Legend
F_ba Decomposition of the basenumber in its prime factors.
F_pp Decomposition of the palindromic pentagonal.
Note : a palindromic pentagonal will always be divisible by its basenumber when this
last one is 'odd'. With 'even' basenumbers you'll notice that the pentagonals
are always divisible by half their basenumbers.
To reconstruct the pentagonals you must take into account the green together with
the purple prime factors but not the black 2.
Date Date of discovery by the author.
Hypertext links to related topics in number theory
Comm Comments about the palindromic pentagonal number.
Factorization
[78]
F_ba 8380905875275233386185451026 =
2 * 163 * 44273 * 580676715625903459987
F_pp 105359374935334388747447001151100744747883433539473953501 =
11 * 31 * 5471 * 86923 * 5035027 * 30793185167
Date September 24, 2024 ( Patrick De Geest / CUDA code by Robert Xiao )
[77]
F_ba 5955785396020895936124499062 =
2 * 3 * 11 * 11 * 23 * 2741693 * 224848699 * 578582617
F_pp 53207069525183670357618776011067781675307638152596070235 =
5 * 7 * 17 * 122163329 * 245811654854059387
Date September 24, 2024 ( Patrick De Geest / CUDA code by Robert Xiao )
[76]
F_ba 829412616490882316063874786 =
2 * 3 * 17 * 8131496240106689373175243
F_pp 1031887932591377142105479799979745012417731952397881301 =
89 * 1619 * 7669 * 47497 * 47407834628939
Date June 16, 2023 ( Patrick De Geest / CUDA code by Robert Xiao )
[75]
F_ba 219838383896945839241529093 =
3 * 11 * 19 * 350619432052545198152359
F_pp 72493372551631403519074864446847091530413615527339427 =
37 * 43 * 269 * 15643 * 49255221548658287
Date January 9, 2023 ( David Griffeath / CUDA code by Robert Xiao )
[74]
F_ba 211567096617431127327768331 =
19 * 61 * 83 * 635057 * 3463170635320639
F_pp 67140954556694156338058353235385083365149665545904176 =
2 * 2 * 2 * 2 * 19834415307884168186978281
Date January 9, 2023 ( David Griffeath / CUDA code by Robert Xiao )
[73]
F_ba 196744195862034221724924905 =
5 * 15443 * 506180999 * 5033782130833
F_pp 58062417908097725661820084648002816652779080971426085 =
55158679 * 301638047 * 17737532789
Date January 9, 2023 ( David Griffeath / CUDA code by Robert Xiao )
[72]
F_ba 140815521353961270534020208 =
2 * 2 * 2 * 2 * 3 * 197 * 619 * 1442743 * 16674907714429
F_pp 29743516581281883860142882928824106838818218561534792 =
11 * 13 * 17566807 * 168167827918672423
Date January 9, 2023 ( David Griffeath / CUDA code by Robert Xiao )
[71]
F_ba 123470453704578756803923204 =
2 * 2 * 23 * 2237 * 599941953045512996851
F_pp 22867429407021789074918527272581947098712070492476822 =
587 * 631024465270419540735553
Date January 9, 2023 ( David Griffeath / CUDA code by Robert Xiao )
[70]
F_ba 115716935699622852551776543 =
37 * 1867 * 1675139126212348941817
F_pp 20085613811565974693953734743735939647956511831658002 =
2 * 13 * 107 * 12941 * 26183 * 2137049 * 86164691
Date January 9, 2023 ( David Griffeath / CUDA code by Robert Xiao )
[69]
F_ba 1997352210935459325350510 =
2 * 5 * 59 * 80021 * 42305678889280109
F_pp 5984123781793151403874475744783041513971873214895 =
5992056632806377976051529
Date December 6, 2022 ( Robert Xiao )
[68]
F_ba 1366335687983609354348844 =
2 * 2 * 3 * 3 * 13 * 53 * 4464754993 * 12337809427
F_pp 2800309818386464643692792972963464646838189030082 =
101 * 601 * 49991 * 1350799828027241
Date December 6, 2022 ( Robert Xiao )
[67]
F_ba 1214693643268411793685388 =
2 * 2 * 71 * 73 * 3037 * 533327 * 36173222191
F_pp 2213220970495031472095671765902741305940790223122 =
337 * 42209 * 256184617678977811
Date December 6, 2022 ( Robert Xiao )
[66]
F_ba 646108029840746975319151 =
19 * 31 * 1096957605841675679659
F_pp 626183379337037375893787787398573730733973381626 =
2 * 7 * 11 * 13 * 484096925455105126363
Date November 11, 2022 ( David Griffeath / Rust code by Robert Xiao )
[65]
F_ba 386808141157899128841063 =
3 * 11 * 17 * 313 * 2749 * 18829687 * 42556957
F_pp 224430807099043827014991199410728340990708034422 =
2 * 199 * 36739 * 140143 * 283142493239
Date November 11, 2022 ( David Griffeath / Rust code by Robert Xiao )
[64]
F_ba 128481111918761748263908 =
2 * 2 * 7 * 19 * 241505849471356669669
F_pp 24761094179822073249932323994237022897149016742 =
71 * 60659 * 11347379 * 7886991733
Date January 6, 2008 ( Feng Yuan )
[63]
F_ba 4181240246129576678503 =
7 * 13 * 2053 * 22380757434200161
F_pp 26224154993780584443322334448508739945142262 =
2 * 11 * 91297 * 3122606024689831
Date January 5, 2008 ( Feng Yuan )
[62]
F_ba 3166575018238865276806 =
2 * 7 * 1052893 * 1090217 * 197044609
F_pp 15040796019201704940688604940710291069704051 =
11 * 13 * 66431643739276893919
Date November 11, 2022 ( Robert Xiao )
[61]
F_ba 1161338314703013743743 =
19 * 173 * 928159 * 380659497671
F_pp 2023060021795854282372732824585971200603202 =
2 * 9733 * 13901 * 6437648365279
Date January 6, 2008 ( Feng Yuan )
[60]
F_ba 226255113072008674109 =
20929 * 22541 * 479597317681
F_pp 76787064286841145600200654114868246078767 =
339382669608013011163
Date November 11, 2022 ( Robert Xiao )
[59]
F_ba 101908013398232552381 =
13 * 43 * 113 * 47431 * 34013850853
F_pp 15577864792161518113031181516129746877551 =
2843 * 53767857930829697
Date January 3, 2008 ( Feng Yuan )
[58]
F_ba 32178927183122554461 =
3 * 3 * 3 * 3 * 3 * 11 * 12038506241347757
F_pp 1553225031985055486446845505891305223551 =
89 * 479 * 170341 * 6646884121
Date January 3, 2008 ( Feng Yuan )
[57]
F_ba 12470286104989637219 =
61 * 17203 * 11883445896293
F_pp 233262053310446425999524644013350262332 =
2 * 2 * 13 * 13 * 719 * 1187 * 32422117201
Date November 4, 2022 ( Robert Xiao )
[56]
F_ba 3225069471604675446 =
2 * 3 * 3 * 19 * 11311 * 833704154783
F_pp 15601609645014690722709641054690610651 =
11 * 463 * 24733 * 76808601073
Date November 4, 2022 ( Robert Xiao )
[55]
F_ba 2215732656045463378 =
2 * 569 * 2221 * 876650607061
F_pp 7364206804599425576755249954086024637 =
7 * 83 * 11440960358238193
Date November 4, 2022 ( Robert Xiao )
[54]
F_ba 642912991153879996 =
2 * 2 * 11 * 41 * 2042077 * 174519337
F_pp 620005671291643466664346192176500026 =
53 * 36391301386068679
Date January 6, 2008 ( Feng Yuan )
[53]
F_ba 222497695855916654 =
2 * 11551 * 9631101023977
F_pp 74257836991787986368978719963875247 =
7 * 95356155366821423
Date January 6, 2008 ( Feng Yuan )
[52]
F_ba 64541848291142556 =
2 * 2 * 3 * 37 * 3156121 * 46057969
F_pp 6248475271255291881925521725748426 =
7 * 11 * 11 * 13 * 17584737523697
Date January 6, 2008 ( Feng Yuan )
[51]
F_ba 1343985615421963 =
179 * 563 * 13336233619
F_pp 2709446001691728271961006449072 =
2 * 2 * 2 * 2 * 510331 * 246895939
Date April 2, 2002 ( Feng Yuan )
[50]
F_ba 1331901641608903 =
17 * 718007 * 109117537
F_pp 2660942974380735370834792490662 =
2 * 97 * 345133 * 29838377
Date April 2, 2002 ( Feng Yuan )
[49]
F_ba 192460705375190 =
2 * 5 * 7 * 87797 * 31315861
F_pp 55561684670273437207648616555 =
29 * 41 * 1439 * 337458739
Date August 5, 2000 ( Patrick De Geest )
[48]
F_ba 189271045290605 =
5 * 7573 * 4998575077
F_pp 53735292878097279087829253735 =
7 * 17 * 127447 * 18719699
[47]
F_ba 62640018209362 =
2 * 11 * 2847273554971
F_pp 5885657821903773091287565885 =
5 * 13 * 13 * 97 * 2292686569
[46]
F_ba 62407875352937 =
3041 * 20522155657
F_pp 5842114359101551019534112485 =
5 * 11 * 1702032964171
[45]
F_ba 22073207482889 =
64609 * 341642921
F_pp 730839732873989378237938037 =
33109811224333
[44]
F_ba 8505462902906 =
2 * 4252731451453
F_pp 108514348789060987843415801 =
1229 * 20761911073
[43]
F_ba 6106091136277 =
11 * 293 * 1894536499
F_pp 55926523446777764432562955 =
5 * 199 * 9205162517
[42]
F_ba 3690877000943 =
11 * 101 * 3322121513
F_pp 20433859554133145595833402 =
2 * 1327 * 2293 * 909737
[41]
F_ba 2704211220546 =
2 * 3 * 3 * 11 * 6907 * 1977361
F_pp 10969137487988978473196901 =
8112633661637
[40]
F_ba 2269269065474 =
2 * 47 * 349 * 69172379
F_pp 7724373137274727313734277 =
7 * 11 * 233 * 239 * 1587679
[39]
F_ba 2118668671851 =
3 * 107 * 31817 * 207443
F_pp 6733135411623261145313376 =
2 * 2 * 2 * 2 * 2 * 66271 * 1498583
[38]
F_ba 1199186171664 =
2 * 2 * 2 * 2 * 3 * 13 * 37 * 463 * 112181
F_pp 2157071211464641121707512 =
7 * 53 * 9696923221
[37]
F_ba 100208264581 =
2383 * 42051307
F_pp 15062544435453444526051 =
7 * 13 * 29 * 56958089
[36]
F_ba 72507025789 =
11 * 9871 * 667769
F_pp 7885903183113813095887 =
71 * 613 * 2498921
[35]
F_ba 20483169156 =
2 * 2 * 3 * 3 * 23 * 2851 * 8677
F_pp 629340327999723043926 =
401 * 153240667
[34]
F_ba 18517422797 =
23 * 805105339
F_pp 514342420555024243415 =
5 * 42641 * 130279
[33]
F_ba 18306458265 =
3 * 5 * 107 * 157 * 72649
F_pp 502689621303126986205 =
127 * 216218011
[32]
F_ba 6693818696 =
2 * 2 * 2 * 367 * 2279911
F_pp 67210813099031801276 =
7 * 11 * 11 * 29 * 817549
[31]
F_ba 2049123156 =
2 * 2 * 3 * 127 * 1344569
F_pp 6298358561658538926 =
6147369467
[30]
F_ba 1345679688 =
2 * 2 * 2 * 3 * 56069987
F_pp 2716280733370826172 =
311 * 317 * 40949
[29]
F_ba 851649306 =
2 * 3 * 17 * 47 * 59 * 3011
F_pp 1087959810189597801 =
19 * 67 * 2007029
[28]
F_ba 818049201 =
3 * 6449 * 42283
F_pp 1003806742476083001 =
1227073801
[27]
F_ba 700457153 =
11 * 457 * 139339
F_pp 735960334433069537 =
101 * 10402829
[26]
F_ba 316882086 =
2 * 3 * 23 * 2296247
F_pp 150621384483126051 =
11 * 86422387
[25]
F_ba 225563533 =
13 * 31 * 347 * 1613
F_pp 76318361016381367 =
577 * 586387
[24]
F_ba 100058581 =
7 * 257 * 55619
F_pp 15017579397571051 =
839 * 178889
[23]
F_ba 84885761 =
827 * 102643
F_pp 10808388588380801 =
11 * 2647 * 4373
[22]
F_ba 59401650 =
2 * 3 * 5 * 5 * 7 * 11 * 37 * 139
F_pp 5292834004382925 =
13 * 1619 * 8467
[21]
F_ba 13280839 =
11 * 11 * 13 * 8443
F_pp 264571020175462 =
2 * 7 * 61 * 23327
[20]
F_ba 2684561 =
11 * 109 * 2239
F_pp 10810300301801 =
7 * 13 * 17 * 19 * 137
[19]
F_ba 1979130 =
2 * 3 * 5 * 37 * 1783
F_pp 5875432345785 =
5937389
[18]
F_ba 1965117 =
3 * 7 * 11 * 47 * 181
F_pp 5792526252975 =
5 * 5 * 157 * 751
[17]
F_ba 1258723 =
PRIME
F_pp 2376574756732 =
2 * 2 * 11 * 11 * 47 * 83
[16]
F_ba 44059 =
PRIME
F_pp 2911771192 =
2 * 2 * 2 * 11 * 751
[15]
F_ba 31926 =
2 * 3 * 17 * 313
F_pp 1528888251 =
11 * 8707
[14]
F_ba 26906 =
2 * 11 * 1223
F_pp 1085885801 =
7 * 13 * 887
[13]
F_ba 26466 =
2 * 3 * 11 * 401
F_pp 1050660501 =
79397
[12]
F_ba 6010 =
2 * 5 * 601
F_pp 54177145 =
11 * 11 * 149
[11]
F_ba 4228 =
2 * 2 * 7 * 151
F_pp 26811862 =
11 * 1153
[10]
F_ba 2229 =
3 * 743
F_pp 7451547 =
3343
[9]
F_ba 2173 =
41 * 53
F_pp 7081807 =
3259
[8]
F_ba 693 =
3 * 3 * 7 * 11
F_pp 720027 =
1039
[7]
F_ba 101 =
PRIME
F_pp 15251 =
151
[6]
F_ba 44 =
2 * 2 * 11
F_pp 2882 =
131
[5]
F_ba 26 =
2 * 13
F_pp 1001 =
7 * 11
[4]
F_ba 4 =
2 * 2
F_pp 22 =
11
[3]
F_ba 2 =
PRIME
F_pp 5 =
PRIME
[2]
F_ba 1 =
1
F_pp 1 =
1
[1]
F_ba 0 =
0
F_pp 0 =
0
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Patrick De Geest - Belgium 
- Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com
Factorization of the
Palindromic Pentagonals