Cube wonders

On Monday, Futility Closet posted — without explanation — five base-ten 12-digit "cube wonders" (my expression). After finding a smaller example (512) I wondered if I might be able to discover larger ones. Alas, my brute-force Mathematica code was taking its time rediscovering even those five examples and I eventually gave up.

A web search soon led me to OEIS A006887 where those five numbers are the cubes of terms #9 - #13. Jack Brennen kindly supplied a C-program that calculated the sequence's additional terms. All I had to do was cull from the newly generated list those terms whose cubes could be split into three equal digit-length parts, wherein (for the sake of aesthetics) the second and third parts did not start with a zero. Here are the first 33 solutions:

512 = (5+1+2)^3

121213882349 = (1212+1388+2349)^3

128711132649 = (1287+1113+2649)^3

162324571375 = (1623+2457+1375)^3

171323771464 = (1713+2377+1464)^3

368910352448 = (3689+1035+2448)^3

171471879319616 = (17147+18793+19616)^3

220721185826504 = (22072+11858+26504)^3

470511577514952 = (47051+15775+14952)^3

109294197946170875 = (109294+197946+170875)^3

116367227503144344 = (116367+227503+144344)^3

120706126590246912 = (120706+126590+246912)^3

160769107975275008 = (160769+107975+275008)^3

175471156639227736 = (175471+156639+227736)^3

214714120150263943 = (214714+120150+263943)^3

293736149984221021 = (293736+149984+221021)^3

435235164725157875 = (435235+164725+157875)^3

495862183018112625 = (495862+183018+112625)^3

526727149679131192 = (526727+149679+131192)^3

119673015472102184000 = (1196730+1547210+2184000)^3

171467712620032578875 = (1714677+1262003+2578875)^3

236392428062461013000 = (2363924+2806246+1013000)^3

104126812463311912000000 = (10412681+24633119+12000000)^3

129994501742459020233216 = (12999450+17424590+20233216)^3

170717891744681120955851 = (17071789+17446811+20955851)^3

176905291183926726606912 = (17690529+11839267+26606912)^3

201817431964353718831681 = (20181743+19643537+18831681)^3

257700981126972226596544 = (25770098+11269722+26596544)^3

339601941949863016309248 = (33960194+19498630+16309248)^3

420352701580617017068241 = (42035270+15806170+17068241)^3

469218322003481810750024 = (46921832+20034818+10750024)^3

526085181538162612736833 = (52608518+15381626+12736833)^3

529262771767141910291487 = (52926277+17671419+10291487)^3

I have placed a larger 236-solutions set here.

554556098 and 8283333125

My program for finding pandigital factorization integer cascades wasn't very efficient. In order to improve on that situation I decided to first calculate a table of possible end-PFIs resulting from the addition of pandigital numbers to all possible start-PFIs. By which I mean the smallest few hundred-thousand start-PFIs because — after that — there are unlikely to be additional solutions:

The graph shows the number of solutions for the smallest 431285 PFIs. I went this far because there is a solution at PFI #431284 (which, after the addition of a pandigital number, becomes PFI #431285). The largest number of solutions is 414 for PFI #39644, which is 554556098 or 2*5861*47309:

  1.   2*5861*47309 + 1026475839 = 23*68740519
  2.   2*5861*47309 + 1029458637 = 5*316802947
  3.   2*5861*47309 + 1029468537 = 5*316804927
  4.   2*5861*47309 + 1032586947 = 5*317428609
  5.   2*5861*47309 + 1039285764 = 2*83*9601457
  6.   2*5861*47309 + 1042586937 = 5*319428607
  7.   2*5861*47309 + 1042856937 = 5*319482607
  8.   2*5861*47309 + 1052836947 = 5*321478609
  9.   2*5861*47309 + 1053486297 = 5*321608479
 10.   2*5861*47309 + 1054968237 = 5*321904867
 11.   2*5861*47309 + 1054986237 = 5*321908467
 12.   2*5861*47309 + 1065924837 = 5*324096187
 13.   2*5861*47309 + 1065983247 = 5*324107869
 14.   2*5861*47309 + 1082693547 = 5*761*430289
 15.   2*5861*47309 + 1089264357 = 5*328764091
 16.   2*5861*47309 + 1093864257 = 5*329684071
 17.   2*5861*47309 + 1243809657 = 5*4013*89627
 18.   2*5861*47309 + 1263498705 = 23*79045861
 19.   2*5861*47309 + 1265983047 = 5*364107829
 20.   2*5861*47309 + 1269480357 = 5*364807291
 21.   2*5861*47309 + 1269483507 = 5*364807921
 22.   2*5861*47309 + 1269804357 = 5*364872091
 23.   2*5861*47309 + 1280657439 = 8573*214069
 24.   2*5861*47309 + 1280965347 = 5*367104289
 25.   2*5861*47309 + 1284965307 = 5*367904281
 26.   2*5861*47309 + 1285904637 = 5*368092147
 27.   2*5861*47309 + 1296473805 = 23*80479561
 28.   2*5861*47309 + 1298536047 = 5*370618429
 29.   2*5861*47309 + 1298650347 = 5*370641289
 30.   2*5861*47309 + 1298653047 = 5*370641829
 31.   2*5861*47309 + 1302856947 = 5*371482609
 32.   2*5861*47309 + 1308247695 = 643*2897051
 33.   2*5861*47309 + 1326085947 = 5*376128409
 34.   2*5861*47309 + 1329468507 = 5*376804921
 35.   2*5861*47309 + 1329658407 = 5*376842901
 36.   2*5861*47309 + 1348650297 = 5*380641279
 37.   2*5861*47309 + 1348690257 = 5*380649271
 38.   2*5861*47309 + 1348906257 = 5*380692471
 39.   2*5861*47309 + 1350264987 = 5*380964217
 40.   2*5861*47309 + 1359248607 = 5*382760941
 41.   2*5861*47309 + 1365084279 = 41*89*526073
 42.   2*5861*47309 + 1368490257 = 5*384609271
 43.   2*5861*47309 + 1369248507 = 5*384760921
 44.   2*5861*47309 + 1397048652 = 2*5^3*7806419
 45.   2*5861*47309 + 1398276405 = 23*84905761
 46.   2*5861*47309 + 1406285937 = 5*392168407
 47.   2*5861*47309 + 1406982753 = 41*53*902687
 48.   2*5861*47309 + 1428965307 = 5*396704281
 49.   2*5861*47309 + 1429308567 = 5*971*408623
 50.   2*5861*47309 + 1430872569 = 283*7015649
 51.   2*5861*47309 + 1457608239 = 31*64908527
 52.   2*5861*47309 + 1463825079 = 6547*308291
 53.   2*5861*47309 + 1463850297 = 5*403681279
 54.   2*5861*47309 + 1465703829 = 7*43^2*156089
 55.   2*5861*47309 + 1489263507 = 5*408763921
 56.   2*5861*47309 + 1493850267 = 5*409681273
 57.   2*5861*47309 + 1508463297 = 5*412603879
 58.   2*5861*47309 + 1508632947 = 5*412637809
 59.   2*5861*47309 + 1508962347 = 5*412703689
 60.   2*5861*47309 + 1526493087 = 5*416209837
 61.   2*5861*47309 + 1529608437 = 5*416832907
 62.   2*5861*47309 + 1529670483 = 23*90618547
 63.   2*5861*47309 + 1536824097 = 5*418276039
 64.   2*5861*47309 + 1538604297 = 5*418632079
 65.   2*5861*47309 + 1538960247 = 5*418703269
 66.   2*5861*47309 + 1548603297 = 5*420631879
 67.   2*5861*47309 + 1564839207 = 5*423879061
 68.   2*5861*47309 + 1582036947 = 5*427318609
 69.   2*5861*47309 + 1586290437 = 5*428169307
 70.   2*5861*47309 + 1589263407 = 5*428763901
 71.   2*5861*47309 + 1594726083 = 40693*52817
 72.   2*5861*47309 + 1596328047 = 5*430176829
 73.   2*5861*47309 + 1596802347 = 5*430271689
 74.   2*5861*47309 + 1603582947 = 5*431627809
 75.   2*5861*47309 + 1604895237 = 5*431890267
 76.   2*5861*47309 + 1605983247 = 5*432107869
 77.   2*5861*47309 + 1608453297 = 5*432601879
 78.   2*5861*47309 + 1608493257 = 5*432609871
 79.   2*5861*47309 + 1608534297 = 5*432618079
 80.   2*5861*47309 + 1608542937 = 5*432619807
 81.   2*5861*47309 + 1608953247 = 5*432701869
 82.   2*5861*47309 + 1609482357 = 5*432807691
 83.   2*5861*47309 + 1609824357 = 5*432876091
 84.   2*5861*47309 + 1624879305 = 23*94758061
 85.   2*5861*47309 + 1628950347 = 5*436701289
 86.   2*5861*47309 + 1628953047 = 5*436701829
 87.   2*5861*47309 + 1629504387 = 5*436812097
 88.   2*5861*47309 + 1629804357 = 5*436872091
 89.   2*5861*47309 + 1638450297 = 5*438601279
 90.   2*5861*47309 + 1638904257 = 5*438692071
 91.   2*5861*47309 + 1638952047 = 5*438701629
 92.   2*5861*47309 + 1639248507 = 5*438760921
 93.   2*5861*47309 + 1639258407 = 5*438762901
 94.   2*5861*47309 + 1652347089 = 41*53826907
 95.   2*5861*47309 + 1672483905 = 41809*53267
 96.   2*5861*47309 + 1690378245 = 23*97605841
 97.   2*5861*47309 + 1690438275 = 23*97608451
 98.   2*5861*47309 + 1708695423 = 467*821*5903
 99.   2*5861*47309 + 1728694305 = 7^2*83*561409
100.   2*5861*47309 + 1728906345 = 67*34081529
101.   2*5861*47309 + 1803526749 = 26347*89501
102.   2*5861*47309 + 1806259347 = 5*472163089
103.   2*5861*47309 + 1806359247 = 5*472183069
104.   2*5861*47309 + 1824097635 = 29453*80761
105.   2*5861*47309 + 1826950347 = 5*476301289
106.   2*5861*47309 + 1829460357 = 5*476803291
107.   2*5861*47309 + 1829504367 = 5*476812093
108.   2*5861*47309 + 1829563407 = 5*476823901
109.   2*5861*47309 + 1836254097 = 5*478162039
110.   2*5861*47309 + 1836509247 = 5*478213069
111.   2*5861*47309 + 1836924057 = 5*478296031
112.   2*5861*47309 + 1842356907 = 5*479382601
113.   2*5861*47309 + 1843072659 = 409*5862173
114.   2*5861*47309 + 1846325097 = 5*480176239
115.   2*5861*47309 + 1849052367 = 5*480721693
116.   2*5861*47309 + 1849250367 = 5*480761293
117.   2*5861*47309 + 1849260357 = 5*480763291
118.   2*5861*47309 + 1850324967 = 5*480976213
119.   2*5861*47309 + 1850472369 = 563*4271809
120.   2*5861*47309 + 1853904267 = 5*481692073
121.   2*5861*47309 + 1853960247 = 5*481703269
122.   2*5861*47309 + 1856409237 = 5*482193067
123.   2*5861*47309 + 1859024367 = 5*482716093
124.   2*5861*47309 + 1864395207 = 5*483790261
125.   2*5861*47309 + 1865024937 = 5*483916207
126.   2*5861*47309 + 1867245309 = 41*59068327
127.   2*5861*47309 + 1893460257 = 5*489603271
128.   2*5861*47309 + 1893504267 = 5*489612073
129.   2*5861*47309 + 1908463257 = 5*492603871
130.   2*5861*47309 + 1926835407 = 5*496278301
131.   2*5861*47309 + 1936482057 = 5*498207631
132.   2*5861*47309 + 1938460257 = 5*498603271
133.   2*5861*47309 + 1938504267 = 5*498612073
134.   2*5861*47309 + 1952843607 = 5*83*6041927
135.   2*5861*47309 + 1968032475 = 941*2680753
136.   2*5861*47309 + 2018395467 = 5*641*802793
137.   2*5861*47309 + 2045916837 = 5*8429*61703
138.   2*5861*47309 + 2147683095 = 41*65908273
139.   2*5861*47309 + 2193486075 = 401*6852973
140.   2*5861*47309 + 2307458619 = 41*69805237
141.   2*5861*47309 + 2310648759 = 53*89*607421
142.   2*5861*47309 + 2371084965 = 401*7295863
143.   2*5861*47309 + 2380954167 = 5*71*8269043
144.   2*5861*47309 + 2385910467 = 5*9473*62081
145.   2*5861*47309 + 2389750461 = 59*83*601247
146.   2*5861*47309 + 2390458617 = 5*83*7096421
147.   2*5861*47309 + 2405367189 = 491*6028357
148.   2*5861*47309 + 2419563087 = 5*8423*70619
149.   2*5861*47309 + 2451683097 = 5*601247839
150.   2*5861*47309 + 2451936087 = 5*601298437
151.   2*5861*47309 + 2467851039 = 4801*629537
152.   2*5861*47309 + 2468739105 = 67*45123809
153.   2*5861*47309 + 2469803517 = 5*604871923
154.   2*5861*47309 + 2481653097 = 5*607241839
155.   2*5861*47309 + 2481693057 = 5*607249831
156.   2*5861*47309 + 2481936057 = 5*607298431
157.   2*5861*47309 + 2486190537 = 5*608149327
158.   2*5861*47309 + 2486315097 = 5*608174239
159.   2*5861*47309 + 2489051367 = 5*608721493
160.   2*5861*47309 + 2489061357 = 5*608723491
161.   2*5861*47309 + 2491683057 = 5*609247831
162.   2*5861*47309 + 2508764931 = 761*4025389
163.   2*5861*47309 + 2509184367 = 5*612748093
164.   2*5861*47309 + 2516809347 = 5*614273089
165.   2*5861*47309 + 2516890437 = 5*614289307
166.   2*5861*47309 + 2516980347 = 5*614307289
167.   2*5861*47309 + 2519460387 = 5*614803297
168.   2*5861*47309 + 2531486097 = 5*617208439
169.   2*5861*47309 + 2531846097 = 5*617280439
170.   2*5861*47309 + 2531864097 = 5*617284039
171.   2*5861*47309 + 2531986047 = 5*617308429
172.   2*5861*47309 + 2534968017 = 5*617904823
173.   2*5861*47309 + 2539068417 = 5*618724903
174.   2*5861*47309 + 2546193087 = 5*620149837
175.   2*5861*47309 + 2546307891 = 41*75630829
176.   2*5861*47309 + 2549018367 = 5*620714893
177.   2*5861*47309 + 2569038417 = 5*624718903
178.   2*5861*47309 + 2569138407 = 5*624738901
179.   2*5861*47309 + 2580961347 = 5*627103489
180.   2*5861*47309 + 2581360947 = 5*627183409
181.   2*5861*47309 + 2581634079 = 6521*480937
182.   2*5861*47309 + 2586130947 = 5*628137409
183.   2*5861*47309 + 2586430917 = 5*628197403
184.   2*5861*47309 + 2596081347 = 5*630127489
185.   2*5861*47309 + 2596803147 = 5*630271849
186.   2*5861*47309 + 2603958147 = 5*631702849
187.   2*5861*47309 + 2604958137 = 5*631902847
188.   2*5861*47309 + 2609184357 = 5*632748091
189.   2*5861*47309 + 2610345987 = 5*632980417
190.   2*5861*47309 + 2618345079 = 50891*62347
191.   2*5861*47309 + 2619508437 = 5*634812907
192.   2*5861*47309 + 2619583407 = 5*634827901
193.   2*5861*47309 + 2631085947 = 5*637128409
194.   2*5861*47309 + 2634589107 = 5*637829041
195.   2*5861*47309 + 2634985107 = 5*637908241
196.   2*5861*47309 + 2639158407 = 5*638742901
197.   2*5861*47309 + 2640985137 = 5*639108247
198.   2*5861*47309 + 2641850937 = 5*639281407
199.   2*5861*47309 + 2643985107 = 5*639708241
200.   2*5861*47309 + 2649108357 = 5*640732891
201.   2*5861*47309 + 2649510387 = 5*640813297
202.   2*5861*47309 + 2649813507 = 5*640873921
203.   2*5861*47309 + 2651834097 = 5*641278039
204.   2*5861*47309 + 2651934087 = 5*641298037
205.   2*5861*47309 + 2651983047 = 5*641307829
206.   2*5861*47309 + 2654089317 = 5*641729083
207.   2*5861*47309 + 2659874301 = 859*3742061
208.   2*5861*47309 + 2670189345 = 67*48130529
209.   2*5861*47309 + 2674190853 = 67*48190253
210.   2*5861*47309 + 2681509347 = 5*647213089
211.   2*5861*47309 + 2681934057 = 5*647298031
212.   2*5861*47309 + 2684953017 = 5*647901823
213.   2*5861*47309 + 2685049317 = 5*647921083
214.   2*5861*47309 + 2685134907 = 5*647938201
215.   2*5861*47309 + 2685349017 = 5*647981023
216.   2*5861*47309 + 2691085437 = 5*649128307
217.   2*5861*47309 + 2719304685 = 41*79850263
218.   2*5861*47309 + 2781543609 = 409*8156723
219.   2*5861*47309 + 2805934617 = 5*672098143
220.   2*5861*47309 + 2805961347 = 5*672103489
221.   2*5861*47309 + 2809653417 = 5*672841903
222.   2*5861*47309 + 2813045967 = 5*71*9486203
223.   2*5861*47309 + 2816059347 = 5*674123089
224.   2*5861*47309 + 2816453097 = 5*674201839
225.   2*5861*47309 + 2816935407 = 5*674298301
226.   2*5861*47309 + 2816953047 = 5*674301829
227.   2*5861*47309 + 2819563407 = 5*674823901
228.   2*5861*47309 + 2836159047 = 5*678143029
229.   2*5861*47309 + 2836491057 = 5*678209431
230.   2*5861*47309 + 2836510947 = 5*678213409
231.   2*5861*47309 + 2836950147 = 5*678301249
232.   2*5861*47309 + 2841596307 = 5*679230481
233.   2*5861*47309 + 2849106357 = 5*680732491
234.   2*5861*47309 + 2851673049 = 67*50839241
235.   2*5861*47309 + 2854961037 = 5*681903427
236.   2*5861*47309 + 2856309147 = 5*682173049
237.   2*5861*47309 + 2856314097 = 5*682174039
238.   2*5861*47309 + 2861305947 = 5*683172409
239.   2*5861*47309 + 2865014937 = 5*683914207
240.   2*5861*47309 + 2865049137 = 5*683921047
241.   2*5861*47309 + 2865314907 = 5*683974201
242.   2*5861*47309 + 2891650437 = 5*689241307
243.   2*5861*47309 + 2910854637 = 5*693082147
244.   2*5861*47309 + 2930564817 = 5*697024183
245.   2*5861*47309 + 2930684517 = 5*697048123
246.   2*5861*47309 + 2930854617 = 5*697082143
247.   2*5861*47309 + 2931485607 = 5*697208341
248.   2*5861*47309 + 2931486057 = 5*697208431
249.   2*5861*47309 + 2931845607 = 5*697280341
250.   2*5861*47309 + 2931846057 = 5*697280431
251.   2*5861*47309 + 2934061785 = 419*8326057
252.   2*5861*47309 + 2935804617 = 5*698072143
253.   2*5861*47309 + 2936154087 = 5*698142037
254.   2*5861*47309 + 2936481057 = 5*698207431
255.   2*5861*47309 + 2936514087 = 5*698214037
256.   2*5861*47309 + 2956841073 = 67*52408913
257.   2*5861*47309 + 2958603147 = 5*702631849
258.   2*5861*47309 + 2963850147 = 5*703681249
259.   2*5861*47309 + 3026574891 = 57389*62401
260.   2*5861*47309 + 3026958147 = 5*716302849
261.   2*5861*47309 + 3026985147 = 5*716308249
262.   2*5861*47309 + 3029468517 = 5*716804923
263.   2*5861*47309 + 3054986217 = 5*721908463
264.   2*5861*47309 + 3056498721 = 571*6324089
265.   2*5861*47309 + 3057426819 = 463*7801259
266.   2*5861*47309 + 3065924817 = 5*724096183
267.   2*5861*47309 + 3069528417 = 5*724816903
268.   2*5861*47309 + 3085961247 = 5*728103469
269.   2*5861*47309 + 3086952147 = 5*728301649
270.   2*5861*47309 + 3096158247 = 5*730142869
271.   2*5861*47309 + 3096528147 = 5*730216849
272.   2*5861*47309 + 3105247689 = 41*89263507
273.   2*5861*47309 + 3125968047 = 5*736104829
274.   2*5861*47309 + 3129648507 = 5*736840921
275.   2*5861*47309 + 3145027869 = 59*62704813
276.   2*5861*47309 + 3146258709 = 769*4812503
277.   2*5861*47309 + 3146852097 = 5*740281639
278.   2*5861*47309 + 3146892057 = 5*740289631
279.   2*5861*47309 + 3149680527 = 5^3*617*48029
280.   2*5861*47309 + 3158602947 = 5*742631809
281.   2*5861*47309 + 3160985247 = 5*743108269
282.   2*5861*47309 + 3164589207 = 5*743829061
283.   2*5861*47309 + 3186452097 = 5*748201639
284.   2*5861*47309 + 3186950247 = 5*748301269
285.   2*5861*47309 + 3198072465 = 57803*64921
286.   2*5861*47309 + 3250184967 = 5*760948213
287.   2*5861*47309 + 3251648097 = 5*761240839
288.   2*5861*47309 + 3251684097 = 5*761248039
289.   2*5861*47309 + 3254986017 = 5*761908423
290.   2*5861*47309 + 3260958147 = 5*763102849
291.   2*5861*47309 + 3260985147 = 5*763108249
292.   2*5861*47309 + 3261085947 = 5*763128409
293.   2*5861*47309 + 3264589107 = 5*763829041
294.   2*5861*47309 + 3264895107 = 5*763890241
295.   2*5861*47309 + 3286514097 = 5*768214039
296.   2*5861*47309 + 3286914057 = 5*768294031
297.   2*5861*47309 + 3286915407 = 5*768294301
298.   2*5861*47309 + 3290864517 = 5*769084123
299.   2*5861*47309 + 3291648057 = 5*769240831
300.   2*5861*47309 + 3291685407 = 5*769248301
301.   2*5861*47309 + 3416985207 = 5*794308261
302.   2*5861*47309 + 3418562907 = 5*794623801
303.   2*5861*47309 + 3425968017 = 5*796104823
304.   2*5861*47309 + 3426958107 = 5*796302841
305.   2*5861*47309 + 3456182097 = 5*802147639
306.   2*5861*47309 + 3456192087 = 5*802149637
307.   2*5861*47309 + 3481256097 = 5*807162439
308.   2*5861*47309 + 3481692057 = 5*807249631
309.   2*5861*47309 + 3491682057 = 5*809247631
310.   2*5861*47309 + 3491825607 = 5*809276341
311.   2*5861*47309 + 3491826057 = 5*809276431
312.   2*5861*47309 + 3508614297 = 5*812634079
313.   2*5861*47309 + 3508914267 = 5*812694073
314.   2*5861*47309 + 3516982047 = 5*814307629
315.   2*5861*47309 + 3518470269 = 56489*72103
316.   2*5861*47309 + 3518604297 = 5*814632079
317.   2*5861*47309 + 3526481097 = 5*816207439
318.   2*5861*47309 + 3549128607 = 5*820736941
319.   2*5861*47309 + 3560981247 = 5*823107469
320.   2*5861*47309 + 3561280947 = 5*823167409
321.   2*5861*47309 + 3564982107 = 5*823907641
322.   2*5861*47309 + 3580961247 = 5*827103469
323.   2*5861*47309 + 3581260947 = 5*827163409
324.   2*5861*47309 + 3584962107 = 5*827903641
325.   2*5861*47309 + 3596081247 = 5*830127469
326.   2*5861*47309 + 3596842107 = 5*830279641
327.   2*5861*47309 + 3619248507 = 5*834760921
328.   2*5861*47309 + 3625980147 = 5*836107249
329.   2*5861*47309 + 3625981047 = 5*836107429
330.   2*5861*47309 + 3628950147 = 5*836701249
331.   2*5861*47309 + 3629148507 = 5*836740921
332.   2*5861*47309 + 3642581907 = 5*839427601
333.   2*5861*47309 + 3651482097 = 5*841207639
334.   2*5861*47309 + 3651824097 = 5*841276039
335.   2*5861*47309 + 3654982017 = 5*841907623
336.   2*5861*47309 + 3674801259 = 59*71684023
337.   2*5861*47309 + 3678102945 = 5801*729643
338.   2*5861*47309 + 3680924517 = 5*847096123
339.   2*5861*47309 + 3681095247 = 5*847130269
340.   2*5861*47309 + 3681925407 = 5*847296301
341.   2*5861*47309 + 3681952047 = 5*847301629
342.   2*5861*47309 + 3691524087 = 5*849216037
343.   2*5861*47309 + 3691825407 = 5*849276301
344.   2*5861*47309 + 3718405629 = 8627*495301
345.   2*5861*47309 + 3801596247 = 5*871230469
346.   2*5861*47309 + 3801625947 = 5*871236409
347.   2*5861*47309 + 3806259147 = 5*872163049
348.   2*5861*47309 + 3816245097 = 5*874160239
349.   2*5861*47309 + 3816259047 = 5*874163029
350.   2*5861*47309 + 3816452097 = 5*874201639
351.   2*5861*47309 + 3816950247 = 5*874301269
352.   2*5861*47309 + 3825904617 = 5*876092143
353.   2*5861*47309 + 3826451097 = 5*876201439
354.   2*5861*47309 + 3826510947 = 5*876213409
355.   2*5861*47309 + 3850417269 = 563*7824109
356.   2*5861*47309 + 3872605491 = 62851*70439
357.   2*5861*47309 + 3908461257 = 5*892603471
358.   2*5861*47309 + 3916254087 = 5*894162037
359.   2*5861*47309 + 3926451087 = 5*896201437
360.   2*5861*47309 + 3954286017 = 5*901768423
361.   2*5861*47309 + 3954806217 = 5*901872463
362.   2*5861*47309 + 3964258107 = 5*903762841
363.   2*5861*47309 + 3964581207 = 5*903827461
364.   2*5861*47309 + 3984561207 = 5*907823461
365.   2*5861*47309 + 3984615207 = 5*907834261
366.   2*5861*47309 + 4032895671 = 6521*703489
367.   2*5861*47309 + 4052836917 = 5*921478603
368.   2*5861*47309 + 4058127639 = 823*5604719
369.   2*5861*47309 + 4068953217 = 5*924701863
370.   2*5861*47309 + 4076859231 = 53401*86729
371.   2*5861*47309 + 4082536917 = 5*927418603
372.   2*5861*47309 + 4086951237 = 5*928301467
373.   2*5861*47309 + 4096285137 = 5*930168247
374.   2*5861*47309 + 4098713625 = 48623*95701
375.   2*5861*47309 + 4105968237 = 5*932104867
376.   2*5861*47309 + 4158629307 = 5*942637081
377.   2*5861*47309 + 4158962307 = 5*942703681
378.   2*5861*47309 + 4160985237 = 5*943108267
379.   2*5861*47309 + 4172905683 = 7*109^2*56843
380.   2*5861*47309 + 4210367859 = 59*80761423
381.   2*5861*47309 + 4216895703 = 9203*518467
382.   2*5861*47309 + 4256098137 = 5*962130847
383.   2*5861*47309 + 4263985107 = 5*963708241
384.   2*5861*47309 + 4280956317 = 5*967102483
385.   2*5861*47309 + 4281635907 = 5*967238401
386.   2*5861*47309 + 4281965307 = 5*967304281
387.   2*5861*47309 + 4286059137 = 5*968123047
388.   2*5861*47309 + 4286159037 = 5*968143027
389.   2*5861*47309 + 4286950137 = 5*968301247
390.   2*5861*47309 + 4293761085 = 9643*502781
391.   2*5861*47309 + 4298561307 = 5*970623481
392.   2*5861*47309 + 4316598207 = 5*974230861
393.   2*5861*47309 + 4316859207 = 5*974283061
394.   2*5861*47309 + 4326850917 = 5*976281403
395.   2*5861*47309 + 4326958107 = 5*976302841
396.   2*5861*47309 + 4358962107 = 5*982703641
397.   2*5861*47309 + 4361825907 = 5*983276401
398.   2*5861*47309 + 4365982017 = 5*984107623
399.   2*5861*47309 + 4368952017 = 5*984701623
400.   2*5861*47309 + 4381625907 = 5*987236401
401.   2*5861*47309 + 4381965207 = 5*987304261
402.   2*5861*47309 + 4382561907 = 5*987423601
403.   2*5861*47309 + 4582693017 = 5*103^2*96847
404.   2*5861*47309 + 4620378591 = 859*6024371
405.   2*5861*47309 + 4816072395 = 6547*820319
406.   2*5861*47309 + 4832795061 = 6359*847201
407.   2*5861*47309 + 4837125609 = 6719*802453
408.   2*5861*47309 + 4965218073 = 563*9804217
409.   2*5861*47309 + 5173428069 = 67*85492301
410.   2*5861*47309 + 5218046739 = 859*6720143
411.   2*5861*47309 + 5703416829 = 67*93402581
412.   2*5861*47309 + 5762408319 = 67*94283051
413.   2*5861*47309 + 6230871945 = 79601*85243
414.   2*5861*47309 + 7023568149 = 941*8053267

Next I calculated a table of all possible PFIs that result from the subtraction of pandigital numbers from a given PFI:

This graph shows (again) the number of solutions for the smallest 431285 PFIs. The largest number of solutions is 575 for PFI #301365, which is 8283333125 or 5^4*1609*8237:

  1.   5^4*1609*8237 - 8197423605 = 2^4*5*1073869

  2.   5^4*1609*8237 - 8137426590 = 5*2789*10463

  3.   5^4*1609*8237 - 8136720459 = 2*4637*15809

  4.   5^4*1609*8237 - 8127509346 = 59*107*24683

  5.   5^4*1609*8237 - 8124903765 = 2^4*5*1980367

  6.   5^4*1609*8237 - 8109472635 = 2*5*17386049

  7.   5^4*1609*8237 - 8109264735 = 2*5*17406839

  8.   5^4*1609*8237 - 8104723695 = 2*5*17860943

  9.   5^4*1609*8237 - 8103724695 = 2*5*17960843

 10.   5^4*1609*8237 - 8103624759 = 2*167*538049

 11.   5^4*1609*8237 - 8096254731 = 2*173*540689

 12.   5^4*1609*8237 - 8057142936 = 83*107*25469

 13.   5^4*1609*8237 - 8051964723 = 2*17*6804953

 14.   5^4*1609*8237 - 8026579431 = 2*83*1546709

 15.   5^4*1609*8237 - 8025471639 = 2*149*865307

 16.   5^4*1609*8237 - 7980651324 = 283*1069547

 17.   5^4*1609*8237 - 7962401358 = 13*24687059

 18.   5^4*1609*8237 - 7946052183 = 2*197*856043

 19.   5^4*1609*8237 - 7942506183 = 2*197*865043

 20.   5^4*1609*8237 - 7934502186 = 17*2543*8069

 21.   5^4*1609*8237 - 7920348156 = 17*53*402869

 22.   5^4*1609*8237 - 7916084532 = 14639*25087

 23.   5^4*1609*8237 - 7908426315 = 2*5*37490681

 24.   5^4*1609*8237 - 7902861435 = 2*5*38047169

 25.   5^4*1609*8237 - 7901628435 = 2*5*38170469

 26.   5^4*1609*8237 - 7895130462 = 149*2605387

 27.   5^4*1609*8237 - 7865043219 = 2*5417*38609

 28.   5^4*1609*8237 - 7861930524 = 157*2684093

 29.   5^4*1609*8237 - 7854312096 = 47*89*102563

 30.   5^4*1609*8237 - 7845629310 = 5*29*3018647

 31.   5^4*1609*8237 - 7829051364 = 2903*156487

 32.   5^4*1609*8237 - 7821946035 = 2*5*46138709

 33.   5^4*1609*8237 - 7819462035 = 2*5*46387109

 34.   5^4*1609*8237 - 7815649320 = 5*1487*62903

 35.   5^4*1609*8237 - 7813256940 = 5*23*4087619

 36.   5^4*1609*8237 - 7809642315 = 2*5*47369081

 37.   5^4*1609*8237 - 7804316295 = 2*5*47901683

 38.   5^4*1609*8237 - 7804269315 = 2*5*47906381

 39.   5^4*1609*8237 - 7802963415 = 2*5*48036971

 40.   5^4*1609*8237 - 7802693415 = 2*5*48063971

 41.   5^4*1609*8237 - 7802619435 = 2*5*48071369

 42.   5^4*1609*8237 - 7802613495 = 2*5*48071963

 43.   5^4*1609*8237 - 7802396415 = 2*5*48093671

 44.   5^4*1609*8237 - 7802369415 = 2*5*48096371

 45.   5^4*1609*8237 - 7801426395 = 2*5*48190673

 46.   5^4*1609*8237 - 7801362495 = 2*5*48197063

 47.   5^4*1609*8237 - 7692381045 = 2^4*5*7386901

 48.   5^4*1609*8237 - 7659428310 = 5*124780963

 49.   5^4*1609*8237 - 7652941380 = 5*126078349

 50.   5^4*1609*8237 - 7652843910 = 5*126097843

 51.   5^4*1609*8237 - 7645931280 = 5*127480369

 52.   5^4*1609*8237 - 7645928310 = 5*127480963

 53.   5^4*1609*8237 - 7645283910 = 5*127609843

 54.   5^4*1609*8237 - 7643528910 = 5*127960843

 55.   5^4*1609*8237 - 7643158290 = 5*128034967

 56.   5^4*1609*8237 - 7642958310 = 5*128074963

 57.   5^4*1609*8237 - 7638512940 = 5*128964037

 58.   5^4*1609*8237 - 7625941380 = 5*41*3206789

 59.   5^4*1609*8237 - 7618492053 = 2^4*7*5936081

 60.   5^4*1609*8237 - 7614852930 = 5*41*3260879

 61.   5^4*1609*8237 - 7614502983 = 2*6803*49157

 62.   5^4*1609*8237 - 7612953840 = 5*461*290837

 63.   5^4*1609*8237 - 7610289354 = 157*4286903

 64.   5^4*1609*8237 - 7609428315 = 2*5*67390481

 65.   5^4*1609*8237 - 7604392815 = 2*5*67894031

 66.   5^4*1609*8237 - 7604298315 = 2*5*67903481

 67.   5^4*1609*8237 - 7602841395 = 2*5*68049173

 68.   5^4*1609*8237 - 7596403128 = 13*52840769

 69.   5^4*1609*8237 - 7596314280 = 5*29*4738061

 70.   5^4*1609*8237 - 7596314208 = 13*52847609

 71.   5^4*1609*8237 - 7594012368 = 479*503*2861

 72.   5^4*1609*8237 - 7593684120 = 5*683*201947

 73.   5^4*1609*8237 - 7589361240 = 5*29*4786013

 74.   5^4*1609*8237 - 7584901632 = 139*5024687

 75.   5^4*1609*8237 - 7583190246 = 47*53*281069

 76.   5^4*1609*8237 - 7582139640 = 5*140238697

 77.   5^4*1609*8237 - 7569342810 = 5*142798063

 78.   5^4*1609*8237 - 7569314280 = 5*142803769

 79.   5^4*1609*8237 - 7562304981 = 2^4*59*763801

 80.   5^4*1609*8237 - 7548069312 = 157*4683209

 81.   5^4*1609*8237 - 7546928310 = 5*147280963

 82.   5^4*1609*8237 - 7542968310 = 5*148072963

 83.   5^4*1609*8237 - 7542936810 = 5*148079263

 84.   5^4*1609*8237 - 7542608391 = 2*587*630941

 85.   5^4*1609*8237 - 7542139608 = 1823*406579

 86.   5^4*1609*8237 - 7541963028 = 13*57028469

 87.   5^4*1609*8237 - 7541386902 = 18257*40639

 88.   5^4*1609*8237 - 7538214690 = 5*149023687

 89.   5^4*1609*8237 - 7534692810 = 5*149728063

 90.   5^4*1609*8237 - 7534296810 = 5*149807263

 91.   5^4*1609*8237 - 7531409628 = 13*57840269

 92.   5^4*1609*8237 - 7519408263 = 2*83*4601957

 93.   5^4*1609*8237 - 7518034296 = 31*24687059

 94.   5^4*1609*8237 - 7509463128 = 6053*127849

 95.   5^4*1609*8237 - 7496513820 = 5*23*6841907

 96.   5^4*1609*8237 - 7490286315 = 2*5*79304681

 97.   5^4*1609*8237 - 7490268315 = 2*5*79306481

 98.   5^4*1609*8237 - 7469280351 = 2*587*693401

 99.   5^4*1609*8237 - 7465932810 = 5*239*684017

100.   5^4*1609*8237 - 7462938510 = 5*164078923

101.   5^4*1609*8237 - 7462153890 = 5*23*7140689

102.   5^4*1609*8237 - 7438621590 = 5*168942307

103.   5^4*1609*8237 - 7436815092 = 29*857*34061

104.   5^4*1609*8237 - 7435916820 = 5*83*2041967

105.   5^4*1609*8237 - 7432159680 = 5*170234689

106.   5^4*1609*8237 - 7421836095 = 2*5*86149703

107.   5^4*1609*8237 - 7419862035 = 2*5*86347109

108.   5^4*1609*8237 - 7419825630 = 5*2069*83471

109.   5^4*1609*8237 - 7412935860 = 5*2069*84137

110.   5^4*1609*8237 - 7409623158 = 13*67208459

111.   5^4*1609*8237 - 7409563182 = 347*2518069

112.   5^4*1609*8237 - 7409263815 = 2*5*87406931

113.   5^4*1609*8237 - 7406392815 = 2*5*87694031

114.   5^4*1609*8237 - 7406135982 = 47*569*32801

115.   5^4*1609*8237 - 7403926815 = 2*5*87940631

116.   5^4*1609*8237 - 7403851926 = 23*59*648107

117.   5^4*1609*8237 - 7392615408 = 8429*105673

118.   5^4*1609*8237 - 7391504862 = 167*5340289

119.   5^4*1609*8237 - 7369251408 = 31*29486507

120.   5^4*1609*8237 - 7368512940 = 5*182964037

121.   5^4*1609*8237 - 7365129480 = 5*183640729

122.   5^4*1609*8237 - 7362951480 = 5*184076329

123.   5^4*1609*8237 - 7362851490 = 5*184096327

124.   5^4*1609*8237 - 7362149580 = 5*184236709

125.   5^4*1609*8237 - 7362148590 = 5*184236907

126.   5^4*1609*8237 - 7361852940 = 5*184296037

127.   5^4*1609*8237 - 7361528490 = 5*184360927

128.   5^4*1609*8237 - 7358204196 = 269*857*4013

129.   5^4*1609*8237 - 7352869410 = 5*186092743

130.   5^4*1609*8237 - 7352861490 = 5*186094327

131.   5^4*1609*8237 - 7352846910 = 5*186097243

132.   5^4*1609*8237 - 7351462980 = 5*186374029

133.   5^4*1609*8237 - 7348629510 = 5*186940723

134.   5^4*1609*8237 - 7346051982 = 1607*583249

135.   5^4*1609*8237 - 7345890126 = 3461*270859

136.   5^4*1609*8237 - 7345286910 = 5*187609243

137.   5^4*1609*8237 - 7340895162 = 149*6325087

138.   5^4*1609*8237 - 7309681542 = 167*5830249

139.   5^4*1609*8237 - 7304692815 = 2*5*97864031

140.   5^4*1609*8237 - 7268059134 = 193*5260487

141.   5^4*1609*8237 - 7235910468 = 1453*720869

142.   5^4*1609*8237 - 7231598640 = 5*210346897

143.   5^4*1609*8237 - 7231485690 = 5*210369487

144.   5^4*1609*8237 - 7213945860 = 5*6287*34019

145.   5^4*1609*8237 - 7198235460 = 5*293*740681

146.   5^4*1609*8237 - 7194835206 = 29*647*58013

147.   5^4*1609*8237 - 7190645238 = 23*47508169

148.   5^4*1609*8237 - 7190354628 = 13*84075269

149.   5^4*1609*8237 - 7162089534 = 13*86249507

150.   5^4*1609*8237 - 7132495680 = 5*230167489

151.   5^4*1609*8237 - 7132459680 = 5*230174689

152.   5^4*1609*8237 - 7123904658 = 269*743*5801

153.   5^4*1609*8237 - 7096584312 = 41*359*80627

154.   5^4*1609*8237 - 7065149328 = 59*20647183

155.   5^4*1609*8237 - 7058439612 = 59*3041*6827

156.   5^4*1609*8237 - 7051942863 = 2*683*901457

157.   5^4*1609*8237 - 7039216854 = 1543*806297

158.   5^4*1609*8237 - 7032691584 = 19^2*43*80567

159.   5^4*1609*8237 - 7028951364 = 643*1950827

160.   5^4*1609*8237 - 7015429368 = 859*1476023

161.   5^4*1609*8237 - 6982415730 = 5*260183479

162.   5^4*1609*8237 - 6981345720 = 5*260397481

163.   5^4*1609*8237 - 6975301482 = 23*56870941

164.   5^4*1609*8237 - 6948135720 = 5*267039481

165.   5^4*1609*8237 - 6943825710 = 5*267901483

166.   5^4*1609*8237 - 6943815720 = 5*267903481

167.   5^4*1609*8237 - 6934815720 = 5*269703481

168.   5^4*1609*8237 - 6931485720 = 5*270369481

169.   5^4*1609*8237 - 6930258471 = 2*89*7601543

170.   5^4*1609*8237 - 6921570384 = 1697*802453

171.   5^4*1609*8237 - 6915327048 = 5683*240719

172.   5^4*1609*8237 - 6914325780 = 5*89*3076421

173.   5^4*1609*8237 - 6879512430 = 5*280764139

174.   5^4*1609*8237 - 6879352410 = 5*280796143

175.   5^4*1609*8237 - 6875293410 = 5*281607943

176.   5^4*1609*8237 - 6874352910 = 5*281796043

177.   5^4*1609*8237 - 6873529410 = 5*281960743

178.   5^4*1609*8237 - 6873512940 = 5*281964037

179.   5^4*1609*8237 - 6859307124 = 293*4860157

180.   5^4*1609*8237 - 6852379410 = 5*286190743

181.   5^4*1609*8237 - 6851293470 = 5*286407931

182.   5^4*1609*8237 - 6851279430 = 5*286410739

183.   5^4*1609*8237 - 6849153270 = 5*47*6102893

184.   5^4*1609*8237 - 6847352910 = 5*287196043

185.   5^4*1609*8237 - 6845237910 = 5*287619043

186.   5^4*1609*8237 - 6843752910 = 5*287916043

187.   5^4*1609*8237 - 6843527910 = 5*287961043

188.   5^4*1609*8237 - 6843512970 = 5*287964031

189.   5^4*1609*8237 - 6842395710 = 5*41*7028963

190.   5^4*1609*8237 - 6841973052 = 89*647*25031

191.   5^4*1609*8237 - 6837512940 = 5*289164037

192.   5^4*1609*8237 - 6835279410 = 5*289610743

193.   5^4*1609*8237 - 6831425790 = 5*290381467

194.   5^4*1609*8237 - 6814325790 = 5*293801467

195.   5^4*1609*8237 - 6813947502 = 239*6148057

196.   5^4*1609*8237 - 6794315820 = 5*297803461

197.   5^4*1609*8237 - 6790431852 = 23*64908751

198.   5^4*1609*8237 - 6780324159 = 2*983*764501

199.   5^4*1609*8237 - 6759341820 = 5*304798261

200.   5^4*1609*8237 - 6758419320 = 5*304982761

201.   5^4*1609*8237 - 6751924380 = 5*306281749

202.   5^4*1609*8237 - 6751243980 = 5*306417829

203.   5^4*1609*8237 - 6743591820 = 5*307948261

204.   5^4*1609*8237 - 6739518420 = 5*308762941

205.   5^4*1609*8237 - 6738519420 = 5*308962741

206.   5^4*1609*8237 - 6738512490 = 5*308964127

207.   5^4*1609*8237 - 6735941820 = 5*309478261

208.   5^4*1609*8237 - 6735241890 = 5*309618247

209.   5^4*1609*8237 - 6715340928 = 4801*326597

210.   5^4*1609*8237 - 6708314952 = 23*68479051

211.   5^4*1609*8237 - 6582419730 = 5*340182679

212.   5^4*1609*8237 - 6579418320 = 5*340782961

213.   5^4*1609*8237 - 6579341820 = 5*340798261

214.   5^4*1609*8237 - 6549318270 = 5*346802971

215.   5^4*1609*8237 - 6549281730 = 5*346810279

216.   5^4*1609*8237 - 6548937120 = 5*346879201

217.   5^4*1609*8237 - 6547918320 = 5*347082961

218.   5^4*1609*8237 - 6543187290 = 5*348029167

219.   5^4*1609*8237 - 6542819730 = 5*348102679

220.   5^4*1609*8237 - 6539847120 = 5*348697201

221.   5^4*1609*8237 - 6539142870 = 5*4013*86927

222.   5^4*1609*8237 - 6538194720 = 5*349027681

223.   5^4*1609*8237 - 6514723890 = 5*83*4261709

224.   5^4*1609*8237 - 6482591730 = 5*360148279

225.   5^4*1609*8237 - 6481925730 = 5*360281479

226.   5^4*1609*8237 - 6473981052 = 859*2106347

227.   5^4*1609*8237 - 6439587120 = 5*368749201

228.   5^4*1609*8237 - 6439527108 = 23*80165479

229.   5^4*1609*8237 - 6438712590 = 5*368924107

230.   5^4*1609*8237 - 6431985720 = 5*370269481

231.   5^4*1609*8237 - 6429130875 = 2*5^3*7416809

232.   5^4*1609*8237 - 6412930875 = 2*5^3*7481609

233.   5^4*1609*8237 - 6379512480 = 5*380764129

234.   5^4*1609*8237 - 6379485210 = 5*41*9287063

235.   5^4*1609*8237 - 6378512490 = 5*380964127

236.   5^4*1609*8237 - 6378451920 = 5*380976241

237.   5^4*1609*8237 - 6378102594 = 2083*914657

238.   5^4*1609*8237 - 6374512980 = 5*381764029

239.   5^4*1609*8237 - 6371549028 = 67*28534091

240.   5^4*1609*8237 - 6371485290 = 5*41*9326087

241.   5^4*1609*8237 - 6371249580 = 5*382416709

242.   5^4*1609*8237 - 6359487120 = 5*384769201

243.   5^4*1609*8237 - 6358419072 = 653*2947801

244.   5^4*1609*8237 - 6351297480 = 5*386407129

245.   5^4*1609*8237 - 6351279480 = 5*386410729

246.   5^4*1609*8237 - 6351247980 = 5*386417029

247.   5^4*1609*8237 - 6351079248 = 503*821*4679

248.   5^4*1609*8237 - 6349107852 = 23*84096751

249.   5^4*1609*8237 - 6348712590 = 5*386924107

250.   5^4*1609*8237 - 6348597120 = 5*386947201

251.   5^4*1609*8237 - 6347891250 = 5^4*29*106783

252.   5^4*1609*8237 - 6345187920 = 5*387629041

253.   5^4*1609*8237 - 6345019278 = 3407*568921

254.   5^4*1609*8237 - 6342157908 = 41*6029*7853

255.   5^4*1609*8237 - 6312805974 = 67*29410853

256.   5^4*1609*8237 - 6310759482 = 5107*386249

257.   5^4*1609*8237 - 6274839510 = 5*401698723

258.   5^4*1609*8237 - 6274513980 = 5*401763829

259.   5^4*1609*8237 - 6273849510 = 5*401896723

260.   5^4*1609*8237 - 6251897430 = 5*406287139

261.   5^4*1609*8237 - 6247518930 = 5*407162839

262.   5^4*1609*8237 - 6247513980 = 5*407163829

263.   5^4*1609*8237 - 6243851970 = 5*407896231

264.   5^4*1609*8237 - 6243518970 = 5*407962831

265.   5^4*1609*8237 - 6239847510 = 5*408697123

266.   5^4*1609*8237 - 6239517480 = 5*408763129

267.   5^4*1609*8237 - 6238751940 = 5*408916237

268.   5^4*1609*8237 - 6238451970 = 5*408976231

269.   5^4*1609*8237 - 6237518940 = 5*409162837

270.   5^4*1609*8237 - 6235189470 = 5*409628731

271.   5^4*1609*8237 - 6234897510 = 5*409687123

272.   5^4*1609*8237 - 6234518970 = 5*409762831

273.   5^4*1609*8237 - 6190485372 = 25943*80671

274.   5^4*1609*8237 - 6189075324 = 23*91054687

275.   5^4*1609*8237 - 6173852940 = 5*421896037

276.   5^4*1609*8237 - 6170845932 = 26357*80149

277.   5^4*1609*8237 - 6152938470 = 5*426078931

278.   5^4*1609*8237 - 6152897430 = 5*426087139

279.   5^4*1609*8237 - 6152478930 = 5*426170839

280.   5^4*1609*8237 - 6145789302 = 607*3521489

281.   5^4*1609*8237 - 6143852970 = 5*427896031

282.   5^4*1609*8237 - 6138529470 = 5*428960731

283.   5^4*1609*8237 - 6138527940 = 5*428961037

284.   5^4*1609*8237 - 6135289470 = 5*429608731

285.   5^4*1609*8237 - 6105789342 = 283*7694501

286.   5^4*1609*8237 - 6048291375 = 2*5^3*8940167

287.   5^4*1609*8237 - 6025973814 = 23*98146057

288.   5^4*1609*8237 - 5982641730 = 5*460138279

289.   5^4*1609*8237 - 5982341760 = 5*460198273

290.   5^4*1609*8237 - 5981436720 = 5*460379281

291.   5^4*1609*8237 - 5980136742 = 409*5631287

292.   5^4*1609*8237 - 5974318260 = 5*461802973

293.   5^4*1609*8237 - 5973412068 = 5297*436081

294.   5^4*1609*8237 - 5973246180 = 5*462017389

295.   5^4*1609*8237 - 5967324180 = 5*463201789

296.   5^4*1609*8237 - 5948236710 = 5*467019283

297.   5^4*1609*8237 - 5948136720 = 5*467039281

298.   5^4*1609*8237 - 5947138620 = 5*467238901

299.   5^4*1609*8237 - 5947021638 = 41*56983207

300.   5^4*1609*8237 - 5943871620 = 5*467892301

301.   5^4*1609*8237 - 5943867120 = 5*467893201

302.   5^4*1609*8237 - 5942381760 = 5*468190273

303.   5^4*1609*8237 - 5938467120 = 5*468973201

304.   5^4*1609*8237 - 5937106428 = 26347*89051

305.   5^4*1609*8237 - 5934826710 = 5*469701283

306.   5^4*1609*8237 - 5934281760 = 5*469810273

307.   5^4*1609*8237 - 5932416780 = 5*470183269

308.   5^4*1609*8237 - 5931486720 = 5*470369281

309.   5^4*1609*8237 - 5921743680 = 5*6029*78341

310.   5^4*1609*8237 - 5917324680 = 5*473201689

311.   5^4*1609*8237 - 5901367482 = 41*58096723

312.   5^4*1609*8237 - 5893214670 = 5*478023691

313.   5^4*1609*8237 - 5879604132 = 571*4209683

314.   5^4*1609*8237 - 5871493620 = 5*482367901

315.   5^4*1609*8237 - 5837249610 = 5*489216703

316.   5^4*1609*8237 - 5837149620 = 5*489236701

317.   5^4*1609*8237 - 5832714690 = 5*490123687

318.   5^4*1609*8237 - 5832694710 = 5*490127683

319.   5^4*1609*8237 - 5831496720 = 5*490367281

320.   5^4*1609*8237 - 5831426790 = 5*490381267

321.   5^4*1609*8237 - 5794326810 = 5*497801263

322.   5^4*1609*8237 - 5793460812 = 41*60728593

323.   5^4*1609*8237 - 5793146820 = 5*498037261

324.   5^4*1609*8237 - 5781493602 = 941*2658703

325.   5^4*1609*8237 - 5742983160 = 5*6317*80429

326.   5^4*1609*8237 - 5742193086 = 43609*58271

327.   5^4*1609*8237 - 5679430218 = 41*63509827

328.   5^4*1609*8237 - 5670498312 = 8527*306419

329.   5^4*1609*8237 - 5609184372 = 31^2*457*6089

330.   5^4*1609*8237 - 5493170826 = 41*68052739

331.   5^4*1609*8237 - 5398760142 = 35149*82067

332.   5^4*1609*8237 - 5391608742 = 41*70529863

333.   5^4*1609*8237 - 5370218946 = 8501*342679

334.   5^4*1609*8237 - 5301948762 = 4271*698053

335.   5^4*1609*8237 - 5276183940 = 5*601429837

336.   5^4*1609*8237 - 5276139480 = 5*601438729

337.   5^4*1609*8237 - 5274691380 = 5*601728349

338.   5^4*1609*8237 - 5274613980 = 5*601743829

339.   5^4*1609*8237 - 5273869410 = 5*601892743

340.   5^4*1609*8237 - 5273468910 = 5*601972843

341.   5^4*1609*8237 - 5267418390 = 5*603182947

342.   5^4*1609*8237 - 5264197380 = 5*603827149

343.   5^4*1609*8237 - 5264187390 = 5*603829147

344.   5^4*1609*8237 - 5263741890 = 5*603918247

345.   5^4*1609*8237 - 5247618930 = 5*607142839

346.   5^4*1609*8237 - 5247386910 = 5*607189243

347.   5^4*1609*8237 - 5247368910 = 5*607192843

348.   5^4*1609*8237 - 5246873910 = 5*607291843

349.   5^4*1609*8237 - 5239618470 = 5*608742931

350.   5^4*1609*8237 - 5238619470 = 5*608942731

351.   5^4*1609*8237 - 5237641890 = 5*609138247

352.   5^4*1609*8237 - 5237468910 = 5*609172843

353.   5^4*1609*8237 - 5236741890 = 5*609318247

354.   5^4*1609*8237 - 5234790618 = 3541*860927

355.   5^4*1609*8237 - 5230476918 = 419*7286053

356.   5^4*1609*8237 - 5219734680 = 5*821*746309

357.   5^4*1609*8237 - 5198607342 = 401*7692583

358.   5^4*1609*8237 - 5179642380 = 5*620738149

359.   5^4*1609*8237 - 5178936420 = 5*620879341

360.   5^4*1609*8237 - 5178642390 = 5*620938147

361.   5^4*1609*8237 - 5173862940 = 5*621894037

362.   5^4*1609*8237 - 5167843920 = 5*623097841

363.   5^4*1609*8237 - 5167839420 = 5*623098741

364.   5^4*1609*8237 - 5164278390 = 5*623810947

365.   5^4*1609*8237 - 5163978420 = 5*623870941

366.   5^4*1609*8237 - 5163948072 = 4793*650821

367.   5^4*1609*8237 - 5163742890 = 5*623918047

368.   5^4*1609*8237 - 5162873940 = 5*624091837

369.   5^4*1609*8237 - 5162839470 = 5*624098731

370.   5^4*1609*8237 - 5162378940 = 5*624190837

371.   5^4*1609*8237 - 5146783920 = 5*627309841

372.   5^4*1609*8237 - 5143867920 = 5*627893041

373.   5^4*1609*8237 - 5142976380 = 5*628071349

374.   5^4*1609*8237 - 5142796380 = 5*628107349

375.   5^4*1609*8237 - 5138796420 = 5*628907341

376.   5^4*1609*8237 - 5138679420 = 5*628930741

377.   5^4*1609*8237 - 5138629470 = 5*628940731

378.   5^4*1609*8237 - 5136742890 = 5*629318047

379.   5^4*1609*8237 - 5136427890 = 5*629381047

380.   5^4*1609*8237 - 5134628970 = 5*629740831

381.   5^4*1609*8237 - 5127890364 = 607*5198423

382.   5^4*1609*8237 - 5063984712 = 41*78520693

383.   5^4*1609*8237 - 4968750132 = 401*8265793

384.   5^4*1609*8237 - 4932175680 = 5*670231489

385.   5^4*1609*8237 - 4907281356 = 4621*730589

386.   5^4*1609*8237 - 4895213706 = 41*82637059

387.   5^4*1609*8237 - 4879621530 = 5*680742319

388.   5^4*1609*8237 - 4879362510 = 5*680794123

389.   5^4*1609*8237 - 4873621590 = 5*681942307

390.   5^4*1609*8237 - 4872593610 = 5*682147903

391.   5^4*1609*8237 - 4863579012 = 409*8361257

392.   5^4*1609*8237 - 4862713590 = 5*684123907

393.   5^4*1609*8237 - 4862379510 = 5*684190723

394.   5^4*1609*8237 - 4861723590 = 5*684321907

395.   5^4*1609*8237 - 4859637120 = 5*684739201

396.   5^4*1609*8237 - 4859372610 = 5*684792103

397.   5^4*1609*8237 - 4837629510 = 5*689140723

398.   5^4*1609*8237 - 4837261590 = 5*689214307

399.   5^4*1609*8237 - 4837162590 = 5*689234107

400.   5^4*1609*8237 - 4837126590 = 5*689241307

401.   5^4*1609*8237 - 4836297510 = 5*689407123

402.   5^4*1609*8237 - 4836271590 = 5*689412307

403.   5^4*1609*8237 - 4832695710 = 5*690127483

404.   5^4*1609*8237 - 4832591760 = 5*690148273

405.   5^4*1609*8237 - 4831695720 = 5*690327481

406.   5^4*1609*8237 - 4769152380 = 5*702836149

407.   5^4*1609*8237 - 4768513920 = 5*702963841

408.   5^4*1609*8237 - 4765183920 = 5*703629841

409.   5^4*1609*8237 - 4762518930 = 5*704162839

410.   5^4*1609*8237 - 4761523980 = 5*704361829

411.   5^4*1609*8237 - 4759236810 = 5*704819263

412.   5^4*1609*8237 - 4758692310 = 5*704928163

413.   5^4*1609*8237 - 4758691320 = 5*704928361

414.   5^4*1609*8237 - 4752613980 = 5*706143829

415.   5^4*1609*8237 - 4752386910 = 5*706189243

416.   5^4*1609*8237 - 4751926380 = 5*706281349

417.   5^4*1609*8237 - 4751623980 = 5*706341829

418.   5^4*1609*8237 - 4739861520 = 5*708694321

419.   5^4*1609*8237 - 4735980612 = 41*86520793

420.   5^4*1609*8237 - 4735926810 = 5*709481263

421.   5^4*1609*8237 - 4735268910 = 5*709612843

422.   5^4*1609*8237 - 4735168920 = 5*709632841

423.   5^4*1609*8237 - 4732159680 = 5*710234689

424.   5^4*1609*8237 - 4681359720 = 5*720394681

425.   5^4*1609*8237 - 4659237810 = 5*724819063

426.   5^4*1609*8237 - 4658791320 = 5*724908361

427.   5^4*1609*8237 - 4652873910 = 5*726091843

428.   5^4*1609*8237 - 4652791380 = 5*726108349

429.   5^4*1609*8237 - 4652783910 = 5*726109843

430.   5^4*1609*8237 - 4651783920 = 5*726309841

431.   5^4*1609*8237 - 4638527910 = 5*728961043

432.   5^4*1609*8237 - 4638517920 = 5*728963041

433.   5^4*1609*8237 - 4638259710 = 5*729014683

434.   5^4*1609*8237 - 4637528910 = 5*729160843

435.   5^4*1609*8237 - 4635917820 = 5*729483061

436.   5^4*1609*8237 - 4635178920 = 5*729630841

437.   5^4*1609*8237 - 4631970582 = 41*89057623

438.   5^4*1609*8237 - 4619325780 = 5*732801469

439.   5^4*1609*8237 - 4610937582 = 41*89570623

440.   5^4*1609*8237 - 4607395182 = 41*89657023

441.   5^4*1609*8237 - 4586319720 = 5*739402681

442.   5^4*1609*8237 - 4582139670 = 5*740238691

443.   5^4*1609*8237 - 4579136820 = 5*740839261

444.   5^4*1609*8237 - 4569317280 = 5*742803169

445.   5^4*1609*8237 - 4539867120 = 5*748693201

446.   5^4*1609*8237 - 4538269710 = 5*749012683

447.   5^4*1609*8237 - 4537916820 = 5*749083261

448.   5^4*1609*8237 - 4536819720 = 5*749302681

449.   5^4*1609*8237 - 4509368712 = 4073*926581

450.   5^4*1609*8237 - 4506893712 = 743*5082691

451.   5^4*1609*8237 - 4395126078 = 67*58032941

452.   5^4*1609*8237 - 4387615290 = 5*9467*82301

453.   5^4*1609*8237 - 4381657920 = 5*83*9401627

454.   5^4*1609*8237 - 4376512980 = 5*781364029

455.   5^4*1609*8237 - 4371298560 = 5*782406913

456.   5^4*1609*8237 - 4368527910 = 5*782961043

457.   5^4*1609*8237 - 4368512970 = 5*782964031

458.   5^4*1609*8237 - 4367851920 = 5*783096241

459.   5^4*1609*8237 - 4367512980 = 5*783164029

460.   5^4*1609*8237 - 4365127980 = 5*783641029

461.   5^4*1609*8237 - 4361852970 = 5*784296031

462.   5^4*1609*8237 - 4361798520 = 5*784306921

463.   5^4*1609*8237 - 4361527980 = 5*784361029

464.   5^4*1609*8237 - 4359871620 = 5*784692301

465.   5^4*1609*8237 - 4359867120 = 5*784693201

466.   5^4*1609*8237 - 4351867920 = 5*786293041

467.   5^4*1609*8237 - 4351627980 = 5*786341029

468.   5^4*1609*8237 - 4351267980 = 5*786413029

469.   5^4*1609*8237 - 4302167598 = 67*59420381

470.   5^4*1609*8237 - 4301952768 = 59*67481023

471.   5^4*1609*8237 - 4276958310 = 5*801274963

472.   5^4*1609*8237 - 4276503918 = 67*59803421

473.   5^4*1609*8237 - 4268751390 = 5*802916347

474.   5^4*1609*8237 - 4267519380 = 5*803162749

475.   5^4*1609*8237 - 4259736810 = 5*804719263

476.   5^4*1609*8237 - 4258697310 = 5*804927163

477.   5^4*1609*8237 - 4251736890 = 5*806319247

478.   5^4*1609*8237 - 4237596810 = 5*809147263

479.   5^4*1609*8237 - 4235976810 = 5*809471263

480.   5^4*1609*8237 - 4231865790 = 5*810293467

481.   5^4*1609*8237 - 4182359760 = 5*820194673

482.   5^4*1609*8237 - 4178659320 = 5*820934761

483.   5^4*1609*8237 - 4173658092 = 8923*460571

484.   5^4*1609*8237 - 4168259730 = 5*823014679

485.   5^4*1609*8237 - 4168235790 = 5*823019467

486.   5^4*1609*8237 - 4167958320 = 5*823074961

487.   5^4*1609*8237 - 4167935820 = 5*823079461

488.   5^4*1609*8237 - 4167529380 = 5*823160749

489.   5^4*1609*8237 - 4165237890 = 5*823619047

490.   5^4*1609*8237 - 4159678320 = 5*824730961

491.   5^4*1609*8237 - 4159367820 = 5*824793061

492.   5^4*1609*8237 - 4138265790 = 5*829013467

493.   5^4*1609*8237 - 4135960872 = 51439*80627

494.   5^4*1609*8237 - 4135267890 = 5*829613047

495.   5^4*1609*8237 - 4132695780 = 5*830127469

496.   5^4*1609*8237 - 4132685790 = 5*830129467

497.   5^4*1609*8237 - 4089573162 = 4253*986071

498.   5^4*1609*8237 - 4031296758 = 59*72068413

499.   5^4*1609*8237 - 3976284510 = 5*861409723

500.   5^4*1609*8237 - 3976214580 = 5*861423709

501.   5^4*1609*8237 - 3974628510 = 5*861740923

502.   5^4*1609*8237 - 3972845061 = 2^10*47*89563

503.   5^4*1609*8237 - 3972815640 = 5*862103497

504.   5^4*1609*8237 - 3972584610 = 5*862149703

505.   5^4*1609*8237 - 3971460258 = 509*8471263

506.   5^4*1609*8237 - 3971264580 = 5*862413709

507.   5^4*1609*8237 - 3962714580 = 5*864123709

508.   5^4*1609*8237 - 3961728540 = 5*864320917

509.   5^4*1609*8237 - 3961478520 = 5*864370921

510.   5^4*1609*8237 - 3958472610 = 5*864972103

511.   5^4*1609*8237 - 3958471620 = 5*864972301

512.   5^4*1609*8237 - 3947065218 = 58109*74623

513.   5^4*1609*8237 - 3946712580 = 5*867324109

514.   5^4*1609*8237 - 3946278510 = 5*867410923

515.   5^4*1609*8237 - 3946271580 = 5*867412309

516.   5^4*1609*8237 - 3946172580 = 5*867432109

517.   5^4*1609*8237 - 3945872610 = 5*867492103

518.   5^4*1609*8237 - 3894560712 = 56093*78241

519.   5^4*1609*8237 - 3765189420 = 5*903628741

520.   5^4*1609*8237 - 3764518920 = 5*903762841

521.   5^4*1609*8237 - 3764251890 = 5*903816247

522.   5^4*1609*8237 - 3764195820 = 5*903827461

523.   5^4*1609*8237 - 3761542890 = 5*139^2*46807

524.   5^4*1609*8237 - 3761489520 = 5*904368721

525.   5^4*1609*8237 - 3759426810 = 5*904781263

526.   5^4*1609*8237 - 3752618940 = 5*906142837

527.   5^4*1609*8237 - 3752468910 = 5*906172843

528.   5^4*1609*8237 - 3751896420 = 5*906287341

529.   5^4*1609*8237 - 3751426890 = 5*906381247

530.   5^4*1609*8237 - 3745209861 = 2^10*967*4583

531.   5^4*1609*8237 - 3745168920 = 5*907632841

532.   5^4*1609*8237 - 3742516890 = 5*908163247

533.   5^4*1609*8237 - 3741965820 = 5*908273461

534.   5^4*1609*8237 - 3681459720 = 5*920374681

535.   5^4*1609*8237 - 3679145820 = 5*920837461

536.   5^4*1609*8237 - 3659427810 = 5*924781063

537.   5^4*1609*8237 - 3652897410 = 5*926087143

538.   5^4*1609*8237 - 3651289470 = 5*926408731

539.   5^4*1609*8237 - 3645927810 = 5*927481063

540.   5^4*1609*8237 - 3645917820 = 5*927483061

541.   5^4*1609*8237 - 3645278910 = 5*927610843

542.   5^4*1609*8237 - 3645178920 = 5*927630841

543.   5^4*1609*8237 - 3642795810 = 5*928107463

544.   5^4*1609*8237 - 3641825790 = 5*928301467

545.   5^4*1609*8237 - 3641597820 = 5*928347061

546.   5^4*1609*8237 - 3615270984 = 563*8291407

547.   5^4*1609*8237 - 3582714690 = 5*940123687

548.   5^4*1609*8237 - 3582174690 = 5*940231687

549.   5^4*1609*8237 - 3579426810 = 5*940781263

550.   5^4*1609*8237 - 3578214690 = 5*941023687

551.   5^4*1609*8237 - 3574296810 = 5*941807263

552.   5^4*1609*8237 - 3569814720 = 5*942703681

553.   5^4*1609*8237 - 3569247810 = 5*942817063

554.   5^4*1609*8237 - 3568940172 = 56039*84127

555.   5^4*1609*8237 - 3568194720 = 5*943027681

556.   5^4*1609*8237 - 3548269710 = 5*947012683

557.   5^4*1609*8237 - 3547916820 = 5*947083261

558.   5^4*1609*8237 - 3526790184 = 9203*516847

559.   5^4*1609*8237 - 3519480726 = 59*80743261

560.   5^4*1609*8237 - 3482715690 = 5*960123487

561.   5^4*1609*8237 - 3481965720 = 5*960273481

562.   5^4*1609*8237 - 3465897120 = 5*963487201

563.   5^4*1609*8237 - 3452891076 = 64381*75029

564.   5^4*1609*8237 - 3061789254 = 643*8120597

565.   5^4*1609*8237 - 2976135048 = 653*8127409

566.   5^4*1609*8237 - 2840195736 = 6521*834709

567.   5^4*1609*8237 - 2793156084 = 61547*89203

568.   5^4*1609*8237 - 2793016584 = 67*81945023

569.   5^4*1609*8237 - 2671049358 = 60457*92831

570.   5^4*1609*8237 - 2638570194 = 67*84250193

571.   5^4*1609*8237 - 2481693750 = 5^4*7*1326089

572.   5^4*1609*8237 - 2463971508 = 6907*842531

573.   5^4*1609*8237 - 1987036254 = 9203*684157

574.   5^4*1609*8237 - 1965407382 = 643*9825701

575.   5^4*1609*8237 - 1937854602 = 76541*82903

With the two tables on hand I can now step through my cascades without having to redo the arithmetic over and over again. I can explore tens of thousands cascades instead of just a few hundred. I'm already finding that 48-term cascades may be the largest possible.