primepolydivisible numbers

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Problem

a polydivisible number in a base b is defined as a number n such that the first m digits of n, taken as a number, are divisible by m. see https://en.wikipedia.org/wiki/Polydivisible_number for further properties. one can define a "primepolydivisible number" to have a similar property, where the first m digits of n must be divisible by the mth prime. for each base 3 to 12, print all such "primepolydivisible numbers," sorted by numerical value, expressed in base 10.

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Sample input:_

*NOTHING*

Sample output:

2
6
20

2
9

2
4
12
21
24
60
105
120
301
525
602
1507
2629
3014

2
4
12
15
24
27
75
90
95
145
165
455
574
875
994

2
4
6
15
18
30
33
42
45
48
105
110
130
210
215
235
295
300
315
320
340
735
770
910
1470
1505
1645
2065
2100
2205
2240
2380
5148
5390
10296
10538
11517
15686
16665
36036
72072
504509
3531568

2
4
6
18
21
33
36
39
48
51
54
145
150
170
175
265
270
290
295
315
385
390
410
415
435
1162
1204
1365
1400
1407
2121
2163
2324
2366
2520
2527
3080
3087
3122
3283
3325
3486
9636
10923
16973
18931
20163
20218
24640
24981
26268
77090
87386
135785
151450
161304
161746
199849
210145
616726
699091
1086283
1211607
1290436
1293972
1598799
1681164

2
4
6
8
18
21
24
36
39
42
54
57
60
72
75
78
165
170
190
195
220
325
330
355
380
385
490
515
520
540
545
650
655
675
680
705
710
1491
1533
1715
1757
1981
1988
2926
2933
2975
3199
3423
3465
3472
4410
4417
4641
4683
4865
4907
5852
5901
6076
6083
6125
6349
6391
6398
13420
13805
15818
17831
17897
26334
26400
28798
30811
31185
31251
39754
42152
43791
44165
52668
54692
54747
55132
57145
57519
57585
120783
142363
160485
237601
277303
280670
357786
394121
397488
474019
492232
492726
514306
517673
518271
1087048
1281273
1444371
2138413
2526030
3577395
4434535
4628760
4664443
11531461
12999344
41979987
103783153
116994100
934048385
1052946906

2
4
6
8
21
24
27
42
45
48
60
63
66
69
81
84
87
210
215
240
245
270
275
420
425
450
455
480
485
600
605
630
635
660
665
690
695
810
815
840
845
870
875
2100
2107
2156
2401
2408
2450
2457
2702
2709
2751
2758
4200
4207
4256
4501
4508
4550
4557
4802
4809
4851
4858
6006
6055
6300
6307
6356
6601
6608
6650
6657
6902
6909
6951
6958
8106
8155
8400
8407
8456
8701
8708
8750
8757
21076
21560
24013
24508
24574
27027
27093
27511
27588
42009
42075
45012
45089
45507
45573
48026
48092
48510
48587
60060
60555
63008
63074
63569
66011
66088
66506
66572
69025
69091
69586
81554
84007
84073
84568
87010
87087
87505
87571
210769
215605
240136
245089
270270
270933
275119
275886
420095
420758
450125
450892
455078
480922
485108
485875
600600
605553
630084
630747
660114
660881
665067
690911
695864
815542
840073
840736
845689
870103
870870
875056
875719
2107694
2156059
2401369
2450890
2751195
2758862
4200955
4207585
4508927
4550781
4851086
4858753
6055536
6300846
6307476
6608818
6650672
6958644
8155427
8400737
8407367
8708709
8750563
8757193
21076947
21560592
27588627
42009551
45507812
63008465
66506726
81554270
84007379
84073670
87571931
210769470
630084655
665067264
875719319
6300846559
8757193191

2
4
6
8
10
24
27
30
45
48
51
54
66
69
72
75
90
93
96
111
114
117
120
265
270
300
305
330
335
340
495
500
505
530
535
565
570
595
600
730
735
760
765
795
800
825
830
835
990
995
1000
1025
1030
1060
1065
1225
1230
1255
1260
1290
1295
1320
1325
1330
2919
2975
3304
3360
3633
3640
3689
3745
5446
5453
5502
5509
5558
5565
5831
5838
5887
5894
6216
6223
6272
6279
6545
6552
6601
6608
8036
8085
8092
8365
8421
8750
8806
9079
9135
9191
10892
10899
10948
10955
11004
11277
11284
11333
11340
11662
11669
11718
11725
13475
13482
13531
13538
13811
13860
13867
14196
14245
14252
14525
14581
14630
14637
32109
32725
36344
36960
39963
40040
40579
41195
59906
59983
60522
60599
61138
61215
64141
64218
64757
64834
68376
68453
68992
69069
71995
72072
72611
72688
88396
88935
89012
92015
92631
96250
96866
99869
100485
101101
119812
119889
120428
120505
121044
124047
124124
124663
124740
128282
128359
128898
128975
148225
148302
148841
148918
151921
152460
152537
156156
156695
156772
159775
160391
160930
161007
359983
399789
406562
439595
440440
453154
658970
659815
665743
673374
706407
712335
713180
752141
752986
758914
759759
791947
792792
799578
972361
978289
979134
1012167
1058759
1065532
1098565
1105338
1112111
1317940
1318785
1324713
1325558
1331486
1364519
1365364
1372150
1411111
1411956
1417884
1418729
1631331
1637259
1638104
1671137
1677065
1677910
1717716
1724502
1757535
1764308
1770236
1771081
4397679
4472190
4835548
4844847
7323175
7407121
7770479
7835691
7844990
8273560
8348054
8357353
8795358
10695975
10761187
11133844
11720854
12158723
14497345
14506644
14581138
14646350
15019007
15093654
15522224
15531523
18009851
18019150
18382508
18447720
18457019
19332893
19472599
19481898
48374475
49194097
53191032
80554927
86192607
91009164
91828596
91930892
117655733
118373059
122472290
128929402
133745959
159470800
160392528
161109854
165209085
170744469
198108364
198210660
202207595
202924921
203027217
212661832
214198590
214300886
541135076
1001100806
1347195192
1418223424
1471205557
1764317810
1772208397
1817299943
2180317269
2339280159
2356184492
11012108868
14819147117
15600457664
19407495913
25732081756
171605034308
213482455048

2
4
6
8
10
24
27
30
33
48
51
54
57
72
75
78
81
96
99
102
105
120
123
126
129
290
295
325
330
335
360
365
370
400
405
580
585
615
620
650
655
685
690
695
865
870
875
900
905
910
940
945
975
980
1155
1160
1190
1195
1225
1230
1235
1260
1265
1270
1440
1445
1450
1480
1485
1515
1520
1550
1555
3486
3542
3549
3906
3962
3969
4025
4326
4382
4389
4445
4802
4809
4865
6965
7021
7028
7385
7441
7448
7805
7861
7868
8225
8281
8288
8344
8351
10381
10388
10444
10451
10500
10507
10801
10808
10864
10871
10920
10927
11284
11291
11340
11347
11704
11711
11760
11767
13860
13867
13923
13930
14280
14287
14343
14350
14700
14707
14763
14770
14826
15120
15127
15183
15190
15246
17283
17290
17346
17402
17409
17766
17822
17829
18186
18242
18249
18606
18662
18669
41833
42504
42515
42592
46882
47553
47630
48301
51920
52591
52668
52679
53350
57629
57717
58388
83589
84260
84337
88627
89298
89386
93665
94336
94424
98703
99374
99462
100133
100221
124575
124663
125334
125422
126005
126093
129613
129701
130372
130460
131043
131131
135410
135498
136081
136169
140448
140459
140536
141130
141207
166320
166331
166408
167079
167167
171369
171446
172117
172205
176407
176484
176495
177166
177243
177914
181445
181533
182204
182281
182952
182963
207405
207482
208153
208824
208835
208912
213202
213873
213950
218240
218911
218988
218999
223278
223949
224037
510055
510185
511108
562588
571571
579618
623051
631098
632021
632151
640211
691548
692614
700661
1011127
1012050
1063530
1071577
1072643
1123980
1132040
1133093
1184443
1192490
1201603
1202656
1494909
1495962
1504009
1505075
1512069
1513122
1555359
1556412
1564472
1565525
1572519
1573572
1624922
1632982
1634035
1685385
1685515
1686438
1693562
1694485
1995851
1995981
1996904
2004951
2006004
2056431
2057354
2065414
2066467
2116894
2117817
2117947
2125994
2126917
2134977
2177344
2178397
2186457
2187380
2195427
2195557
2488863
2489786
2497846
2505893
2506023
2506946
2558426
2566486
2567409
2618889
2626936
2627859
2627989
2679339
2687399
2688452
6120663
6122227
6751057
6858854
7476617
7573177
7584261
7682538
8298584
8311368
12133529
12871720
13487766
13597127
14213326
14309886
14419247
14431878
17938910
18048118
18060902
18144831
18664317
18676948
18786309
18870238
18882869
19499068
19608429
20224628
20237259
20322752
23950212
23951776
24059420
24072051
24677183
24688250
24797611
25413810
25415374
25511934
25619731
26128133
26140764
26237494
26248561
26346685
29866365
29877432
29974162
30070722
30072286
30083353
30701116
30808913
31426676
31523236
32248796
32261427
73447958
73466730
81012694
82306252
89719406
91011140
99583009
145602358
170559922
171718637
173030967
215266922
216730834
223971810
226594437
233988819
235301149
242847113
287402550
287421322
288864619
296259001
306143219
307436777
313537601
314849931
314982741
316160228
359689950
360848665
360867437
361000247
368413401
369706959
377120113
386985559
881375502
881600764
972152339
1076632875
1194996119
1747228304
2583203071
2600770011
2719133255
2807865829
2823613791
2914165366
3448830611
3449055873
3555108022
3673718631
3689241331
4316279406
4330183987
4330409249
4332002965
4525441360
12919594511
14339953437
34969984399
41385967338
41388670486
44270895980
51795352879
54305296325
621544234558
7458530814707
89502369776495
1074028437317946
12888341247815361

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