, 319202417, 319247417, 325353527, 326146127, 326787677, 327575777, 327742277, 328383827, 328858877, 329101427, 329419427, 329787977, 329964977, 335474537, 335843087, 336126137, 336535187, 336797687, 337287737, 337530287, 337570787, 337707287, 337944287, 337969787, 338474837, 339085937, 339348437, 339444437, 339863987, 339934487, 345196547, 345222047, 345712097, 346383647, 346984697, 347212247, 347404247, 347909297, 347994797, 348484847, 348727397, 349257947, 349272947, 349287947, 349515497, 349888997, 2002387001, 2006556551, 2008058051, 2009724551, 2013003101, 2015275151, 2016331151, 2018278151, 2019779651, 2025000251, 2028613751, 2030720801, 2032832801, 2036276351, 2036886851, 2037612851, 2040330401, 2048723951, 2049614951, 2108278061, 2113998611, 2115775661, 2116501661, 2123558711, 2124169211, 2126886761, 2128503761, 2132277311, 2135885861, 2145000461, 2202332021, 2207112071, 2210555621, 2216721671, 2221666721, 2222557721, 2228888771, 2233388321, 2234279321, 2235000371, 2236501871, 2237722871, 2243113421, 2245830971, 2247612971, 2301496031, 2302222031, 2308223081, 2323668731, 2333113331, 2334004331, 2340000431, 2343168431, 2405885591, 2407387091, 2414444141, 2431386341, 2434999841, 2435720891, 2438558891, 2442002441, 2442777941, 2443503941, 3055385057, 3072942707, 3076666757, 3077442257, 3083113307, 3087167357, 3096941957, 3155110067, 3165330167, 3186776867, 3186941867, 3190220417, 3192332417, 3194724917, 3197112467, 3251111027, 3255330077, 3264499127, 3266556677, 3272722727, 3273333227, 3279169277, 3281556827, 3285000377, 3296111477, 3297612977, 3354004037, 3355830587, 3356276087, 3370055237, 3384334337, 3385995887, 3396611987, 3398278487, 3456941597, 3462497147, 3467557697, 3470110247, 3471331247, 3475220297, 3475665797, 3477612797, 3487502897, 3489779897, 3496221497, ...}

...the smaller of twin primes (< length-11) that sum to a palindrome.

The number of entries of length-n is {1, 0, 1, 2, 5, 3, 21, 21, 112, 108, 836, 716, 5569, 5311, 38287, 41428, 327760, 293343, 2659919, 2584485, ...}, making the number of entries less than 10^n {1, 1, 2, 4, 9, 12, 33, 54, 166, 274, 1110, 1826, 7395, 12706, 50993, 92421, 420181, 713524, 3373443, 5957928, ...}.

Least and Greatest Solution for a Given Length:

2111

3167

21011

34847

202751

240041

2025251

3450047

20161151

34894397

200323001

349888997

2002387001

3496221497

20011516001

34988233997

200040040001

349942794497

2000096455001

3499985899997

20000911405001

34998616639997

200000242000001

349998631399997

2000000110000001

3499994724949997

20000005805500001

34999997779999997

200000022220000001

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2000000168665000001

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20000001183160000001

34999998033034999997

200000000606050000001

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2000000010775600000001

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20000000018636500000001

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200000000137786000000001

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2000000000652515500000001

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20000000004600145000000001

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200000000003606350000000001

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2000000000006721550000000001

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20000000000055150550000000001

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200000000000578875550000000001

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20000000000001600115000000000001

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