HOME plateWON | World!OfNumbers Factorization of thePalindromic Heptagonals Palindromic Heptagonals

Legend
```
F_ba  Decomposition of the basenumber in its prime factors.
F_ph  Decomposition of the palindromic heptagonal.
Note : a palindromic heptagonal will always be divisible by its basenumber when this
last one is 'odd'. With 'even' basenumbers you'll notice that the heptagonals
are always divisible by half their basenumbers.
To reconstruct the heptagonals 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 heptagonal number.
```

Factorization
```
[84]
F_ba  1873720564765469611496441763 =
3 * 11 * 233 * 243688459457077592859467
F_ph  8777071887062576002354728033308274532006752607881707778 =
2 * 3 * 3 * 3 * 3 * 3 * 1151 * 8461 * 989718171454565011
Date  June 16, 2023 ( Patrick De Geest / CUDA code by Robert Xiao )

[83]
F_ba  1865550031166736002957872188 =
2 * 2 * 3 * 61 * 573695665997 * 4442365120397
F_ph  8700692296965524180003874993994783000814255696922960078 =
3 * 287549 * 10812939888313157079071
Date  June 16, 2023 ( Patrick De Geest / CUDA code by Robert Xiao )

[82]
F_ba  518868986913124343115029751 =
3 * 11 * 8398822561 * 1872084154598327
F_ph  673062563950630002104548005500845401200036059365260376 =
2 * 2 * 2 * 3 * 31 * 544018147 * 3204877246046107
Date  June 15, 2023 ( Patrick De Geest / CUDA code by Robert Xiao )

[81]
F_ba  136288963956567334982488784 =
2 * 2 * 2 * 2 * 829 * 6113 * 74623 * 2330551 * 9664969
F_ph  46436704240886275409737763336773790457268804240763464 =
681444819782836674912443917
Date  January 11, 2023 ( David Griffeath / CUDA code by Robert Xiao )

[80]
F_ba  81051618456301707752402686 =
2 * 83 * 28297 * 684119 * 25222118180747
F_ph  16423412135964769068005026562050086096746953121432461 =
17 * 17 * 17 * 23 * 31 * 1493 * 1609667 * 48139275893
Date  January 11, 2023 ( David Griffeath / CUDA code by Robert Xiao )

[79]
F_ba  5491380065793004252725102 =
2 * 3 * 3 * 13 * 15281464871 * 1535679751693
F_ph  75388137567471949288446366364488294917476573188357 =
3 * 7 * 11 * 68521 * 1734665874478334557
Date  December 6, 2022 ( Robert Xiao )

[78]
F_ba  2506873575346207242110501 =
5059 * 50411 * 9829749274547749
F_ph  15711037806922690496401855810469409622960873011751 =
11 * 10083936073 * 56500159290217
Date  December 6, 2022 ( Robert Xiao )

[77]
F_ba  1401206868817841389000139 =
79043 * 17727146854469610073
F_ph  4908451723055748417680431340867148475503271548094 =
2 * 7 * 1307 * 26597 * 7197902999653741
Date  December 6, 2022 ( Robert Xiao )

[76]
F_ba  1159363692769172939242993 =
Prime!
F_ph  3360310430278433054615306035164503348720340130633 =
2898409231922932348107481
Date  December 6, 2022 ( Robert Xiao )

[75]
F_ba  885337623337961398168741 =
3469 * 255214074182173940089
F_ph  1959556768244275027387891987837205724428676559591 =
7 * 14983 * 21103384391309231371
Date  December 6, 2022 ( Robert Xiao )

[74]
F_ba  529794084977256736834477 =
7 * 148783 * 508692991016885317
F_ph  701704431192221831007830038700138122291134407107 =
11 * 11 * 14081 * 777370838755900391
Date  November 11, 2022 ( David Griffeath / Rust code by Robert Xiao )

[73]
F_ba  184726169766590240131468 =
2 * 2 * 17 * 631 * 3169 * 1358525873968709
F_ph  85309394491587795230531913503259778519449390358 =
31 * 58799749 * 506712086657723
Date  December 6, 2022 ( Robert Xiao )

[72]
F_ba  155063328766708895002531 =
Prime!
F_ph  60111589820531125801081218010852113502898511106 =
2 * 19 * 85691 * 128939 * 923306740673
Date  December 6, 2022 ( Robert Xiao )

[71]
F_ba  115095375604446234345993 =
3 * 22133 * 55079 * 623717 * 50457149
F_ph  33117363713821393460337673306439312831736371133 =
3 * 443 * 659 * 480429161 * 683845711
Date  January 6, 2008 ( Feng Yuan )

[70]
F_ba  529794084977256736834477 =
7 * 148783 * 508692991016885317
F_ph  701704431192221831007830038700138122291134407107 =
11 * 11 * 14081 * 777370838755900391
Date  November 11, 2022 ( Robert Xiao )

[69]
F_ba  1645934853472802341776 =
2 * 2 * 2 * 2 * 3 * 3 * 9173 * 1512877 * 823635649
F_ph  6772753854691338287602067828331964583572776 =
3 * 2743224755788003902959
Date  January 5, 2008 ( Feng Yuan )

[68]
F_ba  1461903709744855845210 =
2 * 3 * 5 * 23 * 15199073 * 139396726933
F_ph  5342906141414429317798977139244141416092435 =
3 * 2436506182908093075349
Date  November 11, 2022 ( Robert Xiao )

[67]
F_ba  1197770348245060425838 =
2 * 112241 * 5335707754942759
F_ph  3586634517837733317833387133377387154366853 =
7 * 7 * 79 * 2269 * 9907 * 68824605659
Date  January 5, 2008 ( Feng Yuan )

[66]
F_ba  839449225728858371621 =
105019 * 7993308122614559
F_ph  1761687506441949539786879359491446057861671 =
11 * 191 * 619 * 10939 * 147516336311
Date  November 11, 2022 ( Robert Xiao )

[65]
F_ba  584961928628774900043 =
3 * 19 * 19 * 2579 * 209434296768299
F_ph  855451144862739850023320058937268441154558 =
2 * 3  * 11 * 37 * 1289 * 464589118145137
Date  January 5, 2008 ( Feng Yuan )

[64]
F_ba  149974969674243257990 =
2 * 5 * 29 * 517155067842218131
F_ph  56231228821975462213831226457912882213265 =
53 * 6701 * 53551 * 39428087749
Date  January 5, 2008 ( Feng Yuan )

[63]
F_ba  116720282191097780653 =
2 * 17 * 19319 * 355396187816011
F_ph  34059060686923744328082344732968606095043 =
291800705477744451631
Date  November 11, 2022 ( Robert Xiao )

[62]
F_ba  53133142984397396877 =
3 * 11 * 1610095241951436269
F_ph  7057827208501045785995875401058027287507 =
3 * 977 * 45319978662911461
Date  November 4, 2022 ( Robert Xiao )

[61]
F_ba  26678135232269748221 =
401 * 66529015541819821
F_ph  1779307248678181132112311818768427039771 =
11 * 47 * 129004522399757003
Date  January 4, 2008 ( Feng Yuan )

[60]
F_ba  22059819805104914321 =
PRIME
F_ph  1216589124584247550110557424854219856121 =
11 * 101 * 863 * 22067 * 2606596571
Date  January 4, 2008 ( Feng Yuan )

[59]
F_ba  10317264079491259307 =
53 * 109 * 173 * 2179 * 11719 * 404267
F_ph  266114845214901555595555109412548411662 =
2 * 29 * 19094653 * 23289748109
Date  January 4, 2008 ( Feng Yuan )

[58]
F_ba  1743257048371139577 =
3 * 19 * 101 * 302806504841261
F_ph  7597362841739144174714419371482637957 =
3 * 953 * 3613 * 153487 * 2748829
Date  January 4, 2008 ( Feng Yuan )

[57]
F_ba  529189005495906002 =
2 * 13 * 19 * 29 * 22063 * 1674253829
F_ph  700102508844365081180563448805201007 =
7 * 7 * 11 * 101 * 101 * 481226244413
Date  November 4, 2022 ( Robert Xiao )

[56]
F_ba  386569698677663358 =
2 * 3 * 11 * 13 * 1487 * 302990877173
F_ph  373590329839348608806843938923095373 =
3 * 103 * 21329489 * 293264087
Date  January 4, 2008 ( Feng Yuan )

[55]
F_ba  140620708714288539 =
3 * 11 * 11 * 47 * 292363 * 28191773
F_ph  49435459298271961416917289295453494 =
2 * 3 * 7 * 3343 * 11119 * 225184189
Date  April 2, 2002 ( Feng Yuan )

[54]
F_ba  25901555713068486 =
2 * 3 * 11 * 89 * 3719 * 7459 * 158959
F_ph  1677226470892976776792980746227761 =
3 * 17 * 9125951 * 278257927
Date  April 2, 2002 ( Feng Yuan )

[53]
F_ba  8570921185931806 =
2 * 13 * 43 * 1051 * 14561 * 500947
F_ph  183651724938636676636839427156381 =
7 * 73 * 83864199470957
Date  November 4, 2000 ( Jeff Heleen )

[52]
F_ba  1019248876540672 =
2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 47 * 151 * 561003371
F_ph  2597170680823553553280860717952 =
13 * 392018798669489

[51]
F_ba  627391088906934 =
2 * 3 * 11 * 89 * 106808152691
F_ph  984048946099569965990649840489 =
3 * 7 * 1777 * 84062369551

[50]
F_ba  523047977062611 =
3 * 7 * 11 * 13 * 37 * 103 * 1747 * 26161
F_ph  683947965773223322377569749386 =
2 * 3 * 3 * 3 * 41 * 61 * 9682200769

[49]
F_ba  186276561018503 =
659 * 27077 * 10439321
F_ph  86747392962199899126929374768 =
2 * 2 * 2 * 2 * 19 * 1531879613639

[48]
F_ba  139689569097504 =
2 * 2 * 2 * 2 * 2 * 3 * 3 * 3 * 37 * 179 * 3329 * 7333
F_ph  48782939286615651668293928784 =
3 * 401 * 206933 * 2805683

[47]
F_ba  87036116082281 =
53 * 81293 * 20200889
F_ph  18938213756720602765731283981 =
7 * 29 * 1153 * 929638639

[46]
F_ba  47892275461250 =
2 * 5 * 5 * 5 * 5 * 11 * 3483074579
F_ph  5734175122140550412215714375 =
239461377306247

[45]
F_ba  43909485680879 =
7 * 7 * 13 * 101 * 149 * 1229 * 3727
F_ph  4820107331898228981337010284 =
2 * 2 * 11 * 127 * 19644544417

[44]
F_ba  10024819305872 =
2 * 2 * 2 * 2 * 7 * 89507315231
F_ph  251242505288444882505242152 =
2618933 * 19139129

[43]
F_ba  6639848560861 =
593 * 1823 * 2347 * 2617
F_ph  110218972277909772279812011 =
16599621402151

[42]
F_ba  3129887444612 =
2 * 2 * 580607 * 1347679
F_ph  24490488539844893588409442 =
11 * 103 * 13812389429

[41]
F_ba  1755516804297 =
3 * 1607 * 4931 * 73847
F_ph  7704598125420245218954077 =
3 * 3 * 487643556749

[40]
F_ba  1648402664976 =
2 * 2 * 2 * 2 * 3 * 3 * 83 * 673 * 204931
F_ph  6793078364747474638703976 =
3 * 1759 * 5843 * 267307

[39]
F_ba  987706147387 =
17 * 19 * 3057913769
F_ph  2438908583963693858098342 =
2 * 13 * 379 * 250585079

[38]
F_ba  498373323651 =
3 * 3 * 7 * 19 * 416351983
F_ph  620939924316613429939026 =
2 * 3 * 11 * 59 * 319962329

[37]
F_ba  178357794542 =
2 * 131 * 229 * 2972729
F_ph  79528757184448175782597 =
7349 * 121348343

[36]
F_ba  159052425336 =
2 * 2 * 2 * 3 * 3 * 3 * 7 * 7 * 15027629
F_ph  63244185012921058144236 =
3 * 1511 * 175438369

[35]
F_ba  147826795945 =
5 * 76387 * 387047
F_ph  54631903998189930913645 =
41 * 9013829021

[34]
F_ba  71784986521 =
PRIME
F_ph  12882710724442701728821 =
179462466301

[33]
F_ba  36987715853 =
11 * 19 * 176974717
F_ph  3420227810000187220243 =
23 * 71 * 1181 * 47947

[32]
F_ba  29970725867 =
54629 * 548623
F_ph  2245611022442201165422 =
2 * 11 * 43 * 4603 * 17207

[31]
F_ba  17663032822 =
2 * 7331 * 1204681
F_ph  779956821151128659977 =
88315164107

[30]
F_ba  15911875336 =
2 * 2 * 2 * 7 * 284140631
F_ph  632969441747144969236 =
11 * 919 * 1201 * 6553

[29]
F_ba  2850685772 =
2 * 2 * 11 * 53 * 59 * 20719
F_ph  20316023422432061302 =
14253428857

[28]
F_ba  2497949426 =
2 * 7 * 178424959
F_ph  15599378333387399551 =
11 * 13 * 87340889

[27]
F_ba  1820198063 =
101 * 18021763
F_ph  8282802468642082828 =
2 * 2 * 17987 * 63247
Comm  All the digits of the palindromic heptagonal are even!

[26]
F_ba  765609041 =
241 * 3176801
F_ph  1465393008003935641 =
643 * 2976707

[25]
F_ba  496329416 =
2 * 2 * 2 * 11 * 11 * 17 * 30161
F_ph  615857222222758516 =
7 * 13 * 23 * 1185689

[24]
F_ba  88274141 =
43 * 397 * 5171
F_ph  19480809790808491 =
47 * 73 * 131 * 491

[23]
F_ba  16943262 =
2 * 3 * 7 * 37 * 10903
F_ph  717685292586717 =
3 * 3 * 3 * 13 * 19 * 12703

[22]
F_ba  1686537 =
3 * 3 * 187393
F_ph  7111015101117 =
3 * 31 * 45337

[21]
F_ba  1207698 =
2 * 3 * 31 * 43 * 151
F_ph  3646334336463 =
3 * 3 * 7 * 13 * 73 * 101

[20]
F_ba  615769 =
7 * 11 * 11 * 727
F_ph  947927729749 =
13 * 13 * 9109

[19]
F_ba  382173 =
3 * 11 * 37 * 313
F_ph  365139931563 =
3 * 3 * 53 * 2003

[18]
F_ba  371778 =
2 * 3 * 11 * 43 * 131
F_ph  345546645543 =
3 * 3 * 206543

[17]
F_ba  190914 =
2 * 3 * 47 * 677
F_ph  91120102119 =
3 * 3 * 17 * 17 * 367

[16]
F_ba  171657 =
3 * 3 * 19073
F_ph  73665056637 =
3 * 53 * 2699

[15]
F_ba  161656 =
2 * 2 * 2 * 11 * 11 * 167
F_ph  65331413356 =
233 * 3469

[14]
F_ba  158476 =
2 * 2 * 39619
F_ph  62786368726 =
792377

[13]
F_ba  53537 =
11 * 31 * 157
F_ph  7165445617 =
17 * 7873

[12]
F_ba  1556 =
2 * 2 * 389
F_ph  6050506 =
7 * 11 * 101

[11]
F_ba  1470 =
2 * 3 * 5 * 7 * 7
F_ph  5400045 =
3 * 31 * 79

[10]
F_ba  1359 =
3 * 3 * 151
F_ph  4615164 =
2 * 2 * 3 * 283

[9]
F_ba  583 =
11 * 53
F_ph  848848 =
2 * 2 * 2 * 2 * 7 * 13

[8]
F_ba  156 =
2 * 2 * 3 * 13
F_ph  60606 =
3 * 7 * 37

[7]
F_ba  44 =
2 * 2 * 11
F_ph  4774 =
7 * 31

[6]
F_ba  38 =
2 * 19
F_ph  3553 =
11 * 17

[5]
F_ba  16 =
2 * 2 * 2 * 2
F_ph  616 =
7 * 11

[4]
F_ba  5 =
PRIME
F_ph  55 =
11

[3]
F_ba  2 =
PRIME
F_ph  7 =
PRIME

[2]
F_ba  1 =
1
F_ph  1 =
1

[1]
F_ba  0 =
0
F_ph  0 =
0

```

( © All rights reserved ) - Last modified : June 15, 2023.
Patrick De Geest - Belgium - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com