Humble numbers: Difference between revisions
Added C++ direct generation variant
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1272 have 8 digits
1767 have 9 digits</pre>
=== Direct Generation - Variant ===
A direct generation variant. Rather quick, as the humble numbers are not generated in order. And the digits are not counted individually, the log representation of each humble number is just binned into the decade tally with a simple division by log(10).
<lang c>#include <chrono>
#include <cmath>
#include <locale>
using UI = unsigned long long;
using namespace std;
using namespace chrono;
int limc = 100;
const double l2 = log(2), l3 = log(3), l5 = log(5), l7 = log(7), l0 = log(10), fac = 1e12;
static bool IsHum(int num) { if (num <= 1) return true; for (int j : { 2, 3, 5, 7 })
if (num % j == 0) return IsHum(num / j); return false; }
// slow way to determine whether numbers are humble numbers
static void Fisrt_Slow(int firstAmt) { printf("The first %d humble numbers are: ", firstAmt);
for (int gg = 0, g = 1; gg < firstAmt; g++) if (IsHum(g)) { printf("%d ", g); gg++; }
printf("\n\n"); }
int main(int argc, char **argv) {
Fisrt_Slow(50); setlocale(LC_ALL, ""); auto st = steady_clock::now();
if (argc > 1) limc = stoi(argv[1]);
UI *bins = new UI[limc], lb0 = (UI)round(fac * l0),
lb2 = (UI)round(fac * l2), lb3 = (UI)round(fac * l3),
lb5 = (UI)round(fac * l5), lb7 = (UI)round(fac * l7),
tot = 0, lmt = limc * lb0, lm2 = lb5 * 3;
printf("Digits Count Accum\n");
for (int g = 0; g < limc; g++) bins[g] = 0;
for (UI i = 0; i < lmt; i += lb2) for (UI j = i; j < lmt; j += lb3)
for (UI k = j; k < lmt; k += lb5) for (UI l = k; l < lmt; l += lb7)
bins[l / lb0]++;
for (int f = 0, g = 1; f < limc; f = g++) { tot += bins[f];
//if (g < 110 || g % 100 == 0 || (g < 200 && g % 10 == 0)) // uncomment to emulate pascal output
printf ("%4d %'13llu %'18llu\n", g, bins[f], tot); }
delete [] bins;
printf("Counting took %8f seconds\n", duration<double>(steady_clock::now() - st).count());
}</lang>
{{out}}
Seems to give correct values as compared to the pascal (modification of hamming numbers fast alternative) version. And goes noticeably faster, up to 877 digits in about 3 1/4 minutes, where as pascal was taking 1 1/3 hours to get to 877 digits.
<pre style="height:64ex;overflow:scroll;width:130ex;overflow:scroll">The first 50 humble numbers are: 1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 50 54 56 60 63 64 70 72 75 80 81 84 90 96 98 100 105 108 112 120
Digits Count Accum
1 9 9
2 36 45
3 95 140
4 197 337
5 356 693
6 579 1,272
7 882 2,154
8 1,272 3,426
9 1,767 5,193
10 2,381 7,574
11 3,113 10,687
12 3,984 14,671
13 5,002 19,673
14 6,187 25,860
15 7,545 33,405
16 9,081 42,486
17 10,815 53,301
18 12,759 66,060
19 14,927 80,987
20 17,323 98,310
21 19,960 118,270
22 22,853 141,123
23 26,015 167,138
24 29,458 196,596
25 33,188 229,784
26 37,222 267,006
27 41,568 308,574
28 46,245 354,819
29 51,254 406,073
30 56,618 462,691
31 62,338 525,029
32 68,437 593,466
33 74,917 668,383
34 81,793 750,176
35 89,083 839,259
36 96,786 936,045
37 104,926 1,040,971
38 113,511 1,154,482
39 122,546 1,277,028
40 132,054 1,409,082
41 142,038 1,551,120
42 152,515 1,703,635
43 163,497 1,867,132
44 174,986 2,042,118
45 187,004 2,229,122
46 199,565 2,428,687
47 212,675 2,641,362
48 226,346 2,867,708
49 240,590 3,108,298
50 255,415 3,363,713
51 270,843 3,634,556
52 286,880 3,921,436
53 303,533 4,224,969
54 320,821 4,545,790
55 338,750 4,884,540
56 357,343 5,241,883
57 376,599 5,618,482
58 396,533 6,015,015
59 417,160 6,432,175
60 438,492 6,870,667
61 460,533 7,331,200
62 483,307 7,814,507
63 506,820 8,321,327
64 531,076 8,852,403
65 556,104 9,408,507
66 581,902 9,990,409
67 608,483 10,598,892
68 635,864 11,234,756
69 664,053 11,898,809
70 693,065 12,591,874
71 722,911 13,314,785
72 753,593 14,068,378
73 785,141 14,853,519
74 817,554 15,671,073
75 850,847 16,521,920
76 885,037 17,406,957
77 920,120 18,327,077
78 956,120 19,283,197
79 993,058 20,276,255
80 1,030,928 21,307,183
81 1,069,748 22,376,931
82 1,109,528 23,486,459
83 1,150,287 24,636,746
84 1,192,035 25,828,781
85 1,234,774 27,063,555
86 1,278,527 28,342,082
87 1,323,301 29,665,383
88 1,369,106 31,034,489
89 1,415,956 32,450,445
90 1,463,862 33,914,307
91 1,512,840 35,427,147
92 1,562,897 36,990,044
93 1,614,050 38,604,094
94 1,666,302 40,270,396
95 1,719,669 41,990,065
96 1,774,166 43,764,231
97 1,829,805 45,594,036
98 1,886,590 47,480,626
99 1,944,540 49,425,166
100 2,003,661 51,428,827
101 2,063,972 53,492,799
102 2,125,486 55,618,285
103 2,188,204 57,806,489
104 2,252,146 60,058,635
105 2,317,319 62,375,954
106 2,383,733 64,759,687
107 2,451,413 67,211,100
108 2,520,360 69,731,460
109 2,590,584 72,322,044
110 2,662,102 74,984,146
111 2,734,927 77,719,073
112 2,809,069 80,528,142
113 2,884,536 83,412,678
114 2,961,346 86,374,024
115 3,039,502 89,413,526
116 3,119,022 92,532,548
117 3,199,918 95,732,466
118 3,282,203 99,014,669
119 3,365,883 102,380,552
120 3,450,981 105,831,533
121 3,537,499 109,369,032
122 3,625,444 112,994,476
123 3,714,838 116,709,314
124 3,805,692 120,515,006
125 3,898,015 124,413,021
126 3,991,818 128,404,839
127 4,087,110 132,491,949
128 4,183,914 136,675,863
129 4,282,228 140,958,091
130 4,382,079 145,340,170
131 4,483,467 149,823,637
132 4,586,405 154,410,042
133 4,690,902 159,100,944
134 4,796,979 163,897,923
135 4,904,646 168,802,569
136 5,013,909 173,816,478
137 5,124,783 178,941,261
138 5,237,275 184,178,536
139 5,351,407 189,529,943
140 5,467,187 194,997,130
141 5,584,624 200,581,754
142 5,703,728 206,285,482
143 5,824,512 212,109,994
144 5,946,992 218,056,986
145 6,071,177 224,128,163
146 6,197,080 230,325,243
147 6,324,708 236,649,951
148 6,454,082 243,104,033
149 6,585,205 249,689,238
150 6,718,091 256,407,329
151 6,852,749 263,260,078
152 6,989,204 270,249,282
153 7,127,454 277,376,736
154 7,267,511 284,644,247
155 7,409,395 292,053,642
156 7,553,112 299,606,754
157 7,698,677 307,305,431
158 7,846,103 315,151,534
159 7,995,394 323,146,928
160 8,146,567 331,293,495
161 8,299,638 339,593,133
162 8,454,607 348,047,740
163 8,611,505 356,659,245
164 8,770,324 365,429,569
165 8,931,081 374,360,650
166 9,093,797 383,454,447
167 9,258,476 392,712,923
168 9,425,127 402,138,050
169 9,593,778 411,731,828
170 9,764,417 421,496,245
171 9,937,068 431,433,313
172 10,111,745 441,545,058
173 10,288,458 451,833,516
174 10,467,215 462,300,731
175 10,648,032 472,948,763
176 10,830,920 483,779,683
177 11,015,896 494,795,579
178 11,202,959 505,998,538
179 11,392,128 517,390,666
180 11,583,420 528,974,086
181 11,776,838 540,750,924
182 11,972,395 552,723,319
183 12,170,108 564,893,427
184 12,369,985 577,263,412
185 12,572,037 589,835,449
186 12,776,285 602,611,734
187 12,982,725 615,594,459
188 13,191,377 628,785,836
189 13,402,256 642,188,092
190 13,615,367 655,803,459
191 13,830,730 669,634,189
192 14,048,347 683,682,536
193 14,268,236 697,950,772
194 14,490,415 712,441,187
195 14,714,880 727,156,067
196 14,941,651 742,097,718
197 15,170,748 757,268,466
198 15,402,165 772,670,631
199 15,635,928 788,306,559
200 15,872,045 804,178,604
201 16,110,527 820,289,131
202 16,351,384 836,640,515
203 16,594,632 853,235,147
204 16,840,283 870,075,430
205 17,088,342 887,163,772
206 17,338,826 904,502,598
207 17,591,739 922,094,337
208 17,847,107 939,941,444
209 18,104,934 958,046,378
210 18,365,234 976,411,612
211 18,628,013 995,039,625
212 18,893,289 1,013,932,914
213 19,161,068 1,033,093,982
214 19,431,375 1,052,525,357
215 19,704,205 1,072,229,562
216 19,979,576 1,092,209,138
217 20,257,500 1,112,466,638
218 20,537,988 1,133,004,626
219 20,821,062 1,153,825,688
220 21,106,720 1,174,932,408
221 21,394,982 1,196,327,390
222 21,685,859 1,218,013,249
223 21,979,347 1,239,992,596
224 22,275,484 1,262,268,080
225 22,574,265 1,284,842,345
226 22,875,700 1,307,718,045
227 23,179,816 1,330,897,861
228 23,486,609 1,354,384,470
229 23,796,098 1,378,180,568
230 24,108,300 1,402,288,868
231 24,423,216 1,426,712,084
232 24,740,870 1,451,452,954
233 25,061,260 1,476,514,214
234 25,384,397 1,501,898,611
235 25,710,307 1,527,608,918
236 26,038,994 1,553,647,912
237 26,370,474 1,580,018,386
238 26,704,760 1,606,723,146
239 27,041,843 1,633,764,989
240 27,381,757 1,661,146,746
241 27,724,512 1,688,871,258
242 28,070,118 1,716,941,376
243 28,418,579 1,745,359,955
244 28,769,910 1,774,129,865
245 29,124,123 1,803,253,988
246 29,481,235 1,832,735,223
247 29,841,260 1,862,576,483
248 30,204,196 1,892,780,679
249 30,570,067 1,923,350,746
250 30,938,881 1,954,289,627
251 31,310,645 1,985,600,272
252 31,685,379 2,017,285,651
253 32,063,093 2,049,348,744
254 32,443,792 2,081,792,536
255 32,827,496 2,114,620,032
256 33,214,214 2,147,834,246
257 33,603,951 2,181,438,197
258 33,996,731 2,215,434,928
259 34,392,563 2,249,827,491
260 34,791,447 2,284,618,938
261 35,193,409 2,319,812,347
262 35,598,451 2,355,410,798
263 36,006,588 2,391,417,386
264 36,417,835 2,427,835,221
265 36,832,207 2,464,667,428
266 37,249,701 2,501,917,129
267 37,670,346 2,539,587,475
268 38,094,140 2,577,681,615
269 38,521,101 2,616,202,716
270 38,951,249 2,655,153,965
271 39,384,582 2,694,538,547
272 39,821,110 2,734,359,657
273 40,260,860 2,774,620,517
274 40,703,832 2,815,324,349
275 41,150,044 2,856,474,393
276 41,599,505 2,898,073,898
277 42,052,225 2,940,126,123
278 42,508,220 2,982,634,343
279 42,967,499 3,025,601,842
280 43,430,073 3,069,031,915
281 43,895,955 3,112,927,870
282 44,365,160 3,157,293,030
283 44,837,693 3,202,130,723
284 45,313,573 3,247,444,296
285 45,792,800 3,293,237,096
286 46,275,398 3,339,512,494
287 46,761,379 3,386,273,873
288 47,250,752 3,433,524,625
289 47,743,528 3,481,268,153
290 48,239,713 3,529,507,866
291 48,739,321 3,578,247,187
292 49,242,372 3,627,489,559
293 49,748,878 3,677,238,437
294 50,258,835 3,727,497,272
295 50,772,270 3,778,269,542
296 51,289,181 3,829,558,723
297 51,809,596 3,881,368,319
298 52,333,528 3,933,701,847
299 52,860,969 3,986,562,816
300 53,391,941 4,039,954,757
301 53,926,465 4,093,881,222
302 54,464,535 4,148,345,757
303 55,006,178 4,203,351,935
304 55,551,405 4,258,903,340
305 56,100,219 4,315,003,559
306 56,652,634 4,371,656,193
307 57,208,666 4,428,864,859
308 57,768,319 4,486,633,178
309 58,331,610 4,544,964,788
310 58,898,562 4,603,863,350
311 59,469,169 4,663,332,519
312 60,043,451 4,723,375,970
313 60,621,404 4,783,997,374
314 61,203,070 4,845,200,444
315 61,788,445 4,906,988,889
316 62,377,542 4,969,366,431
317 62,970,363 5,032,336,794
318 63,566,920 5,095,903,714
319 64,167,245 5,160,070,959
320 64,771,341 5,224,842,300
321 65,379,217 5,290,221,517
322 65,990,881 5,356,212,398
323 66,606,345 5,422,818,743
324 67,225,617 5,490,044,360
325 67,848,732 5,557,893,092
326 68,475,682 5,626,368,774
327 69,106,479 5,695,475,253
328 69,741,139 5,765,216,392
329 70,379,662 5,835,596,054
330 71,022,084 5,906,618,138
331 71,668,401 5,978,286,539
332 72,318,631 6,050,605,170
333 72,972,775 6,123,577,945
334 73,630,849 6,197,208,794
335 74,292,868 6,271,501,662
336 74,958,848 6,346,460,510
337 75,628,800 6,422,089,310
338 76,302,729 6,498,392,039
339 76,980,651 6,575,372,690
340 77,662,572 6,653,035,262
341 78,348,501 6,731,383,763
342 79,038,476 6,810,422,239
343 79,732,485 6,890,154,724
344 80,430,535 6,970,585,259
345 81,132,652 7,051,717,911
346 81,838,839 7,133,556,750
347 82,549,112 7,216,105,862
348 83,263,504 7,299,369,366
349 83,981,986 7,383,351,352
350 84,704,585 7,468,055,937
351 85,431,326 7,553,487,263
352 86,162,202 7,639,649,465
353 86,897,253 7,726,546,718
354 87,636,466 7,814,183,184
355 88,379,852 7,902,563,036
356 89,127,430 7,991,690,466
357 89,879,218 8,081,569,684
358 90,635,220 8,172,204,904
359 91,395,454 8,263,600,358
360 92,159,923 8,355,760,281
361 92,928,637 8,448,688,918
362 93,701,621 8,542,390,539
363 94,478,883 8,636,869,422
364 95,260,421 8,732,129,843
365 96,046,268 8,828,176,111
366 96,836,421 8,925,012,532
367 97,630,889 9,022,643,421
368 98,429,696 9,121,073,117
369 99,232,843 9,220,305,960
370 100,040,353 9,320,346,313
371 100,852,238 9,421,198,551
372 101,668,499 9,522,867,050
373 102,489,144 9,625,356,194
374 103,314,199 9,728,670,393
375 104,143,674 9,832,814,067
376 104,977,576 9,937,791,643
377 105,815,912 10,043,607,555
378 106,658,705 10,150,266,260
379 107,505,954 10,257,772,214
380 108,357,683 10,366,129,897
381 109,213,906 10,475,343,803
382 110,074,614 10,585,418,417
383 110,939,841 10,696,358,258
384 111,809,588 10,808,167,846
385 112,683,864 10,920,851,710
386 113,562,690 11,034,414,400
387 114,446,071 11,148,860,471
388 115,334,026 11,264,194,497
389 116,226,561 11,380,421,058
390 117,123,693 11,497,544,751
391 118,025,424 11,615,570,175
392 118,931,765 11,734,501,940
393 119,842,745 11,854,344,685
394 120,758,360 11,975,103,045
395 121,678,631 12,096,781,676
396 122,603,562 12,219,385,238
397 123,533,164 12,342,918,402
398 124,467,455 12,467,385,857
399 125,406,460 12,592,792,317
400 126,350,163 12,719,142,480
401 127,298,591 12,846,441,071
402 128,251,745 12,974,692,816
403 129,209,646 13,103,902,462
404 130,172,320 13,234,074,782
405 131,139,753 13,365,214,535
406 132,111,971 13,497,326,506
407 133,088,973 13,630,415,479
408 134,070,789 13,764,486,268
409 135,057,421 13,899,543,689
410 136,048,875 14,035,592,564
411 137,045,182 14,172,637,746
412 138,046,338 14,310,684,084
413 139,052,346 14,449,736,430
414 140,063,238 14,589,799,668
415 141,079,018 14,730,878,686
416 142,099,700 14,872,978,386
417 143,125,297 15,016,103,683
418 144,155,805 15,160,259,488
419 145,191,242 15,305,450,730
420 146,231,641 15,451,682,371
421 147,276,992 15,598,959,363
422 148,327,320 15,747,286,683
423 149,382,623 15,896,669,306
424 150,442,914 16,047,112,220
425 151,508,210 16,198,620,430
426 152,578,540 16,351,198,970
427 153,653,894 16,504,852,864
428 154,734,281 16,659,587,145
429 155,819,722 16,815,406,867
430 156,910,218 16,972,317,085
431 158,005,799 17,130,322,884
432 159,106,484 17,289,429,368
433 160,212,251 17,449,641,619
434 161,323,131 17,610,964,750
435 162,439,131 17,773,403,881
436 163,560,269 17,936,964,150
437 164,686,558 18,101,650,708
438 165,818,012 18,267,468,720
439 166,954,623 18,434,423,343
440 168,096,417 18,602,519,760
441 169,243,407 18,771,763,167
442 170,395,599 18,942,158,766
443 171,553,023 19,113,711,789
444 172,715,671 19,286,427,460
445 173,883,550 19,460,311,010
446 175,056,690 19,635,367,700
447 176,235,089 19,811,602,789
448 177,418,768 19,989,021,557
449 178,607,751 20,167,629,308
450 179,802,013 20,347,431,321
451 181,001,587 20,528,432,908
452 182,206,494 20,710,639,402
453 183,416,728 20,894,056,130
454 184,632,321 21,078,688,451
455 185,853,274 21,264,541,725
456 187,079,580 21,451,621,305
457 188,311,276 21,639,932,581
458 189,548,370 21,829,480,951
459 190,790,870 22,020,271,821
460 192,038,791 22,212,310,612
461 193,292,138 22,405,602,750
462 194,550,919 22,600,153,669
463 195,815,161 22,795,968,830
464 197,084,876 22,993,053,706
465 198,360,060 23,191,413,766
466 199,640,733 23,391,054,499
467 200,926,905 23,591,981,404
468 202,218,584 23,794,199,988
469 203,515,800 23,997,715,788
470 204,818,544 24,202,534,332
471 206,126,832 24,408,661,164
472 207,440,685 24,616,101,849
473 208,760,119 24,824,861,968
474 210,085,119 25,034,947,087
475 211,415,716 25,246,362,803
476 212,751,926 25,459,114,729
477 214,093,747 25,673,208,476
478 215,441,203 25,888,649,679
479 216,794,302 26,105,443,981
480 218,153,048 26,323,597,029
481 219,517,464 26,543,114,493
482 220,887,563 26,764,002,056
483 222,263,344 26,986,265,400
484 223,644,828 27,209,910,228
485 225,032,028 27,434,942,256
486 226,424,942 27,661,367,198
487 227,823,599 27,889,190,797
488 229,228,006 28,118,418,803
489 230,638,169 28,349,056,972
490 232,054,102 28,581,111,074
491 233,475,830 28,814,586,904
492 234,903,336 29,049,490,240
493 236,336,654 29,285,826,894
494 237,775,798 29,523,602,692
495 239,220,764 29,762,823,456
496 240,671,580 30,003,495,036
497 242,128,250 30,245,623,286
498 243,590,771 30,489,214,057
499 245,059,183 30,734,273,240
500 246,533,493 30,980,806,733
501 248,013,699 31,228,820,432
502 249,499,809 31,478,320,241
503 250,991,840 31,729,312,081
504 252,489,811 31,981,801,892
505 253,993,740 32,235,795,632
506 255,503,630 32,491,299,262
507 257,019,487 32,748,318,749
508 258,541,318 33,006,860,067
509 260,069,150 33,266,929,217
510 261,602,998 33,528,532,215
511 263,142,858 33,791,675,073
512 264,688,761 34,056,363,834
513 266,240,686 34,322,604,520
514 267,798,667 34,590,403,187
515 269,362,724 34,859,765,911
516 270,932,863 35,130,698,774
517 272,509,090 35,403,207,864
518 274,091,421 35,677,299,285
519 275,679,853 35,952,979,138
520 277,274,402 36,230,253,540
521 278,875,111 36,509,128,651
522 280,481,965 36,789,610,616
523 282,094,975 37,071,705,591
524 283,714,160 37,355,419,751
525 285,339,516 37,640,759,267
526 286,971,071 37,927,730,338
527 288,608,851 38,216,339,189
528 290,252,842 38,506,592,031
529 291,903,058 38,798,495,089
530 293,559,520 39,092,054,609
531 295,222,219 39,387,276,828
532 296,891,211 39,684,168,039
533 298,566,487 39,982,734,526
534 300,248,040 40,282,982,566
535 301,935,890 40,584,918,456
536 303,630,050 40,888,548,506
537 305,330,541 41,193,879,047
538 307,037,382 41,500,916,429
539 308,750,566 41,809,666,995
540 310,470,102 42,120,137,097
541 312,196,005 42,432,333,102
542 313,928,307 42,746,261,409
543 315,667,000 43,061,928,409
544 317,412,108 43,379,340,517
545 319,163,637 43,698,504,154
546 320,921,580 44,019,425,734
547 322,685,975 44,342,111,709
548 324,456,823 44,666,568,532
549 326,234,148 44,992,802,680
550 328,017,955 45,320,820,635
551 329,808,237 45,650,628,872
552 331,605,020 45,982,233,892
553 333,408,329 46,315,642,221
554 335,218,158 46,650,860,379
555 337,034,532 46,987,894,911
556 338,857,458 47,326,752,369
557 340,686,929 47,667,439,298
558 342,522,977 48,009,962,275
559 344,365,622 48,354,327,897
560 346,214,855 48,700,542,752
561 348,070,697 49,048,613,449
562 349,933,166 49,398,546,615
563 351,802,250 49,750,348,865
564 353,677,982 50,104,026,847
565 355,560,389 50,459,587,236
566 357,449,446 50,817,036,682
567 359,345,186 51,176,381,868
568 361,247,622 51,537,629,490
569 363,156,743 51,900,786,233
570 365,072,599 52,265,858,832
571 366,995,178 52,632,854,010
572 368,924,482 53,001,778,492
573 370,860,550 53,372,639,042
574 372,803,377 53,745,442,419
575 374,752,970 54,120,195,389
576 376,709,351 54,496,904,740
577 378,672,538 54,875,577,278
578 380,642,517 55,256,219,795
579 382,619,329 55,638,839,124
580 384,602,972 56,023,442,096
581 386,593,454 56,410,035,550
582 388,590,789 56,798,626,339
583 390,595,010 57,189,221,349
584 392,606,094 57,581,827,443
585 394,624,074 57,976,451,517
586 396,648,961 58,373,100,478
587 398,680,746 58,771,781,224
588 400,719,473 59,172,500,697
589 402,765,138 59,575,265,835
590 404,817,751 59,980,083,586
591 406,877,325 60,386,960,911
592 408,943,877 60,795,904,788
593 411,017,405 61,206,922,193
594 413,097,937 61,620,020,130
595 415,185,486 62,035,205,616
596 417,280,043 62,452,485,659
597 419,381,640 62,871,867,299
598 421,490,275 63,293,357,574
599 423,605,964 63,716,963,538
600 425,728,730 64,142,692,268
601 427,858,584 64,570,550,852
602 429,995,514 65,000,546,366
603 432,139,549 65,432,685,915
604 434,290,700 65,866,976,615
605 436,448,976 66,303,425,591
606 438,614,403 66,742,039,994
607 440,786,981 67,182,826,975
608 442,966,711 67,625,793,686
609 445,153,610 68,070,947,296
610 447,347,703 68,518,294,999
611 449,549,001 68,967,844,000
612 451,757,501 69,419,601,501
613 453,973,228 69,873,574,729
614 456,196,175 70,329,770,904
615 458,426,365 70,788,197,269
616 460,663,826 71,248,861,095
617 462,908,554 71,711,769,649
618 465,160,561 72,176,930,210
619 467,419,860 72,644,350,070
620 469,686,448 73,114,036,518
621 471,960,360 73,585,996,878
622 474,241,618 74,060,238,496
623 476,530,204 74,536,768,700
624 478,826,132 75,015,594,832
625 481,129,428 75,496,724,260
626 483,440,089 75,980,164,349
627 485,758,145 76,465,922,494
628 488,083,618 76,954,006,112
629 490,416,477 77,444,422,589
630 492,756,760 77,937,179,349
631 495,104,481 78,432,283,830
632 497,459,641 78,929,743,471
633 499,822,266 79,429,565,737
634 502,192,373 79,931,758,110
635 504,569,937 80,436,328,047
636 506,954,994 80,943,283,041
637 509,347,557 81,452,630,598
638 511,747,640 81,964,378,238
639 514,155,264 82,478,533,502
640 516,570,420 82,995,103,922
641 518,993,113 83,514,097,035
642 521,423,376 84,035,520,411
643 523,861,218 84,559,381,629
644 526,306,648 85,085,688,277
645 528,759,684 85,614,447,961
646 531,220,323 86,145,668,284
647 533,688,567 86,679,356,851
648 536,164,458 87,215,521,309
649 538,648,000 87,754,169,309
650 541,139,199 88,295,308,508
651 543,638,069 88,838,946,577
652 546,144,610 89,385,091,187
653 548,658,840 89,933,750,027
654 551,180,786 90,484,930,813
655 553,710,454 91,038,641,267
656 556,247,840 91,594,889,107
657 558,792,969 92,153,682,076
658 561,345,844 92,715,027,920
659 563,906,480 93,278,934,400
660 566,474,914 93,845,409,314
661 569,051,115 94,414,460,429
662 571,635,117 94,986,095,546
663 574,226,937 95,560,322,483
664 576,826,567 96,137,149,050
665 579,434,030 96,716,583,080
666 582,049,366 97,298,632,446
667 584,672,536 97,883,304,982
668 587,303,581 98,470,608,563
669 589,942,514 99,060,551,077
670 592,589,322 99,653,140,399
671 595,244,049 100,248,384,448
672 597,906,695 100,846,291,143
673 600,577,260 101,446,868,403
674 603,255,766 102,050,124,169
675 605,942,236 102,656,066,405
676 608,636,654 103,264,703,059
677 611,339,057 103,876,042,116
678 614,049,454 104,490,091,570
679 616,767,836 105,106,859,406
680 619,494,237 105,726,353,643
681 622,228,669 106,348,582,312
682 624,971,111 106,973,553,423
683 627,721,619 107,601,275,042
684 630,480,188 108,231,755,230
685 633,246,807 108,865,002,037
686 636,021,523 109,501,023,560
687 638,804,337 110,139,827,897
688 641,595,238 110,781,423,135
689 644,394,268 111,425,817,403
690 647,201,430 112,073,018,833
691 650,016,725 112,723,035,558
692 652,840,181 113,375,875,739
693 655,671,798 114,031,547,537
694 658,511,580 114,690,059,117
695 661,359,560 115,351,418,677
696 664,215,752 116,015,634,429
697 667,080,136 116,682,714,565
698 669,952,749 117,352,667,314
699 672,833,595 118,025,500,909
700 675,722,681 118,701,223,590
701 678,620,041 119,379,843,631
702 681,525,676 120,061,369,307
703 684,439,577 120,745,808,884
704 687,361,771 121,433,170,655
705 690,292,278 122,123,462,933
706 693,231,099 122,816,694,032
707 696,178,256 123,512,872,288
708 699,133,759 124,212,006,047
709 702,097,596 124,914,103,643
710 705,069,795 125,619,173,438
711 708,050,393 126,327,223,831
712 711,039,368 127,038,263,199
713 714,036,747 127,752,299,946
714 717,042,543 128,469,342,489
715 720,056,742 129,189,399,231
716 723,079,380 129,912,478,611
717 726,110,482 130,638,589,093
718 729,150,037 131,367,739,130
719 732,198,064 132,099,937,194
720 735,254,569 132,835,191,763
721 738,319,559 133,573,511,322
722 741,393,060 134,314,904,382
723 744,475,094 135,059,379,476
724 747,565,659 135,806,945,135
725 750,664,744 136,557,609,879
726 753,772,388 137,311,382,267
727 756,888,595 138,068,270,862
728 760,013,385 138,828,284,247
729 763,146,783 139,591,431,030
730 766,288,759 140,357,719,789
731 769,439,338 141,127,159,127
732 772,598,558 141,899,757,685
733 775,766,400 142,675,524,085
734 778,942,907 143,454,466,992
735 782,128,077 144,236,595,069
736 785,321,894 145,021,916,963
737 788,524,396 145,810,441,359
738 791,735,604 146,602,176,963
739 794,955,517 147,397,132,480
740 798,184,157 148,195,316,637
741 801,421,525 148,996,738,162
742 804,667,618 149,801,405,780
743 807,922,471 150,609,328,251
744 811,186,096 151,420,514,347
745 814,458,498 152,234,972,845
746 817,739,685 153,052,712,530
747 821,029,676 153,873,742,206
748 824,328,464 154,698,070,670
749 827,636,092 155,525,706,762
750 830,952,560 156,356,659,322
751 834,277,871 157,190,937,193
752 837,612,047 158,028,549,240
753 840,955,082 158,869,504,322
754 844,306,994 159,713,811,316
755 847,667,815 160,561,479,131
756 851,037,549 161,412,516,680
757 854,416,192 162,266,932,872
758 857,803,768 163,124,736,640
759 861,200,279 163,985,936,919
760 864,605,743 164,850,542,662
761 868,020,193 165,718,562,855
762 871,443,606 166,590,006,461
763 874,876,004 167,464,882,465
764 878,317,410 168,343,199,875
765 881,767,824 169,224,967,699
766 885,227,258 170,110,194,957
767 888,695,753 170,998,890,710
768 892,173,277 171,891,063,987
769 895,659,858 172,786,723,845
770 899,155,529 173,685,879,374
771 902,660,259 174,588,539,633
772 906,174,094 175,494,713,727
773 909,697,050 176,404,410,777
774 913,229,102 177,317,639,879
775 916,770,298 178,234,410,177
776 920,320,644 179,154,730,821
777 923,880,129 180,078,610,950
778 927,448,783 181,006,059,733
779 931,026,635 181,937,086,368
780 934,613,655 182,871,700,023
781 938,209,881 183,809,909,904
782 941,815,324 184,751,725,228
783 945,429,974 185,697,155,202
784 949,053,881 186,646,209,083
785 952,687,045 187,598,896,128
786 956,329,448 188,555,225,576
787 959,981,129 189,515,206,705
788 963,642,105 190,478,848,810
789 967,312,357 191,446,161,167
790 970,991,935 192,417,153,102
791 974,680,833 193,391,833,935
792 978,379,049 194,370,212,984
793 982,086,613 195,352,299,597
794 985,803,536 196,338,103,133
795 989,529,810 197,327,632,943
796 993,265,478 198,320,898,421
797 997,010,545 199,317,908,966
798 1,000,764,994 200,318,673,960
799 1,004,528,858 201,323,202,818
800 1,008,302,151 202,331,504,969
801 1,012,084,878 203,343,589,847
802 1,015,877,069 204,359,466,916
803 1,019,678,727 205,379,145,643
804 1,023,489,826 206,402,635,469
805 1,027,310,417 207,429,945,886
806 1,031,140,520 208,461,086,406
807 1,034,980,118 209,496,066,524
808 1,038,829,250 210,534,895,774
809 1,042,687,909 211,577,583,683
810 1,046,556,085 212,624,139,768
811 1,050,433,829 213,674,573,597
812 1,054,321,168 214,728,894,765
813 1,058,218,065 215,787,112,830
814 1,062,124,559 216,849,237,389
815 1,066,040,649 217,915,278,038
816 1,069,966,339 218,985,244,377
817 1,073,901,670 220,059,146,047
818 1,077,846,651 221,136,992,698
819 1,081,801,268 222,218,793,966
820 1,085,765,541 223,304,559,507
821 1,089,739,494 224,394,299,001
822 1,093,723,121 225,488,022,122
823 1,097,716,454 226,585,738,576
824 1,101,719,513 227,687,458,089
825 1,105,732,275 228,793,190,364
826 1,109,754,761 229,902,945,125
827 1,113,786,994 231,016,732,119
828 1,117,828,979 232,134,561,098
829 1,121,880,744 233,256,441,842
830 1,125,942,303 234,382,384,145
831 1,130,013,622 235,512,397,767
832 1,134,094,745 236,646,492,512
833 1,138,185,692 237,784,678,204
834 1,142,286,467 238,926,964,671
835 1,146,397,089 240,073,361,760
836 1,150,517,555 241,223,879,315
837 1,154,647,866 242,378,527,181
838 1,158,788,047 243,537,315,228
839 1,162,938,143 244,700,253,371
840 1,167,098,124 245,867,351,495
841 1,171,268,015 247,038,619,510
842 1,175,447,830 248,214,067,340
843 1,179,637,549 249,393,704,889
844 1,183,837,229 250,577,542,118
845 1,188,046,885 251,765,589,003
846 1,192,266,486 252,957,855,489
847 1,196,496,074 254,154,351,563
848 1,200,735,653 255,355,087,216
849 1,204,985,220 256,560,072,436
850 1,209,244,821 257,769,317,257
851 1,213,514,457 258,982,831,714
852 1,217,794,109 260,200,625,823
853 1,222,083,827 261,422,709,650
854 1,226,383,592 262,649,093,242
855 1,230,693,429 263,879,786,671
856 1,235,013,363 265,114,800,034
857 1,239,343,402 266,354,143,436
858 1,243,683,533 267,597,826,969
859 1,248,033,793 268,845,860,762
860 1,252,394,180 270,098,254,942
861 1,256,764,708 271,355,019,650
862 1,261,145,413 272,616,165,063
863 1,265,536,277 273,881,701,340
864 1,269,937,307 275,151,638,647
865 1,274,348,541 276,425,987,188
866 1,278,769,968 277,704,757,156
867 1,283,201,615 278,987,958,771
868 1,287,643,503 280,275,602,274
869 1,292,095,618 281,567,697,892
870 1,296,557,975 282,864,255,867
871 1,301,030,613 284,165,286,480
872 1,305,513,506 285,470,799,986
873 1,310,006,698 286,780,806,684
874 1,314,510,190 288,095,316,874
875 1,319,023,979 289,414,340,853
876 1,323,548,095 290,737,888,948
877 1,328,082,553 292,065,971,501
Counting took 196.092327 seconds</pre>
=={{header|Crystal}}==
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