Legend
F_ba Decomposition of the basenumber in its prime factors.
F_po Decomposition of the palindromic nonagonal.
Note : a palindromic nonagonal will always be divisible by its basenumber when this
last one is 'odd'. With 'even' basenumbers you'll notice that the nonagonals
are always divisible by half their basenumbers.
To reconstruct the nonagonals 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 nonagonal number.
Factorization
[68]
F_ba 5322627062113007506846668678 =
2 * 3^3 * 61 * 1961657 * 823719544300169941
F_po 99156255948182109153103300355300330135190128184955265199 =
11 * 1933 * 36365519 * 48184765357845253
Date September 27, 2024 ( Patrick De Geest / CUDA code by Robert Xiao )
[67]
F_ba 5224357235987816105862153702 =
2 * 3^2 * 7^2 * 11 * 29 * 31 * 38971 * 111001771 * 138465139
F_po 95528679852263887827488512533521588472878836225897682559 =
13 * 37 * 76030146885477573266185189
Date September 27, 2024 ( Patrick De Geest / CUDA code by Robert Xiao )
[66]
F_ba 1876119816345331309680746929 =
11 * 1787 * 282080044487 * 338353730831
F_po 12319389478492738888658361622616385688883729487498391321 =
19 * 203982763 * 1243925387 * 1362031691
Date September 27, 2024 ( Patrick De Geest / CUDA code by Robert Xiao )
[65]
F_ba 1679181506340335801791780993 =
80677 * 20813633456131683153709
F_po 9868776859323897215794481742471844975127983239586778689 =
131 * 23567586043 * 1903615752166481
Date June 16, 2023 ( Patrick De Geest / CUDA code by Robert Xiao )
[64]
F_ba 1362471141388162023922065804 =
2 * 2 * 3 * 3 * 13 * 7019 * 889909 * 2760053 * 168866381
F_po 6497146638904463473409108182818019043743644098366417946 =
839 * 252314658653 * 45052708899469
Date June 16, 2023 ( Patrick De Geest / CUDA code by Robert Xiao )
[63]
F_ba 1111577857223148207649572652 =
2 * 2 * 48795367 * 289549621 * 19668820009
F_po 4324618664340819816841803754573081486189180434668164234 =
31 * 251001451631033466243451889
Date June 16, 2023 ( Patrick De Geest / CUDA code by Robert Xiao )
[62]
F_ba 371144372961223228658331227 =
11 * 37 * 37 * 20939 * 1177038884208520427
F_po 482118509532728488099286553355682990884827235905811284 =
2 * 2 * 3 * 1879 * 1973266487 * 29195583440917
Date January 11, 2023 ( David Griffeath / CUDA code by Robert Xiao )
[61]
F_ba 352831654128834221222546852 =
2 * 2 * 11 * 1277 * 5701 * 6779 * 7963 * 20404717027
F_po 435715616543512545618365652256563816545215345616517534 =
3 * 1319 * 3433 * 8179351 * 22228332351989
Date January 11, 2023 ( David Griffeath / CUDA code by Robert Xiao )
[60]
F_ba 2056602438516214335318946 =
2 * 11 * 127 * 353 * 11789 * 176461 * 1002359557
F_po 14803647565387937078765122156787073978356574630841 =
13 * 4787737 * 231299528994009557
Date November 13, 2022 ( David Griffeath / Rust code by Robert Xiao )
[59]
F_ba 115254230534871709541072 =
2 * 2 * 2 * 2 * 7203389408429481846317
F_po 46492381796648740224886168842204784669718329464 =
3 * 139 * 358051 * 5403485241907897
Date January 6, 2008 ( Feng Yuan )
[58]
F_ba 12771589611884159330405 =
5 * 5519 * 462822598727456399
F_po 570897254250355800456888654008553052452798075 =
3 * 5 * 2663 * 88975949 * 12577025603
Date December 6, 2022 ( Robert Xiao )
[57]
F_ba 1660812452251980426673 =
37 * 2511703 * 17871071155243
F_po 9654043005443328676169616768233445003404569 =
5812843582881931493353
Date November 11, 2022 ( Robert Xiao )
[56]
F_ba 1639652478336096510562 =
2 * 163 * 5029608829251829787
F_po 9409610873997962029122219202697993780169049 =
41 * 279940667032992087169
Date November 11, 2022 ( Robert Xiao )
[55]
F_ba 522755911437759066613 =
7 x 7 x 7 x 13 x 43 x 2726421668419549
F_po 956458100300927701829928107729003001854659 =
11 * 49380497 * 3368362743829
Date January 6, 2008 ( Feng Yuan )
[54]
F_ba 198343896557195374949 =
83 * 30689 * 77867819110727
F_po 137691054555219967590095769912555450196731 =
3 * 3 * 11 * 73943 * 5106781 * 18569807
Date January 6, 2008 ( Feng Yuan )
[53]
F_ba 51828177547322738562 =
2 * 3 * 7 * 11 * 13 * 701 * 12310128660527
F_po 9401559957568830940550490388657599551049 =
37 * 79 * 124118112497864923
Date November 4, 2022 ( Robert Xiao )
[52]
F_ba 21052483436370199814 =
2 * 7 * 11 * 13 * 59 * 61 * 103 * 28367442931
F_po 1551224705935245659449565425395074221551 =
3 * 41 * 419 * 1069 * 2674881423881
Date January 4, 2008 ( Feng Yuan )
[51]
F_ba 11547031421292227747 =
707886083 * 16311991009
F_po 466668771255085018151810580552177866664 =
2 * 2 * 2 * 3 * 11 * 19 * 1259 * 110749 * 57785027
Date January 4, 2008 ( Feng Yuan )
[50]
F_ba 10973370993981638987 =
23 * 31 * 47 * 89 * 181081 * 20318413
F_po 421452048400451542646245154004840254124 =
2 * 2 * 3 * 3 * 101 * 23879 * 442352103283
Date January 4, 2008 ( Feng Yuan )
[49]
F_ba 4152074121197238599 =
11 * 19 * 337 * 409 * 144133722367
F_po 60339018277705374211247350777281093306 =
2 * 3 * 557 * 4348372059901357
Date November 4, 2022 ( Robert Xiao )
[48]
F_ba 3672784064195630087 =
11 * 23 * 42250391 * 343592869
F_po 47212699737732795788759723773799621274 =
2 * 3 * 49211 * 193873 * 224560139
Date January 4, 2008 ( Feng Yuan )
[47]
F_ba 1172098775019783163 =
7 * 31 * 199 * 15527 * 1748090243
F_po 4808354384410066932396600144834538084 =
2 * 2 * 19 * 23143 * 2332378389151
Date November 4, 2022 ( Robert Xiao )
[46]
F_ba 587730406426154761 =
7 * 7 * 11 * 431 * 2529951084229
F_po 1208994607232485700075842327064998021 =
31 * 107 * 620155689626633
Date November 4, 2022 ( Robert Xiao )
[45]
F_ba 446339713063722379 =
11 * 40576337551247489
F_po 697266988102321088880123201889662796 =
2 * 2 * 101 * 3866804444858981
Date January 4, 2008 ( Feng Yuan )
[44]
F_ba 18287529802802806 =
2 * 7 * 13 * 353 * 3511 * 81073351
F_po 1170518112009402882049002118150711 =
11 * 17 * 641 * 1067956223311
Date April 5, 2002 ( Feng Yuan )
[43]
F_ba 16084074672143002 =
2 * 7 * 83 * 463 * 29895716167
F_po 905441103206752020257602301144509 =
4519 * 872033 * 28570567
Date April 5, 2002 ( Feng Yuan )
[42]
F_ba 14107415463308179 =
83 * 227 * 67489 * 11094571
F_po 696567098690353494353096890765696 =
2 * 2 * 2 * 2 * 2 * 2 * 2 * 37 * 63901 * 163153409
Date April 5, 2002 ( Feng Yuan )
[41]
F_ba 13543695809405311 =
11 * 151 * 2720239 * 2997509
F_po 642010936621960404069126639010246 =
2 * 23701467666459293
Date April 5, 2002 ( Feng Yuan )
[40]
F_ba 13267696935194771 =
761 * 30553 * 570633187
F_po 616111236874618484816478632111616 =
2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 23 * 101 * 86249 * 150893
Date April 5, 2002 ( Feng Yuan )
[39]
F_ba 4340322549816 =
2 * 2 * 2 * 3 * 11 * 11 * 1494601429
F_po 65934399427533572499343956 =
1913 * 75937 * 209147
Date April 5, 2002 ( Feng Yuan )
[38]
F_ba 3696823830487 =
137 * 26984115551
F_po 47832772517788771527723874 =
2 * 11 * 73 * 101 * 79768217
Date April 5, 2002 ( Feng Yuan )
[37]
F_ba 2053636735146 =
2 * 3 * 23 * 61 * 14653 * 16649
F_po 14760983439788793438906741 =
11 * 1306859740547
Date April 5, 2002 ( Feng Yuan )
[36]
F_ba 386688531610 =
2 * 5 * 37537 * 1030153
F_po 523348071674476170843325 =
5 * 11 * 49214904023
Date April 5, 2002 ( Feng Yuan )
[35]
F_ba 172428811826 =
2 * 23 * 3748452431
F_po 104060933016610339060401 =
3 * 11 * 877 * 929 * 44893
Date April 5, 2002 ( Feng Yuan )
[34]
F_ba 139168803139 =
307 * 453318577
F_po 67787845184648154878776 =
2 * 2 * 2 * 953 * 63889141
Date April 5, 2002 ( Feng Yuan )
[33]
F_ba 115589719272 =
2 * 2 * 2 * 3 * 149 * 32323747
F_po 46763441204540214436764 =
107069 * 7557071
Date April 5, 2002 ( Feng Yuan )
[32]
F_ba 75356090494 =
2 * 19 * 89 * 22281517
F_po 19874891310701319847891 =
127487 * 4137619
Date April 5, 2002 ( Feng Yuan )
[31]
F_ba 21633254881 =
7 * 571 * 1949 * 2777
F_po 1637992008558002997361 =
11 * 23 * 11047 * 27091
Date April 5, 2002 ( Feng Yuan )
[30]
F_ba 11947307367 =
3 * 3982435789
F_po 499583536595635385994 =
2 * 19 * 197 * 2029 * 2753
Date April 5, 2002 ( Feng Yuan )
[29]
F_ba 1641773578 =
2 * 29 * 31 * 41 * 22271
F_po 9433971680861793349 =
6679 * 1720679
Date April 5, 2002 ( Feng Yuan )
[28]
F_ba 1121857192 =
2 * 2 * 2 * 140232149
F_po 4404972454542794044 =
8527 * 920957
Date April 5, 2002 ( Feng Yuan )
[27]
F_ba 708609429 =
3 * 3 * 11 * 83 * 83 * 1039
F_po 1757445628265447571 =
2480132999
Date April 5, 2002 ( Feng Yuan )
[26]
F_ba 521037077 =
11 * 503 * 94169
F_po 950178723327871059 =
3 * 37 * 1153 * 14249
Date April 5, 2002 ( Feng Yuan )
[25]
F_ba 350096787 =
3 * 3 * 29 * 137 * 9791
F_po 428987160061789824 =
2 * 2 * 2 * 2 * 2 * 2 * 2 * 11 * 487 * 1787
Date April 5, 2002 ( Feng Yuan )
[24]
F_ba 168566853 =
3 * 7 * 13 * 13 * 47497
F_po 99451743334715499 =
107 * 467 * 11807
Date April 5, 2002 ( Feng Yuan )
[23]
F_ba 446904 =
2 * 2 * 2 * 3 * 3 * 3 * 2069
F_po 699030030996 =
11 * 17 * 16729
Date April 5, 2002 ( Feng Yuan )
[22]
F_ba 435644 =
2 * 2 * 11 * 9901
F_po 664248842466 =
3 * 37 * 83 * 331
Date April 5, 2002 ( Feng Yuan )
[21]
F_ba 132619 =
PRIME
F_po 61556965516 =
2 * 2 * 116041
Date April 5, 2002 ( Feng Yuan )
[20]
F_ba 52642 =
2 * 26321
F_po 9698998969 =
11 * 139 * 241
Date April 5, 2002 ( Feng Yuan )
[19]
F_ba 18729 =
3 * 3 * 2081
F_po 1227667221 =
11 * 59 * 101
Date April 5, 2002 ( Feng Yuan )
[18]
F_ba 16853 =
19 * 887
F_po 994040499 =
3 * 19661
Date April 5, 2002 ( Feng Yuan )
[17]
F_ba 16318 =
2 * 41 * 199
F_po 931929139 =
114221
Date April 5, 2002 ( Feng Yuan )
[16]
F_ba 12870 =
2 * 3 * 3 * 5 * 11 * 13
F_po 579696975 =
5 * 43 * 419
Date April 5, 2002 ( Feng Yuan )
[15]
F_ba 11472 =
2 * 2 * 2 * 2 * 3 * 239
F_po 460595064 =
59 * 1361
Date April 5, 2002 ( Feng Yuan )
[14]
F_ba 11323 =
13 * 13 * 67
F_po 448707844 =
2 * 2 * 9907
Date April 5, 2002 ( Feng Yuan )
[13]
F_ba 4070 =
2 * 5 * 11 * 37
F_po 57966975 =
3 * 3 * 3 * 5 * 211
Date April 5, 2002 ( Feng Yuan )
[12]
F_ba 2101 =
11 * 191
F_po 15444451 =
7351
Date April 5, 2002 ( Feng Yuan )
[11]
F_ba 1411 =
17 * 83
F_po 6964696 =
2 * 2 * 2 * 617
Date April 5, 2002 ( Feng Yuan )
[10]
F_ba 1123 =
PRIME
F_po 4411144 =
2 * 2 * 2 * 491
Date April 5, 2002 ( Feng Yuan )
[9]
F_ba 139 =
PRIME
F_po 67267 =
491
Date April 5, 2002 ( Feng Yuan )
[8]
F_ba 74 =
2 * 37
F_po 18981 =
3 * 3 * 3 * 19
Date April 5, 2002 ( Feng Yuan )
[7]
F_ba 44 =
2 * 2 * 11
F_po 6666 =
3 * 101
Date April 5, 2002 ( Feng Yuan )
[6]
F_ba 17 =
PRIME
F_po 969 =
57
Date April 5, 2002 ( Feng Yuan )
[5]
F_ba 12 =
2 * 2 * 3
F_po 474 =
79
Date April 5, 2002 ( Feng Yuan )
[4]
F_ba 6 =
2 * 3
F_po 111 =
37
Date April 5, 2002 ( Feng Yuan )
[3]
F_ba 2 =
PRIME
F_po 9 =
3 * 3
Date April 5, 2002 ( Feng Yuan )
[2]
F_ba 1 =
1
F_po 1 =
1
Date April 5, 2002 ( Feng Yuan )
[1]
F_ba 0 =
0
F_po 0 =
0
Date April 5, 2002 ( Feng Yuan )
[
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Patrick De Geest - Belgium 
- Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com
Factorization of the
Palindromic Nonagonals