## Searching for Wieferich prime (Fermat quotient) (A3 Mersenne primes. Repunits. Fermat numbers. Primes of shape k.2n+1)

(April 01, 2009)

### A program for UBASIC

``` 10   print=print+"fermat.txt"
20   ' fermat.ub
30   dim T%(999)
40   for I%=2 to 999:T%(I%)=0:next I%
50   for I%=2 to 31:T%(I%^2)=1:next I%
60   for I%=2 to 9:T%(I%^3)=1:next I%
70   for I%=2 to 5:T%(I%^4)=1:next I%
80   T%(3^5)=1:T%(2^5)=1:T%(2^7)=1:T%(2^9)=1
90   J%=0
100   for I%=2 to 999
110     if T%(I%)=0 then inc J%:T%(J%)=I%
120   next I%:' total number is 959
130   ' case p=2
140   for I%=1 to J%
150     if T%(I%)@4=1 then print T%(I%);":";P
160   next I%
170   ' case p>2
180   P=3:N=2^32-5
190   Pm=(P-1)\2:P2=P^2:P2m=P2-1
200     for I%=1 to J%:A=modpow(T%(I%),Pm,P2)
210       if or{A=1,A=P2m} then print T%(I%);":";P
220     next I%
230   if P<N then P=nxtprm(P):goto 190
```

For much larger range, insert the following code

```122   L%=2*3*5*7*11*13:dim Diff%(L%):C%=0:' L=30030
124   for I%=1 to L%-1
126     if gcd(I%,L%)=1 then inc C%:Diff%(C%)=I%
128   next I%:' c%=5760
```

```200   Base=((2^32-5)\L%)*L%:N=10^11
210   for K%=1 to C%:P=Base+Diff%(K%):if prmdiv(P)<>P then 260
220     Pm=P-1:P2=P^2:P2m=P2-1
230     for I%=1 to J%:A=modpow(T%(I%),Pm,P2)
240       if or{A=1,A=P2m} then print T%(I%);":";P
250     next I%
260   next K%
270   Base=Base+L%:if Base<N then 210
```

This program covers up to 10^11.

Wilfrid Keller and Jörg Richstein computed for;

100 < a < 1000,  104 < p < 1011
a < 100,    232 < p

(Wilfrid Keller, Jörg Richstein,
Solutions of the congruence  ap-1≡1 (mod pr),
Mathematics of Computation, 74(2005), 927-936.)

Richard Fischer computed up to 2.311E+12.
For some data, the range reached 1.2E+13.
Current status is uploaded at here (in German). (February 23, 2009).

### Solution

Now the search range of this page is larger than Wilfrid Keller and Jörg Richstein's results.

ap-1- 1≡0  (mod p2), where

a : 2 ≤ a ≤ 999, non perfect power number
p : p ≤ 1.72 x 1012, prime

I searched up to 8.6 x 109
The search results larger than 8.6 x 109 are owe to Richard Fischer (June 18, 2008).

[In case of prime number]

```  a | p
----+-------------------------------------------------------
2 | 1093, 3511
3 | 11, 1006003
5 | 2, 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801
7 | 5, 491531
11 | 71
13 | 2, 863, 1747591
17 | 2, 3, 46021, 48947, 478225523351
19 | 3, 7, 13, 43, 137, 63061489
23 | 13, 2481757, 13703077, 15546404183, 2549536629329
29 | 2
31 | 7, 79, 6451, 2806861
37 | 2, 3, 77867, 76407520781
41 | 2, 29, 1025273, 138200401
43 | 5, 103
47 | (could not find)
53 | 2, 3, 47, 59, 97
59 | 2777
61 | 2
67 | 7, 47, 268573
71 | 3, 47, 331
73 | 2, 3
79 | 7, 263, 3037, 1012573, 60312841
83 | 4871, 13691, 315746063
89 | 2, 3, 13
97 | 2, 7, 2914393, 76704103313
----+-------------------------------------------------------
101 | 2, 5, 1050139
107 | 3, 5, 97, 613181
103 | 24490789
109 | 2, 3, 20252173
113 | 2, 405697846751
127 | 3, 19, 907, 13778951
131 | 17, 754480919
137 | 2, 29, 59, 6733, 18951271, 4483681903
139 | 1822333408543
149 | 2, 5, 29573, 121456243, 2283131621
151 | 5, 2251, 14107, 5288341, 15697215641
157 | 2, 5, 122327, 4242923, 5857727461, 275318049829
163 | 3, 3898031
167 | 64661497
173 | 2, 3079, 56087
179 | 3, 17, 35059, 126443
181 | 2, 3, 101
191 | 13, 379133
193 | 2, 5, 4877
197 | 2, 3, 7, 653, 6237773
199 | 3, 5, 77263, 1843757
----+-------------------------------------------------------
211 | 279311
223 | 71, 349
227 | 7, 40277
229 | 2, 31
233 | 2, 3, 11, 157, 86735239
239 | 11, 13, 74047, 212855197, 361552687, 12502228667
241 | 2, 11, 523, 1163, 35407
251 | 3, 5, 11, 17, 421, 395696461
257 | 2, 5, 359, 49559, 648258371
263 | 7, 23, 251, 267541, 159838801
269 | 2, 3, 11, 83, 8779, 65684482177
271 | 3, 168629, 16774141, 235558417, 12145092821
277 | 2, 1993, 243547988443
281 | 2, 3443059
283 | 46301
293 | 2, 5, 7, 19, 83
----+-------------------------------------------------------
307 | 3, 5, 19, 487
311 | (could not find)
313 | 2, 7, 41, 149, 181, 1259389
317 | 2, 107, 349, 2227301
331 | 211, 359, 6134718817
337 | 2, 13, 30137417
347 | (could not find)
349 | 2, 5, 197, 433, 7499
353 | 2, 8123, 465989, 17283818861
359 | 3, 23, 307, 24350087
367 | 43, 2213
373 | 2, 7, 113
379 | 3
383 | 28067251
389 | 2, 19, 373, 29569, 211850543
397 | 2, 3, 279421, 13315373041
----+-------------------------------------------------------
401 | 2, 5, 83, 347, 115849
409 | 2, 34583, 1894600969
419 | 173, 349, 983, 3257, 22891217
421 | 2, 101, 1483, 350677, 1083982004309
431 | 3, 2393, 12755833
433 | 2, 3, 129497, 244403
439 | 31, 79, 170899693
443 | 5, 3406223
449 | 2, 3, 5, 1789
457 | 2, 5, 11, 919, 1589513
461 | 2, 1697, 5081
463 | 1667
467 | 3, 29, 743, 7393
479 | 47, 2833, 500239
487 | 3, 11, 23, 41, 1069
491 | 7, 79, 661763933, 121261604419
499 | 5, 109, 81307, 24117560837
----+-------------------------------------------------------
503 | 3, 17, 229, 659, 6761
509 | 2, 7, 41, 7215975149
521 | 2, 3, 7, 31, 53, 8938997
523 | 3, 9907, 19289
541 | 2, 3
547 | 31, 1691778551
557 | 2, 3, 5, 7, 23, 39829
563 | 18920521
569 | 2, 7, 263, 25359067
571 | 23, 29, 308383
577 | 2, 3, 13, 17, 71, 1381277
587 | 7, 13, 31, 22091, 6343317671
593 | 2, 3, 5
599 | 5, 35771
----+-------------------------------------------------------
601 | 2, 5, 61
607 | 5, 7, 40303229, 22035814429
613 | 2, 3, 4073, 81371669, 18419352383
617 | 2, 101, 1087, 6007
619 | 7, 73, 11682481, 52649183399
631 | 3, 1787, 5741
641 | 2, 43, 24481
643 | 5, 17, 307, 859, 460609, 7354807
647 | 3, 23, 15266862761
653 | 2, 13, 17, 19, 1381, 22171, 637699
659 | 23, 131, 2221, 9161, 65983
661 | 2, 441583073, 462147547073
673 | 2, 61
677 | 2, 13, 211
683 | 3, 1279
691 | 37, 509, 1091, 9157, 84131, 10843045487, 312679516579
----+-------------------------------------------------------
701 | 2, 3, 5
709 | 2, 17, 199, 1663
719 | 3, 41, 4414200313
727 | 11
733 | 2, 17
739 | 3, 9719, 5681059
743 | 5
751 | 5, 151, 409
757 | 2, 3, 5, 17, 71, 242789
761 | 2, 41, 907
769 | 2, 1305827821
773 | 2, 3, 787711, 26259199, 142719149
787 | 37, 41, 427541
797 | 2, 8273, 14607661
----+-------------------------------------------------------
809 | 2, 3, 59, 448110371
811 | 3, 211
821 | 2, 19, 83, 233, 293, 1229, 37871, 209140301
823 | 13, 2309
827 | 3, 17, 29, 9323
829 | 2, 3, 17
839 | 5227, 11840951
853 | 2, 1125407
857 | 2, 5, 41, 157, 1697, 32478247
859 | 71
863 | 3, 7, 23, 467, 12049
877 | 2, 78926821
881 | 2, 3, 7, 23, 22385723, 94626144313
883 | 3, 7
887 | 11, 607, 60623
----+-------------------------------------------------------
907 | 5, 17, 3497891
911 | 127, 318917
919 | 3
929 | 2, 62199604679
937 | 2, 3, 41, 113, 853, 22343, 500861, 1031299, 258469889
941 | 2, 11, 1499
947 | 5021
953 | 2, 3, 513405611, 220564434997, 1082305363079
967 | 11, 19, 4813, 44830663
971 | 3, 11, 401, 9257, 401839, 7672759
977 | 2, 11, 17, 109, 239, 401, 37589
983 | (could not find)
991 | 3, 13, 431, 26437
997 | 2, 197, 1223
```

[In case of composite a]

```  a | p
----+-------------------------------------------------------
6 | 66161, 534851, 3152573
----+-------------------------------------------------------
10 | 3, 487, 56598313
12 | 2693, 123653
14 | 29, 353, 7596952219
15 | 29131, 119327070011
18 | 5, 7, 37, 331, 33923, 1284043
----+-------------------------------------------------------
20 | 281, 46457, 9377747, 122959073
21 | 2
22 | 13, 673, 1595813, 492366587, 9809862296159
24 | 5, 25633
26 | 3, 5, 71, 486999673, 6695256707
28 | 3, 19, 23
----+-------------------------------------------------------
30 | 7, 160541, 94727075783
33 | 2, 233, 47441, 9639595369
34 | 46145917691
35 | 3, 1613, 3571
38 | 17, 127
39 | 8039
----+-------------------------------------------------------
40 | 11, 17, 307, 66431, 7036306088681
42 | 23, 719867822369
44 | 3, 229, 5851
45 | 2, 1283, 131759, 157635607
46 | 3, 829
48 | 7, 257
----+-------------------------------------------------------
50 | 7
51 | 5, 41
52 | 461, 1228488439
54 | 19, 1949
55 | 3, 30109, 7278001, 27207490529, 902060958301
56 | 647, 7079771, 115755260963
57 | 2, 5, 47699, 86197
58 | 131, 42250279
----+-------------------------------------------------------
60 | 29, 9566295763, 6683052151409
62 | 3, 19, 127, 1291
63 | 23, 29, 36713, 401771
65 | 2, 17, 163
66 | 89351671, 588024812497
68 | 5, 7, 19, 113, 2741
69 | 2, 19, 223, 631, 2503037
----+-------------------------------------------------------
70 | 13, 142963
72 | (could not find)
74 | 5, 1251922253819
75 | 17, 43, 347, 31247
76 | 5, 37, 1109, 9241, 661049, 20724663983
77 | 2, 32687
78 | 43, 151, 181, 1163, 56149, 4229335793, 5744393199187
----+-------------------------------------------------------
80 | 3, 7, 13, 6343
82 | 3, 5
84 | 163, 653, 20101, 663840051067
85 | 2, 11779
86 | 68239, 6232426549
87 | 1999, 48121, 604807523183
88 | 2535619637
----+-------------------------------------------------------
90 | 6590291053
91 | 3, 293
92 | 727, 383951, 12026117, 18768727, 1485161969
93 | 2, 5, 509, 9221, 81551
94 | 11, 241, 32143, 463033
95 | 2137, 15061, 96185643031
96 | 109, 5437, 8329, 12925267, 103336004179
98 | 3, 28627, 61001527
99 | 5, 7, 13, 19, 83
----+-------------------------------------------------------
102 | 7559, 11813, 139409857
104 | 313, 237977, 11950711691
105 | 2, 7669
106 | 79399, 672799
108 | 3761, 10271, 1296018233
----+-------------------------------------------------------
110 | 17, 5381, 9431, 1219715607577
111 | 131
112 | 11, 1037888513
114 | 9181
115 | 31, 2743780307
116 | 3, 7, 19, 47
117 | 2, 7, 31, 37, 182111
118 | 3, 5, 11, 23, 3152249, 10404887
119 | 1741
----+-------------------------------------------------------
120 | 11, 653, 2074031, 124148023
122 | 11, 2791, 16522744709
123 | 34849
124 | 5, 11, 22511
126 | 5
129 | 2, 7, 113
----+-------------------------------------------------------
130 | 11, 23, 62351, 70439
132 | 5
133 | 2, 5277179
134 | 3, 17, 406531, 73629977, 4962859085059
135 | 23147324413
136 | 3, 5153, 87249620417
138 | 97, 4889
----+-------------------------------------------------------
140 | 14591
141 | 2, 192047, 42039743
142 | 143111, 12838109
143 | 3, 5, 67, 197, 1999, 12848347, 65451824959, 225413072431
145 | 2, 3, 31
146 | 7, 13, 79, 22639
147 | 13, 79, 103, 283, 24203, 4058948753
148 | 7, 11, 41, 14879, 161141, 2805469039
----+-------------------------------------------------------
150 | 13, 21199069, 85877201, 103053130679
152 | 3, 22554863, 54504719
153 | 2, 8539, 5540099
154 | 3
155 | 17, 211691, 309131, 6282943, 1196757167
156 | 347, 1297
158 | 17, 1031, 820279
159 | 367, 5356051
----+-------------------------------------------------------
160 | 72669541193
161 | 2, 3, 11, 83, 137, 6188401, 93405163
162 | 607, 142946059423
164 | 103, 107, 1493
165 | 2, 7, 211, 25102757, 11699444843
166 | 7, 877, 61819
168 | 5, 13, 739, 27427
----+-------------------------------------------------------
170 | 3, 13, 23, 1163, 170613512651
171 | 269, 1803383
172 | 3, 47, 91303
174 | 5, 113, 199, 379
175 | 397, 487, 2199439603
176 | 5, 191, 5611481459
177 | 2, 7, 23, 42397, 123681208241
178 | 7, 1213, 67751, 296036443
----+-------------------------------------------------------
180 | 269, 5737
182 | 5, 211, 8934721
183 | 1231487
184 | 89, 661, 1187, 2203, 6043
185 | 2, 12577
186 | (could not find)
187 | (could not find)
188 | 3, 13
189 | 2, 1847, 6199
----+-------------------------------------------------------
190 | 3, 29, 236981, 382351, 753743
192 | 13, 4049, 302279, 465435739
194 | 439, 8338826207
195 | 7, 23, 13421, 3132631
198 | 147647, 545639981
----+-------------------------------------------------------
200 | (could not find)
201 | 2, 5, 86722091
202 | 11, 47
203 | (could not find)
204 | 5431, 142061, 1070347, 15028133
205 | 2, 367
206 | 3, 151, 1201, 2087
207 | 5, 41, 269, 809, 26240063
208 | 3, 947
209 | 2, 229, 2203, 511654217, 6802750783
----+-------------------------------------------------------
210 | 43, 449
212 | 1960573
213 | 2, 313, 1877
214 | 7, 17
215 | 3, 7, 11, 3327697, 502095466241
217 | 2, 3, 127447, 8468323
218 | 5, 163
219 | 7891033151
----+-------------------------------------------------------
220 | 3581, 9619, 79867, 717967, 13477271, 32376410527, 34816906301
221 | 2, 29, 1669, 15233, 103361803, 406833359, 455317162337, 1180548631831
222 | (could not find)
224 | 3, 5, 17, 130677149
226 | 3, 5, 7, 97, 157
228 | 1361, 182353
----+-------------------------------------------------------
230 | 47, 384533887
231 | (could not find)
232 | 5, 30851, 838667, 2250741293
234 | 19, 46441, 817766595407
235 | 3, 31, 118022689
236 | 29, 229
237 | 2
238 | 977, 8609, 4997219, 863039377, 64904716187
----+-------------------------------------------------------
240 | 227797
242 | 3, 373, 2386301, 2434609, 167962252433, 2706669242327
244 | 3, 7, 16906680221
245 | 2, 11, 19, 229, 218173429
246 | 7, 877441867
247 | 5081, 105527103139
248 | 67, 101, 663893, 502608046943, 668677573093
249 | 2, 5, 13, 17
----+-------------------------------------------------------
250 | 131, 509
252 | 211, 997, 3613, 394213789
253 | 2, 3, 167, 90901, 2905031
254 | 89, 2269, 18042251, 32984389
255 | 23, 463
258 | 13, 17827
259 | 173
----+-------------------------------------------------------
260 | 3, 83, 15263, 27827, 1749229, 6647339, 19148231, 3977977109
261 | 2, 43, 71, 257
262 | 3, 19, 571
264 | 7, 61, 176051, 1446587
265 | 2, 10853
266 | 23, 163, 21401, 4673329018717
267 | 29, 20411, 46926349
268 | 5, 13, 101
----+-------------------------------------------------------
270 | 29
272 | 3833, 14084849
273 | 2, 1086731, 7558891900249
274 | 5, 23, 16631
275 | 7, 6323, 134513, 138641, 455471, 40196043527, 279203122727
276 | 5, 7, 43, 193
278 | 3, 1741
279 | 67, 97, 557142359
----+-------------------------------------------------------
280 | 3, 47, 401
282 | 5, 11, 13120561
284 | 197, 1103, 9127, 16189, 1601147, 10723208449, 4019853486967
285 | 2, 5791, 157907
286 | 71, 619, 15017, 1016689, 6489382948837
287 | 3, 653, 967, 10322313269, 405469792823
288 | 17, 43, 36979, 376721, 670507
----+-------------------------------------------------------
290 | 17, 6659, 319811, 273354437
291 | 109, 16766930077
292 | 19, 43, 887, 941, 3239857
294 | 356135477, 592538407, 367003576739
295 | 7, 47, 26249
296 | 3, 971
297 | 2, 2480497, 2779225651
298 | 3, 59, 101, 181, 598421, 4809986918441
299 | 5, 19, 59, 374893957
----+-------------------------------------------------------
300 | 37, 59, 29599
301 | 2, 5
302 | 607, 22621771, 123644663
303 | 43, 33873179
304 | (could not find)
305 | 2, 3, 1149209
306 | 73
308 | 521
309 | 2
----+-------------------------------------------------------
310 | 67, 3617
312 | 7, 13622501
314 | 3, 181, 827, 3143117
315 | 13, 257, 1187, 40471, 4767799
316 | 3, 13, 51461, 898508623
318 | 5, 197, 131959, 11496420743, 69578772701
319 | 13, 79, 1439
----+-------------------------------------------------------
320 | 13121, 27397, 452983, 6818771
321 | 2, 1401979, 78793807
322 | 3307, 4297, 2768017244933
323 | 3, 11, 291721
325 | 2, 3, 7, 157, 953, 568231, 68992603, 4507000559
326 | 5, 1249, 30589393, 302908877
327 | 17
328 | 139, 911, 1399
329 | 2, 17, 487068061
----+-------------------------------------------------------
330 | 227
332 | 3, 5, 239, 15773
333 | 2, 19, 31, 3266479
334 | 3, 23, 257
335 | (could not find)
336 | 11, 78666481
338 | 31, 53
339 | 13, 47, 199, 466751783977
----+-------------------------------------------------------
340 | 173, 641, 115574081561
341 | 2, 3, 101
342 | 7, 17167837
344 | 7, 55351, 7493623, 102089209
345 | 2, 463, 8941
346 | 499
348 | 37, 103, 161561
----+-------------------------------------------------------
350 | 3, 103, 167
351 | 5
352 | 3, 23, 7723, 423017653829
354 | 11, 17, 37, 977, 13513, 1336241
355 | (could not find)
356 | 37, 113
357 | 2, 5, 13
358 | 157, 6382723111
----+-------------------------------------------------------
360 | 11, 13, 19
362 | 7, 11, 19, 80233, 1794830107009
363 | 4153, 94565579, 1249344562091
364 | 11, 17, 1824271
365 | 2, 1453, 128587933
366 | 11, 36857
368 | 3, 5, 73, 21503, 70399321039
369 | 2, 139, 173, 211, 419
----+-------------------------------------------------------
370 | 3, 22020497, 66065773, 4436281892011
371 | 1619, 101113
372 | 11, 2687
374 | 5, 7, 29, 31, 27463248607
375 | 701
376 | 5, 12799
377 | 2, 3, 79
378 | 41, 1453, 517298279
----+-------------------------------------------------------
380 | 83, 109, 12007, 120313541
381 | 2, 827, 14449, 16943
382 | 5, 97, 1238371
384 | 519488341, 75918457357
385 | 2, 1548149, 4605659
386 | 3, 103
387 | 174426871193
388 | 3, 31
----+-------------------------------------------------------
390 | 11, 5713733, 15819863
391 | 7, 103, 25679, 68903, 6259286339, 11993961787, 311215043773
392 | 101, 769, 773, 1553, 883201742719
393 | 2, 5, 7, 823, 22381, 1845595127527
394 | 251
395 | 3, 191, 651742019113
396 | 1947241, 17344004261
398 | 139, 205319
399 | 5, 17, 23
----+-------------------------------------------------------
402 | 97, 109, 269
403 | 11, 43, 373, 1321
404 | 3, 3659
405 | 2, 601
406 | 3, 53, 216141619
407 | 5, 103001
408 | 13, 50513
----+-------------------------------------------------------
410 | 7, 109, 239, 653, 11328969257, 19111351313
411 | 7, 23, 1367, 25888367
412 | 97
413 | 2, 3, 53, 249745603, 2832308863
414 | 31
415 | 3, 19, 10337, 107777, 924528047, 1465092947347
416 | 29, 181, 6988511
417 | 2, 101
418 | 5, 13, 822949
----+-------------------------------------------------------
420 | 17, 181
422 | 3, 7, 571, 367277, 29170663
423 | 7, 17, 19, 43, 1669
424 | 3, 5, 37, 43, 131, 3037
425 | 2, 29, 1097, 64951, 106357, 433703
426 | 5, 89, 56861249, 2215508401
427 | 13, 547, 577, 1657, 93703, 568689487
428 | 6361, 1878059
429 | 2, 19, 1381, 2473, 36510613, 12994232161
----+-------------------------------------------------------
430 | 19, 31, 557, 344621
432 | 5, 61, 1680023, 7308036881
434 | 863, 1831, 63527, 346517902547
435 | (could not find)
436 | 193, 30348797, 677213275049
437 | 2, 13, 37
438 | 47, 71, 6449465131
----+-------------------------------------------------------
440 | 3, 7, 31, 797
442 | 3, 7, 29417408507
444 | 11, 17, 15667, 220688906759
445 | 2, 2659, 2753
446 | 797, 2687, 8629, 269063
447 | 17, 82780601
448 | 31, 67, 111121
----+-------------------------------------------------------
450 | 1199923, 9445297441
451 | 3, 5, 53, 48869, 4855900311901
452 | 2141, 94847, 402341, 1454683, 163880093939
453 | 2, 1597, 405179
454 | (could not find)
455 | 101, 238931257
456 | 192037
458 | 3
459 | 7, 14537
----+-------------------------------------------------------
460 | 3, 7, 19, 53, 8819831
462 | 849571, 14532863
464 | 73861878877
465 | 2, 795071
466 | 23
468 | 5, 17, 9858955373
469 | 2, 3, 107
----+-------------------------------------------------------
470 | 79, 103, 83401
471 | 7, 41, 691409
472 | 7, 101, 1531, 363047
473 | 2, 37, 2311
474 | 5, 2141, 197699, 16069969
475 | 11, 117133
476 | 3, 5, 37, 109, 337, 401, 5527, 1169759
477 | 2, 19, 1576721
478 | 3
----+-------------------------------------------------------
480 | 8293, 243589
481 | 2, 11, 54371927, 143432275871
482 | 5, 71
483 | 11, 1160559731
485 | 2, 3, 11, 13, 19051
486 | 563, 572843
488 | 13, 19, 1493, 3505277
489 | 2, 7
----+-------------------------------------------------------
490 | 4787
492 | 1034239, 211096013
493 | 2, 5, 11, 163001522539
494 | 3, 37, 4271, 121607, 601961
495 | 1522057
496 | 3
497 | 2, 127, 157, 505780258937
498 | 61, 1187387, 45525923, 2149153512589
----+-------------------------------------------------------
500 | 53, 109, 157, 49429
501 | 2, 5, 23, 14890530569, 24112920253
502 | 22877, 34318033
504 | 67, 229793929
505 | 2, 3, 41, 463, 297377071847
506 | 13, 59
507 | 5, 2377, 5153, 363211, 6111681437
508 | 7, 13, 1061, 1274084375749, 1311889799369
----+-------------------------------------------------------
510 | 107, 19846129, 175868149, 228490481, 34656130219
511 | 11, 4787
513 | 2, 17, 31, 43787
514 | 3, 22549
515 | 101, 2089, 175186789, 2115451213
516 | 571
517 | 2, 59547517
518 | 5, 12650270891
519 | 157, 223, 8649842813, 37898634329
----+-------------------------------------------------------
520 | 7, 36161687
522 | 31, 17477, 499292741
524 | 5, 11, 778717
525 | 2, 97, 34687, 497557, 2651387
526 | 5, 13, 83, 499, 647, 247073, 2394147047
527 | 73, 3373
528 | 23, 1303, 54467681
----+-------------------------------------------------------
530 | 3, 13, 23, 5157793
531 | 31, 86384479603
532 | 3, 5, 179, 62929
533 | 2, 283, 417860291
534 | 101, 139, 631, 9931
535 | 13009, 574477
536 | 1619, 556072481, 1240525163
537 | 2, 43, 5021, 112142108971
538 | 7, 17, 2267, 28307
539 | 3, 101, 172297, 184693, 1178753, 4673137127
----+-------------------------------------------------------
540 | 7, 17, 41, 9041
542 | (could not find)
543 | 5, 313
544 | 12527, 24095129
545 | 2, 11149, 2042119241
546 | (could not find)
548 | 3, 30949, 256561
549 | 2, 5, 10133, 512811707, 481691968193
----+-------------------------------------------------------
550 | 3, 110619193, 332718585593
551 | 5, 1021, 108289, 1254577, 10781849409623
552 | 89925422513
553 | 2, 139, 347, 7541, 737291
554 | (could not find)
555 | 541, 162203773
556 | 197, 617, 19009
558 | 7, 193, 461, 1621, 65257, 47652991
559 | 3, 59, 151, 599, 12613
----+-------------------------------------------------------
560 | 67, 2671, 5107, 18757, 411823, 712346863
561 | 2, 135913, 3458677
562 | 83, 337, 5229031
564 | 4813, 4388171
565 | 2, 11, 782707, 14615527, 362941373
566 | 3, 326537
567 | 67, 101
568 | 3, 5, 373, 1553
----+-------------------------------------------------------
570 | 7
572 | 61, 4049, 29922449, 111170909, 7654073743
573 | 2, 31, 283, 50647
574 | 5, 29, 61, 2213, 598967
575 | 3, 46271, 61169, 6501209375021
578 | 11, 107747, 205657
579 | 17, 199, 1097
----+-------------------------------------------------------
580 | 239, 57251, 974147, 69722080903
581 | 2, 37, 176431, 6924427
582 | 5, 37, 151
583 | 241, 479, 1889
584 | 3, 1447, 69857
585 | 2, 1327, 1580431
586 | 3, 136544960191
588 | 43, 599, 292969
589 | 2, 7, 17191, 1524529, 3501139
----+-------------------------------------------------------
590 | 163, 443, 376021, 2239201, 4176404107, 3219042433511
591 | 419, 8447
592 | 23, 51217, 2070323
594 | 32485136899, 8784820622857
595 | 3, 19, 88499, 96727678693, 386120172551
596 | 11, 13, 94327
597 | 2, 558793
598 | 151, 3571
----+-------------------------------------------------------
600 | 47, 14582963
602 | 3, 11, 1166849, 37310783
603 | 1579, 290512619
604 | 3, 11, 79, 157
605 | 2, 29, 89
606 | 7, 11, 13, 19, 71, 848297, 319155270953
608 | 11, 7759, 664579, 50092921
609 | 2
----+-------------------------------------------------------
610 | (could not find)
611 | 3, 18503, 39569
612 | 59
614 | 11, 18234089
615 | 83
616 | 17, 479, 123001704037
618 | 5, 7, 17, 61, 1163, 220169
----+-------------------------------------------------------
620 | 3, 29, 113, 5861, 81163, 7358177, 3533794899013
621 | 2, 73, 17609, 963223, 2031264307
622 | 3, 577, 1193
623 | 19, 31, 47
624 | 5, 109, 37199
626 | 5, 5641
627 | 181048811
628 | 31
629 | 2, 3, 47, 101
----+-------------------------------------------------------
630 | 67, 163
632 | 5, 11, 37, 179, 389, 829
633 | 2, 71, 4513, 22643, 7329659
634 | 800243
635 | 8641, 3245689, 12675040709
636 | 7, 1270333
637 | 2, 547, 1021, 521429, 78225448229
638 | 3, 7, 3253
639 | (could not find)
----+-------------------------------------------------------
640 | 3
642 | 5302111
644 | 41, 223, 883
645 | 2, 11, 29, 319117, 1350061, 549461839
646 | 4136689
648 | 12295820941
649 | 2, 3, 5, 101, 179, 45840199
----+-------------------------------------------------------
650 | 6211, 2135417656303
651 | 5, 29, 105021277
652 | 2113, 51059, 524251867, 5269346021
654 | 13, 19
655 | 7, 47, 53, 3940249, 54674441
656 | 3, 7, 4259, 404890928047
657 | 2, 5, 13, 883, 2899751
658 | 3, 242831101
----+-------------------------------------------------------
660 | 19, 43, 3646427
662 | (could not find)
663 | 6961
664 | 24223, 245183
665 | 2, 3, 61
666 | 4503454574621, 4977652953109
667 | 3, 7, 199, 839, 4421, 59239
668 | 5, 7, 19
669 | 2, 397, 5857, 482683
----+-------------------------------------------------------
670 | 83, 52289, 122323, 7267303
671 | 5397037
672 | 59, 73, 617, 2963, 483251, 880751, 8755297
674 | 3, 5
675 | 13, 761, 993913
678 | 37, 23841761
679 | 534607, 18514999
----+-------------------------------------------------------
680 | 2677, 8737, 13125811
681 | 2, 71, 109, 16088557
682 | 5, 61, 857, 17934551077
684 | 2092667
685 | 2, 3, 7, 119659261
686 | 11, 118163, 283099, 1031483, 85481059, 464136932507
687 | 7, 103, 199337, 2747873, 36926501
688 | 17, 1429, 84391410869
689 | 2, 6547, 1863787, 24028099019
----+-------------------------------------------------------
690 | 113
692 | 3
693 | 2, 5, 561931, 1362299, 112102492193
694 | 3, 19, 233
695 | 13, 107, 18127, 52667
696 | 617
697 | 2
698 | 13
699 | 5, 11, 13, 23, 67, 73, 398969
----+-------------------------------------------------------
700 | 67, 3001
702 | 677, 40361, 100213
703 | 3, 4049, 591377
704 | 7, 29, 1949
705 | 2, 7, 1019, 3847, 48109, 16130783
706 | 23, 27297539, 209941187
707 | 5, 89, 317, 22469, 44417, 4728169429
708 | 701, 4146409, 51381922303
----+-------------------------------------------------------
710 | 3, 163, 42834427
711 | 73, 163
712 | 3, 17, 9463, 476513, 1287467, 2686283
713 | 2, 11097981800233
714 | 191, 613
715 | 781059256409
716 | 7, 552341, 440416759, 5626714979
717 | 2, 7, 11, 643, 23917, 1304111, 16621877, 8512494329
718 | 5
----+-------------------------------------------------------
720 | 69193
721 | 2, 3, 19, 379
722 | 67, 547, 15607
723 | 11, 19, 233, 239, 660658181, 2938943531
724 | 5, 23
725 | 2, 11
726 | 5, 31, 17377
728 | 3, 163, 18541, 57384358463
----+-------------------------------------------------------
730 | 3, 107
731 | 277, 1873
732 | 5, 31, 9143354797
734 | 7, 73, 65957
735 | 11, 457, 79181
736 | 7, 17, 127, 5839
737 | 2, 3, 37, 53, 6007, 140846899, 43638688993, 3684324840109
738 | 3191, 8269, 3947883749
----+-------------------------------------------------------
740 | 1087, 281975833, 15373986241
741 | 2, 269, 1433798129
742 | 113, 7027, 968761, 1859111
744 | 41, 2729, 29123
745 | 2, 31147, 474535783, 280232633477
746 | 3, 13, 191, 1621
747 | 101, 257, 271, 80567
748 | 3, 433, 1719107231
749 | 2, 5, 29759, 34549943161
----+-------------------------------------------------------
750 | 19, 79, 97, 60773, 4888164324599
752 | 53, 876381797
753 | 2, 7, 11, 173, 491
754 | 7, 883, 5420057
755 | 3, 3583, 1299821, 143337647
756 | 13, 2551, 49822776853
758 | 1272207150661
759 | 257
----+-------------------------------------------------------
760 | (could not find)
762 | 31019
763 | 61, 1822517
764 | 3, 43, 4943, 7459
765 | 2, 7, 13, 377369, 5330933, 17206283
766 | 3, 7, 11, 10163, 8922301
767 | 2203, 68903, 422249, 74991254231
768 | 5, 41, 345727
----+-------------------------------------------------------
770 | 73, 4861, 1170023, 2771298845851
771 | 907, 2662193
772 | (could not find)
774 | 5, 8419
775 | 3, 13
776 | 5, 19, 41, 73, 1097, 33328795891
777 | 2
778 | 29, 15373, 1965283087
779 | 257, 2477, 4534883
----+-------------------------------------------------------
780 | 53, 269, 48869, 10671151
781 | 2, 29, 499, 778187
782 | 3, 5, 563, 5683
783 | 7, 442084061
785 | 2, 7, 151, 74923, 123407, 111646712561, 559491826637
786 | 73, 3469, 14026409
788 | 37, 632114867, 22824986839, 118941702367
789 | 2, 2307345676481
----+-------------------------------------------------------
790 | 19, 89, 461, 5125753
791 | 3, 19, 10998428929
792 | 17, 23, 21011, 255133, 80766939707
793 | 2, 3, 5, 173, 1103, 53407
794 | 1286720879
795 | 23, 79, 98909, 166657, 11173405591
796 | 54914297
798 | (could not find)
799 | 5, 2891032049
----+-------------------------------------------------------
800 | 3, 29
801 | 2, 5, 683, 13807
802 | 3, 7, 17, 215420011
803 | 7, 23, 1973, 222216074029
804 | 148173282913
805 | 2, 59, 17401, 163193
806 | 59, 1051, 961613
807 | 5, 11
808 | (could not find)
----+-------------------------------------------------------
810 | 79, 35608871, 128710108069
812 | (could not find)
813 | 2, 193, 607, 142595731
814 | 7, 670786483, 122493320143
815 | 7, 233, 2030845176271
816 | 31, 1241086902527
817 | 2, 547, 659077
818 | 3, 5, 35097043, 89127571697
819 | 809, 1041203, 9411713, 7263800119
----+-------------------------------------------------------
820 | 3, 11, 187477
822 | 13, 83, 17377, 18965973137
824 | 5, 41, 951427
825 | 2, 444113, 4100307667
826 | 5, 13, 89, 23459, 29264621
828 | 577, 1867, 7315489
----+-------------------------------------------------------
830 | 84407
831 | 547, 2179, 16212571, 312049583
832 | 5, 7, 2213, 112246723, 223818256729
833 | 2, 498254423201
834 | 7, 41
835 | 131, 125941, 323294483, 954340601
836 | 3, 181
837 | 2, 109
838 | 3, 11, 19, 61
----+-------------------------------------------------------
840 | 29, 730637329
842 | 29, 89
843 | 5, 509
844 | 11, 13, 31, 36052871, 70457839, 2025248413, 2816027947
845 | 2, 3
846 | 11, 13, 31
847 | 3, 41, 1319033, 28276121, 221393539, 409765111823
848 | 11, 101863
849 | 2, 5, 19, 13697, 590123, 10720751, 8987928353
----+-------------------------------------------------------
850 | 11, 151, 17286019, 11046585983
851 | 5, 7, 53, 701
852 | 7, 269, 27457
854 | 3, 7377061, 230377339
855 | 29, 1549, 6779, 375481, 13214599, 7245558091, 30994657849
856 | 3, 11, 53, 229, 4951, 9947819971, 48082633801
858 | (could not find)
----+-------------------------------------------------------
860 | (could not find)
861 | 2, 84948797
862 | 53, 413952542813
864 | 7, 13, 121403
865 | 2, 3, 167, 2161, 8663
866 | 17, 97, 233, 1997
867 | 13, 47, 167, 431
868 | 5, 13, 17, 38201
869 | 2, 53
----+-------------------------------------------------------
870 | 12907
871 | (could not find)
872 | 3, 7583
873 | 2, 193, 4547, 485509, 575959, 20856007, 58800361
874 | 3, 5, 11, 47, 193, 1181, 1607
875 | 37, 67, 937477, 1530709
876 | 5, 226451, 1299343, 3587347, 171702372643, 369801222673
878 | 277
879 | 243343
----+-------------------------------------------------------
880 | 61, 1168308143, 12782825651, 38563175939, 107905234979
882 | 5, 29, 317, 60761, 2669321
884 | 1373, 7196186279251
885 | 2, 194057
886 | 29082802901
888 | 23, 143159
889 | 2, 491, 2014139
----+-------------------------------------------------------
890 | 3, 162611, 321371
891 | 43, 43997, 112808526497
892 | 3, 157, 2339, 568091, 4742137, 6336193, 8672659, 234988626427
893 | 2, 5, 37, 59, 147341
894 | 41, 193, 389, 644519, 3319051, 21227900821
895 | 53, 193, 65927, 129169
896 | 37, 31238183, 8535320569
897 | 2, 67, 269, 1123
898 | 239
899 | 3, 5, 131, 1013
----+-------------------------------------------------------
901 | 2, 3, 5, 7, 29, 3877, 175474967, 6338370677, 14981029537
902 | 407059, 482936260489
903 | 13831
904 | 29, 135469, 235523
905 | 2, 17, 41
906 | 1579, 17701979
908 | 3, 103, 269, 40819
909 | 2, 11487079, 54828001
----+-------------------------------------------------------
910 | 3, 142886951, 1514654268719
912 | 7
913 | 2, 7, 41, 6079, 93187777, 89834287327
914 | 139, 769
915 | 13, 2549
916 | 5923
917 | 2, 3, 1061, 11909, 312589
918 | 5, 14009, 164071, 693582176263
----+-------------------------------------------------------
920 | 41
921 | 2, 262739, 152874167483
922 | 16883
923 | 73, 283, 1627, 2447
924 | 5, 67399, 7084547
925 | 2, 13, 53, 83, 877, 8363, 604859, 3519539, 90281266927
926 | 3, 5, 14900443
927 | 89, 22511
928 | 3, 11, 23, 13913, 199549335169
----+-------------------------------------------------------
930 | 7, 709, 70619, 85201
931 | 281
932 | 5, 7, 17, 37, 2851
933 | 2, 8592109
934 | 13, 1511, 12119, 19175934991
935 | 3, 593, 913331, 626872115449
936 | 61, 412330367, 446377909, 2607195499
938 | 191, 9467581
939 | 179, 83761
----+-------------------------------------------------------
940 | 23, 419, 2837, 104479, 378289, 2514119
942 | 17, 313
943 | 5, 39025823
944 | 3, 13
945 | 2, 37, 5857, 1125121069, 2705324826961
946 | 3, 59, 211
948 | 409, 470461, 2584062913, 11058282821
949 | 2, 5, 7, 14806159, 30446387
----+-------------------------------------------------------
950 | 7, 925577, 1179757
951 | 5, 848378279311
952 | 2856871
954 | 113, 193
955 | 3, 107, 607, 5521
956 | 19, 656300459, 2482219343
957 | 2, 5, 149, 2113, 67129, 196961579, 51716885683
958 | 43, 14479, 25229, 189713, 1813979414189
959 | 11, 736433, 933107653
----+-------------------------------------------------------
960 | 31, 149, 449, 12157, 349227224611, 644232442639
962 | 3, 7, 31, 41, 5711
963 | 1933, 36758171
964 | 3, 9533
965 | 2, 11, 2356997
966 | 599, 7687, 2337073, 32558972119
968 | 5, 7669, 107641, 9506431657
969 | 2, 11, 71, 911, 103421, 2391503, 319792007
----+-------------------------------------------------------
970 | 59, 269, 230551
972 | 227
973 | 2, 3, 26713, 21581257, 1108107413579
974 | 5, 7129, 1404071, 4204968197
975 | 2879
976 | 5, 991
978 | 29, 71, 97, 733
979 | 7, 191, 157799
----+-------------------------------------------------------
980 | 3
981 | 2, 7, 719, 2153
982 | 3, 5, 1747, 2459, 1222777, 5494786229
984 | 19, 78791
985 | 2, 53, 1895057
986 | (could not find)
987 | 1399, 36721, 57943, 24858506161
988 | 14401, 63754777477
989 | 2, 3, 12743, 2085799, 1423932997, 10577489843279
----+-------------------------------------------------------
990 | 1009
992 | 13, 140729, 24922021, 5043756649
993 | 2, 5, 25301, 92177, 31187620943
994 | 5431, 5449, 9029
995 | 11, 13, 23, 15324691
996 | 16931, 34031371421
998 | 3, 7, 17, 1551083, 627934621
999 | 5, 7, 50119, 806812352251, 5879307404213
```

E-mail : kc2h-msm@asahi-net.or.jp
Hisanori Mishima