Prime Factors

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Script Name Prime Factors
Description Prime factors calculation
Area SQL General
Contributor jackattack
Created Saturday June 10, 2017

Statement 1

Prime factors of a Natural number (ie. 21)

WITH naturals AS (  
    SELECT  level+1 i  
    FROM    dual  
    CONNECT BY LEVEL <= 999  
)  
, primes AS ( 
    SELECT  n.i  
    FROM    naturals n  
    WHERE   NOT EXISTS (  
                SELECT 1  
                FROM   naturals n2  
                WHERE  n2.i <= SQRT(n.i)   
                AND REMAINDER(n.i, n2.i) = 0  
    ) 
) 
SELECT  p.i 
FROM    primes p 
WHERE   REMAINDER(21, p.i) = 0


I
3
7

2 rows selected.

I
3
7

Statement 2

Natural numbers < 1000 with at least 4 prime factors

WITH  
    naturals AS (  
        SELECT  level+1 i  
        FROM    dual  
        CONNECT BY LEVEL <= 999  
    ),  
    primes AS ( 
        SELECT  n.i  
        FROM    naturals n  
        WHERE   NOT EXISTS (  
                    SELECT 1  
                    FROM   naturals n2  
                    WHERE  n2.i <= SQRT(n.i)   
                    AND REMAINDER(n.i, n2.i) = 0  
        ) 
    ) 
SELECT  n.i n, LISTAGG(p.i, ', ') WITHIN GROUP (ORDER BY p.i) prime_factors 
FROM    naturals n CROSS JOIN primes p 
WHERE   REMAINDER(n.i, p.i) = 0 
group   by n.i 
HAVING  COUNT(*) > 3 
order   by 1


N PRIME_FACTORS
210 2, 3, 5, 7
330 2, 3, 5, 11
390 2, 3, 5, 13
420 2, 3, 5, 7
462 2, 3, 7, 11
510 2, 3, 5, 17
546 2, 3, 7, 13
570 2, 3, 5, 19
630 2, 3, 5, 7
660 2, 3, 5, 11
690 2, 3, 5, 23
714 2, 3, 7, 17
770 2, 5, 7, 11
780 2, 3, 5, 13
798 2, 3, 7, 19
840 2, 3, 5, 7
858 2, 3, 11, 13
870 2, 3, 5, 29
910 2, 5, 7, 13
924 2, 3, 7, 11
930 2, 3, 5, 31
966 2, 3, 7, 23
990 2, 3, 5, 11

23 rows selected.

N	PRIME_FACTORS
210	2, 3, 5, 7
330	2, 3, 5, 11
390	2, 3, 5, 13
420	2, 3, 5, 7
462	2, 3, 7, 11
510	2, 3, 5, 17
546	2, 3, 7, 13
570	2, 3, 5, 19
630	2, 3, 5, 7
660	2, 3, 5, 11
690	2, 3, 5, 23
714	2, 3, 7, 17
770	2, 5, 7, 11
780	2, 3, 5, 13
798	2, 3, 7, 19
840	2, 3, 5, 7
858	2, 3, 11, 13
870	2, 3, 5, 29
910	2, 5, 7, 13
924	2, 3, 7, 11
930	2, 3, 5, 31
966	2, 3, 7, 23
990	2, 3, 5, 11

Statement 3

Natural numbers < 1000, prime factors

WITH  
    naturals AS (  
        SELECT  level+1 i  
        FROM    dual  
        CONNECT BY LEVEL <= 999  
    ),  
    primes AS ( 
        SELECT  n.i  
        FROM    naturals n  
        WHERE   NOT EXISTS (  
                    SELECT 1  
                    FROM   naturals n2  
                    WHERE  n2.i <= SQRT(n.i)   
                    AND REMAINDER(n.i, n2.i) = 0  
        ) 
    ) 
SELECT  n.i n, LISTAGG(p.i, ', ') WITHIN GROUP (ORDER BY p.i) prime_factors 
FROM    naturals n CROSS JOIN primes p 
WHERE   REMAINDER(n.i, p.i) = 0 
GROUP   BY n.i 
ORDER   BY 1


N PRIME_FACTORS
2 2
3 3
4 2
5 5
6 2, 3
7 7
8 2
9 3
10 2, 5
11 11
12 2, 3
13 13
14 2, 7
15 3, 5
16 2
17 17
18 2, 3
19 19
20 2, 5
21 3, 7
22 2, 11
23 23
24 2, 3
25 5
26 2, 13
27 3
28 2, 7
29 29
30 2, 3, 5
31 31
32 2
33 3, 11
34 2, 17
35 5, 7
36 2, 3
37 37
38 2, 19
39 3, 13
40 2, 5
41 41
42 2, 3, 7
43 43
44 2, 11
45 3, 5
46 2, 23
47 47
48 2, 3
49 7
50 2, 5
51 3, 17
52 2, 13
53 53
54 2, 3
55 5, 11
56 2, 7
57 3, 19
58 2, 29
59 59
60 2, 3, 5
61 61
62 2, 31
63 3, 7
64 2
65 5, 13
66 2, 3, 11
67 67
68 2, 17
69 3, 23
70 2, 5, 7
71 71
72 2, 3
73 73
74 2, 37
75 3, 5
76 2, 19
77 7, 11
78 2, 3, 13
79 79
80 2, 5
81 3
82 2, 41
83 83
84 2, 3, 7
85 5, 17
86 2, 43
87 3, 29
88 2, 11
89 89
90 2, 3, 5
91 7, 13
92 2, 23
93 3, 31
94 2, 47
95 5, 19
96 2, 3
97 97
98 2, 7
99 3, 11
100 2, 5
101 101
102 2, 3, 17
103 103
104 2, 13
105 3, 5, 7
106 2, 53
107 107
108 2, 3
109 109
110 2, 5, 11
111 3, 37
112 2, 7
113 113
114 2, 3, 19
115 5, 23
116 2, 29
117 3, 13
118 2, 59
119 7, 17
120 2, 3, 5
121 11
122 2, 61
123 3, 41
124 2, 31
125 5
126 2, 3, 7
127 127
128 2
129 3, 43
130 2, 5, 13
131 131
132 2, 3, 11
133 7, 19
134 2, 67
135 3, 5
136 2, 17
137 137
138 2, 3, 23
139 139
140 2, 5, 7
141 3, 47
142 2, 71
143 11, 13
144 2, 3
145 5, 29
146 2, 73
147 3, 7
148 2, 37
149 149
150 2, 3, 5
151 151
152 2, 19
153 3, 17
154 2, 7, 11
155 5, 31
156 2, 3, 13
157 157
158 2, 79
159 3, 53
160 2, 5
161 7, 23
162 2, 3
163 163
164 2, 41
165 3, 5, 11
166 2, 83
167 167
168 2, 3, 7
169 13
170 2, 5, 17
171 3, 19
172 2, 43
173 173
174 2, 3, 29
175 5, 7
176 2, 11
177 3, 59
178 2, 89
179 179
180 2, 3, 5
181 181
182 2, 7, 13
183 3, 61
184 2, 23
185 5, 37
186 2, 3, 31
187 11, 17
188 2, 47
189 3, 7
190 2, 5, 19
191 191
192 2, 3
193 193
194 2, 97
195 3, 5, 13
196 2, 7
197 197
198 2, 3, 11
199 199
200 2, 5
201 3, 67
202 2, 101
203 7, 29
204 2, 3, 17
205 5, 41
206 2, 103
207 3, 23
208 2, 13
209 11, 19
210 2, 3, 5, 7
211 211
212 2, 53
213 3, 71
214 2, 107
215 5, 43
216 2, 3
217 7, 31
218 2, 109
219 3, 73
220 2, 5, 11
221 13, 17
222 2, 3, 37
223 223
224 2, 7
225 3, 5
226 2, 113
227 227
228 2, 3, 19
229 229
230 2, 5, 23
231 3, 7, 11
232 2, 29
233 233
234 2, 3, 13
235 5, 47
236 2, 59
237 3, 79
238 2, 7, 17
239 239
240 2, 3, 5
241 241
242 2, 11
243 3
244 2, 61
245 5, 7
246 2, 3, 41
247 13, 19
248 2, 31
249 3, 83
250 2, 5
251 251
252 2, 3, 7
253 11, 23
254 2, 127
255 3, 5, 17
256 2
257 257
258 2, 3, 43
259 7, 37
260 2, 5, 13
261 3, 29
262 2, 131
263 263
264 2, 3, 11
265 5, 53
266 2, 7, 19
267 3, 89
268 2, 67
269 269
270 2, 3, 5
271 271
272 2, 17
273 3, 7, 13
274 2, 137
275 5, 11
276 2, 3, 23
277 277
278 2, 139
279 3, 31
280 2, 5, 7
281 281
282 2, 3, 47
283 283
284 2, 71
285 3, 5, 19
286 2, 11, 13
287 7, 41
288 2, 3
289 17
290 2, 5, 29
291 3, 97
292 2, 73
293 293
294 2, 3, 7
295 5, 59
296 2, 37
297 3, 11
298 2, 149
299 13, 23
300 2, 3, 5
301 7, 43
302 2, 151
303 3, 101
304 2, 19
305 5, 61
306 2, 3, 17
307 307
308 2, 7, 11
309 3, 103
310 2, 5, 31
311 311
312 2, 3, 13
313 313
314 2, 157
315 3, 5, 7
316 2, 79
317 317
318 2, 3, 53
319 11, 29
320 2, 5
321 3, 107
322 2, 7, 23
323 17, 19
324 2, 3
325 5, 13
326 2, 163
327 3, 109
328 2, 41
329 7, 47
330 2, 3, 5, 11
331 331
332 2, 83
333 3, 37
334 2, 167
335 5, 67
336 2, 3, 7
337 337
338 2, 13
339 3, 113
340 2, 5, 17
341 11, 31
342 2, 3, 19
343 7
344 2, 43
345 3, 5, 23
346 2, 173
347 347
348 2, 3, 29
349 349
350 2, 5, 7
351 3, 13
352 2, 11
353 353
354 2, 3, 59
355 5, 71
356 2, 89
357 3, 7, 17
358 2, 179
359 359
360 2, 3, 5
361 19
362 2, 181
363 3, 11
364 2, 7, 13
365 5, 73
366 2, 3, 61
367 367
368 2, 23
369 3, 41
370 2, 5, 37
371 7, 53
372 2, 3, 31
373 373
374 2, 11, 17
375 3, 5
376 2, 47
377 13, 29
378 2, 3, 7
379 379
380 2, 5, 19
381 3, 127
382 2, 191
383 383
384 2, 3
385 5, 7, 11
386 2, 193
387 3, 43
388 2, 97
389 389
390 2, 3, 5, 13
391 17, 23
392 2, 7
393 3, 131
394 2, 197
395 5, 79
396 2, 3, 11
397 397
398 2, 199
399 3, 7, 19
400 2, 5
401 401
402 2, 3, 67
403 13, 31
404 2, 101
405 3, 5
406 2, 7, 29
407 11, 37
408 2, 3, 17
409 409
410 2, 5, 41
411 3, 137
412 2, 103
413 7, 59
414 2, 3, 23
415 5, 83
416 2, 13
417 3, 139
418 2, 11, 19
419 419
420 2, 3, 5, 7
421 421
422 2, 211
423 3, 47
424 2, 53
425 5, 17
426 2, 3, 71
427 7, 61
428 2, 107
429 3, 11, 13
430 2, 5, 43
431 431
432 2, 3
433 433
434 2, 7, 31
435 3, 5, 29
436 2, 109
437 19, 23
438 2, 3, 73
439 439
440 2, 5, 11
441 3, 7
442 2, 13, 17
443 443
444 2, 3, 37
445 5, 89
446 2, 223
447 3, 149
448 2, 7
449 449
450 2, 3, 5
451 11, 41
452 2, 113
453 3, 151
454 2, 227
455 5, 7, 13
456 2, 3, 19
457 457
458 2, 229
459 3, 17
460 2, 5, 23
461 461
462 2, 3, 7, 11
463 463
464 2, 29
465 3, 5, 31
466 2, 233
467 467
468 2, 3, 13
469 7, 67
470 2, 5, 47
471 3, 157
472 2, 59
473 11, 43
474 2, 3, 79
475 5, 19
476 2, 7, 17
477 3, 53
478 2, 239
479 479
480 2, 3, 5
481 13, 37
482 2, 241
483 3, 7, 23
484 2, 11
485 5, 97
486 2, 3
487 487
488 2, 61
489 3, 163
490 2, 5, 7
491 491
492 2, 3, 41
493 17, 29
494 2, 13, 19
495 3, 5, 11
496 2, 31
497 7, 71
498 2, 3, 83
499 499
500 2, 5
501 3, 167
502 2, 251
503 503
504 2, 3, 7
505 5, 101
506 2, 11, 23
507 3, 13
508 2, 127
509 509
510 2, 3, 5, 17
511 7, 73
512 2
513 3, 19
514 2, 257
515 5, 103
516 2, 3, 43
517 11, 47
518 2, 7, 37
519 3, 173
520 2, 5, 13
521 521
522 2, 3, 29
523 523
524 2, 131
525 3, 5, 7
526 2, 263
527 17, 31
528 2, 3, 11
529 23
530 2, 5, 53
531 3, 59
532 2, 7, 19
533 13, 41
534 2, 3, 89
535 5, 107
536 2, 67
537 3, 179
538 2, 269
539 7, 11
540 2, 3, 5
541 541
542 2, 271
543 3, 181
544 2, 17
545 5, 109
546 2, 3, 7, 13
547 547
548 2, 137
549 3, 61
550 2, 5, 11
551 19, 29
552 2, 3, 23
553 7, 79
554 2, 277
555 3, 5, 37
556 2, 139
557 557
558 2, 3, 31
559 13, 43
560 2, 5, 7
561 3, 11, 17
562 2, 281
563 563
564 2, 3, 47
565 5, 113
566 2, 283
567 3, 7
568 2, 71
569 569
570 2, 3, 5, 19
571 571
572 2, 11, 13
573 3, 191
574 2, 7, 41
575 5, 23
576 2, 3
577 577
578 2, 17
579 3, 193
580 2, 5, 29
581 7, 83
582 2, 3, 97
583 11, 53
584 2, 73
585 3, 5, 13
586 2, 293
587 587
588 2, 3, 7
589 19, 31
590 2, 5, 59
591 3, 197
592 2, 37
593 593
594 2, 3, 11
595 5, 7, 17
596 2, 149
597 3, 199
598 2, 13, 23
599 599
600 2, 3, 5
601 601
602 2, 7, 43
603 3, 67
604 2, 151
605 5, 11
606 2, 3, 101
607 607
608 2, 19
609 3, 7, 29
610 2, 5, 61
611 13, 47
612 2, 3, 17
613 613
614 2, 307
615 3, 5, 41
616 2, 7, 11
617 617
618 2, 3, 103
619 619
620 2, 5, 31
621 3, 23
622 2, 311
623 7, 89
624 2, 3, 13
625 5
626 2, 313
627 3, 11, 19
628 2, 157
629 17, 37
630 2, 3, 5, 7
631 631
632 2, 79
633 3, 211
634 2, 317
635 5, 127
636 2, 3, 53
637 7, 13
638 2, 11, 29
639 3, 71
640 2, 5
641 641
642 2, 3, 107
643 643
644 2, 7, 23
645 3, 5, 43
646 2, 17, 19
647 647
648 2, 3
649 11, 59
650 2, 5, 13
651 3, 7, 31
652 2, 163
653 653
654 2, 3, 109
655 5, 131
656 2, 41
657 3, 73
658 2, 7, 47
659 659
660 2, 3, 5, 11
661 661
662 2, 331
663 3, 13, 17
664 2, 83
665 5, 7, 19
666 2, 3, 37
667 23, 29
668 2, 167
669 3, 223
670 2, 5, 67
671 11, 61
672 2, 3, 7
673 673
674 2, 337
675 3, 5
676 2, 13
677 677
678 2, 3, 113
679 7, 97
680 2, 5, 17
681 3, 227
682 2, 11, 31
683 683
684 2, 3, 19
685 5, 137
686 2, 7
687 3, 229
688 2, 43
689 13, 53
690 2, 3, 5, 23
691 691
692 2, 173
693 3, 7, 11
694 2, 347
695 5, 139
696 2, 3, 29
697 17, 41
698 2, 349
699 3, 233
700 2, 5, 7
701 701
702 2, 3, 13
703 19, 37
704 2, 11
705 3, 5, 47
706 2, 353
707 7, 101
708 2, 3, 59
709 709
710 2, 5, 71
711 3, 79
712 2, 89
713 23, 31
714 2, 3, 7, 17
715 5, 11, 13
716 2, 179
717 3, 239
718 2, 359
719 719
720 2, 3, 5
721 7, 103
722 2, 19
723 3, 241
724 2, 181
725 5, 29
726 2, 3, 11
727 727
728 2, 7, 13
729 3
730 2, 5, 73
731 17, 43
732 2, 3, 61
733 733
734 2, 367
735 3, 5, 7
736 2, 23
737 11, 67
738 2, 3, 41
739 739
740 2, 5, 37
741 3, 13, 19
742 2, 7, 53
743 743
744 2, 3, 31
745 5, 149
746 2, 373
747 3, 83
748 2, 11, 17
749 7, 107
750 2, 3, 5
751 751
752 2, 47
753 3, 251
754 2, 13, 29
755 5, 151
756 2, 3, 7
757 757
758 2, 379
759 3, 11, 23
760 2, 5, 19
761 761
762 2, 3, 127
763 7, 109
764 2, 191
765 3, 5, 17
766 2, 383
767 13, 59
768 2, 3
769 769
770 2, 5, 7, 11
771 3, 257
772 2, 193
773 773
774 2, 3, 43
775 5, 31
776 2, 97
777 3, 7, 37
778 2, 389
779 19, 41
780 2, 3, 5, 13
781 11, 71
782 2, 17, 23
783 3, 29
784 2, 7
785 5, 157
786 2, 3, 131
787 787
788 2, 197
789 3, 263
790 2, 5, 79
791 7, 113
792 2, 3, 11
793 13, 61
794 2, 397
795 3, 5, 53
796 2, 199
797 797
798 2, 3, 7, 19
799 17, 47
800 2, 5
801 3, 89
802 2, 401
803 11, 73
804 2, 3, 67
805 5, 7, 23
806 2, 13, 31
807 3, 269
808 2, 101
809 809
810 2, 3, 5
811 811
812 2, 7, 29
813 3, 271
814 2, 11, 37
815 5, 163
816 2, 3, 17
817 19, 43
818 2, 409
819 3, 7, 13
820 2, 5, 41
821 821
822 2, 3, 137
823 823
824 2, 103
825 3, 5, 11
826 2, 7, 59
827 827
828 2, 3, 23
829 829
830 2, 5, 83
831 3, 277
832 2, 13
833 7, 17
834 2, 3, 139
835 5, 167
836 2, 11, 19
837 3, 31
838 2, 419
839 839
840 2, 3, 5, 7
841 29
842 2, 421
843 3, 281
844 2, 211
845 5, 13
846 2, 3, 47
847 7, 11
848 2, 53
849 3, 283
850 2, 5, 17
851 23, 37
852 2, 3, 71
853 853
854 2, 7, 61
855 3, 5, 19
856 2, 107
857 857
858 2, 3, 11, 13
859 859
860 2, 5, 43
861 3, 7, 41
862 2, 431
863 863
864 2, 3
865 5, 173
866 2, 433
867 3, 17
868 2, 7, 31
869 11, 79
870 2, 3, 5, 29
871 13, 67
872 2, 109
873 3, 97
874 2, 19, 23
875 5, 7
876 2, 3, 73
877 877
878 2, 439
879 3, 293
880 2, 5, 11
881 881
882 2, 3, 7
883 883
884 2, 13, 17
885 3, 5, 59
886 2, 443
887 887
888 2, 3, 37
889 7, 127
890 2, 5, 89
891 3, 11
892 2, 223
893 19, 47
894 2, 3, 149
895 5, 179
896 2, 7
897 3, 13, 23
898 2, 449
899 29, 31
900 2, 3, 5
901 17, 53
902 2, 11, 41
903 3, 7, 43
904 2, 113
905 5, 181
906 2, 3, 151
907 907
908 2, 227
909 3, 101
910 2, 5, 7, 13
911 911
912 2, 3, 19
913 11, 83
914 2, 457
915 3, 5, 61
916 2, 229
917 7, 131
918 2, 3, 17
919 919
920 2, 5, 23
921 3, 307
922 2, 461
923 13, 71
924 2, 3, 7, 11
925 5, 37
926 2, 463
927 3, 103
928 2, 29
929 929
930 2, 3, 5, 31
931 7, 19
932 2, 233
933 3, 311
934 2, 467
935 5, 11, 17
936 2, 3, 13
937 937
938 2, 7, 67
939 3, 313
940 2, 5, 47
941 941
942 2, 3, 157
943 23, 41
944 2, 59
945 3, 5, 7
946 2, 11, 43
947 947
948 2, 3, 79
949 13, 73
950 2, 5, 19
951 3, 317
952 2, 7, 17
953 953
954 2, 3, 53
955 5, 191
956 2, 239
957 3, 11, 29
958 2, 479
959 7, 137
960 2, 3, 5
961 31
962 2, 13, 37
963 3, 107
964 2, 241
965 5, 193
966 2, 3, 7, 23
967 967
968 2, 11
969 3, 17, 19
970 2, 5, 97
971 971
972 2, 3
973 7, 139
974 2, 487
975 3, 5, 13
976 2, 61
977 977
978 2, 3, 163
979 11, 89
980 2, 5, 7
981 3, 109
982 2, 491
983 983
984 2, 3, 41
985 5, 197
986 2, 17, 29
987 3, 7, 47
988 2, 13, 19
989 23, 43
990 2, 3, 5, 11
991 991
992 2, 31
993 3, 331
994 2, 7, 71
995 5, 199
996 2, 3, 83
997 997
998 2, 499
999 3, 37
1000 2, 5

999 rows selected.

N	PRIME_FACTORS
2	2
3	3
4	2
5	5
6	2, 3
7	7
8	2
9	3
10	2, 5
11	11
12	2, 3
13	13
14	2, 7
15	3, 5
16	2
17	17
18	2, 3
19	19
20	2, 5
21	3, 7
22	2, 11
23	23
24	2, 3
25	5
26	2, 13
27	3
28	2, 7
29	29
30	2, 3, 5
31	31
32	2
33	3, 11
34	2, 17
35	5, 7
36	2, 3
37	37
38	2, 19
39	3, 13
40	2, 5
41	41
42	2, 3, 7
43	43
44	2, 11
45	3, 5
46	2, 23
47	47
48	2, 3
49	7
50	2, 5
51	3, 17
52	2, 13
53	53
54	2, 3
55	5, 11
56	2, 7
57	3, 19
58	2, 29
59	59
60	2, 3, 5
61	61
62	2, 31
63	3, 7
64	2
65	5, 13
66	2, 3, 11
67	67
68	2, 17
69	3, 23
70	2, 5, 7
71	71
72	2, 3
73	73
74	2, 37
75	3, 5
76	2, 19
77	7, 11
78	2, 3, 13
79	79
80	2, 5
81	3
82	2, 41
83	83
84	2, 3, 7
85	5, 17
86	2, 43
87	3, 29
88	2, 11
89	89
90	2, 3, 5
91	7, 13
92	2, 23
93	3, 31
94	2, 47
95	5, 19
96	2, 3
97	97
98	2, 7
99	3, 11
100	2, 5
101	101
102	2, 3, 17
103	103
104	2, 13
105	3, 5, 7
106	2, 53
107	107
108	2, 3
109	109
110	2, 5, 11
111	3, 37
112	2, 7
113	113
114	2, 3, 19
115	5, 23
116	2, 29
117	3, 13
118	2, 59
119	7, 17
120	2, 3, 5
121	11
122	2, 61
123	3, 41
124	2, 31
125	5
126	2, 3, 7
127	127
128	2
129	3, 43
130	2, 5, 13
131	131
132	2, 3, 11
133	7, 19
134	2, 67
135	3, 5
136	2, 17
137	137
138	2, 3, 23
139	139
140	2, 5, 7
141	3, 47
142	2, 71
143	11, 13
144	2, 3
145	5, 29
146	2, 73
147	3, 7
148	2, 37
149	149
150	2, 3, 5
151	151
152	2, 19
153	3, 17
154	2, 7, 11
155	5, 31
156	2, 3, 13
157	157
158	2, 79
159	3, 53
160	2, 5
161	7, 23
162	2, 3
163	163
164	2, 41
165	3, 5, 11
166	2, 83
167	167
168	2, 3, 7
169	13
170	2, 5, 17
171	3, 19
172	2, 43
173	173
174	2, 3, 29
175	5, 7
176	2, 11
177	3, 59
178	2, 89
179	179
180	2, 3, 5
181	181
182	2, 7, 13
183	3, 61
184	2, 23
185	5, 37
186	2, 3, 31
187	11, 17
188	2, 47
189	3, 7
190	2, 5, 19
191	191
192	2, 3
193	193
194	2, 97
195	3, 5, 13
196	2, 7
197	197
198	2, 3, 11
199	199
200	2, 5
201	3, 67
202	2, 101
203	7, 29
204	2, 3, 17
205	5, 41
206	2, 103
207	3, 23
208	2, 13
209	11, 19
210	2, 3, 5, 7
211	211
212	2, 53
213	3, 71
214	2, 107
215	5, 43
216	2, 3
217	7, 31
218	2, 109
219	3, 73
220	2, 5, 11
221	13, 17
222	2, 3, 37
223	223
224	2, 7
225	3, 5
226	2, 113
227	227
228	2, 3, 19
229	229
230	2, 5, 23
231	3, 7, 11
232	2, 29
233	233
234	2, 3, 13
235	5, 47
236	2, 59
237	3, 79
238	2, 7, 17
239	239
240	2, 3, 5
241	241
242	2, 11
243	3
244	2, 61
245	5, 7
246	2, 3, 41
247	13, 19
248	2, 31
249	3, 83
250	2, 5
251	251
252	2, 3, 7
253	11, 23
254	2, 127
255	3, 5, 17
256	2
257	257
258	2, 3, 43
259	7, 37
260	2, 5, 13
261	3, 29
262	2, 131
263	263
264	2, 3, 11
265	5, 53
266	2, 7, 19
267	3, 89
268	2, 67
269	269
270	2, 3, 5
271	271
272	2, 17
273	3, 7, 13
274	2, 137
275	5, 11
276	2, 3, 23
277	277
278	2, 139
279	3, 31
280	2, 5, 7
281	281
282	2, 3, 47
283	283
284	2, 71
285	3, 5, 19
286	2, 11, 13
287	7, 41
288	2, 3
289	17
290	2, 5, 29
291	3, 97
292	2, 73
293	293
294	2, 3, 7
295	5, 59
296	2, 37
297	3, 11
298	2, 149
299	13, 23
300	2, 3, 5
301	7, 43
302	2, 151
303	3, 101
304	2, 19
305	5, 61
306	2, 3, 17
307	307
308	2, 7, 11
309	3, 103
310	2, 5, 31
311	311
312	2, 3, 13
313	313
314	2, 157
315	3, 5, 7
316	2, 79
317	317
318	2, 3, 53
319	11, 29
320	2, 5
321	3, 107
322	2, 7, 23
323	17, 19
324	2, 3
325	5, 13
326	2, 163
327	3, 109
328	2, 41
329	7, 47
330	2, 3, 5, 11
331	331
332	2, 83
333	3, 37
334	2, 167
335	5, 67
336	2, 3, 7
337	337
338	2, 13
339	3, 113
340	2, 5, 17
341	11, 31
342	2, 3, 19
343	7
344	2, 43
345	3, 5, 23
346	2, 173
347	347
348	2, 3, 29
349	349
350	2, 5, 7
351	3, 13
352	2, 11
353	353
354	2, 3, 59
355	5, 71
356	2, 89
357	3, 7, 17
358	2, 179
359	359
360	2, 3, 5
361	19
362	2, 181
363	3, 11
364	2, 7, 13
365	5, 73
366	2, 3, 61
367	367
368	2, 23
369	3, 41
370	2, 5, 37
371	7, 53
372	2, 3, 31
373	373
374	2, 11, 17
375	3, 5
376	2, 47
377	13, 29
378	2, 3, 7
379	379
380	2, 5, 19
381	3, 127
382	2, 191
383	383
384	2, 3
385	5, 7, 11
386	2, 193
387	3, 43
388	2, 97
389	389
390	2, 3, 5, 13
391	17, 23
392	2, 7
393	3, 131
394	2, 197
395	5, 79
396	2, 3, 11
397	397
398	2, 199
399	3, 7, 19
400	2, 5
401	401
402	2, 3, 67
403	13, 31
404	2, 101
405	3, 5
406	2, 7, 29
407	11, 37
408	2, 3, 17
409	409
410	2, 5, 41
411	3, 137
412	2, 103
413	7, 59
414	2, 3, 23
415	5, 83
416	2, 13
417	3, 139
418	2, 11, 19
419	419
420	2, 3, 5, 7
421	421
422	2, 211
423	3, 47
424	2, 53
425	5, 17
426	2, 3, 71
427	7, 61
428	2, 107
429	3, 11, 13
430	2, 5, 43
431	431
432	2, 3
433	433
434	2, 7, 31
435	3, 5, 29
436	2, 109
437	19, 23
438	2, 3, 73
439	439
440	2, 5, 11
441	3, 7
442	2, 13, 17
443	443
444	2, 3, 37
445	5, 89
446	2, 223
447	3, 149
448	2, 7
449	449
450	2, 3, 5
451	11, 41
452	2, 113
453	3, 151
454	2, 227
455	5, 7, 13
456	2, 3, 19
457	457
458	2, 229
459	3, 17
460	2, 5, 23
461	461
462	2, 3, 7, 11
463	463
464	2, 29
465	3, 5, 31
466	2, 233
467	467
468	2, 3, 13
469	7, 67
470	2, 5, 47
471	3, 157
472	2, 59
473	11, 43
474	2, 3, 79
475	5, 19
476	2, 7, 17
477	3, 53
478	2, 239
479	479
480	2, 3, 5
481	13, 37
482	2, 241
483	3, 7, 23
484	2, 11
485	5, 97
486	2, 3
487	487
488	2, 61
489	3, 163
490	2, 5, 7
491	491
492	2, 3, 41
493	17, 29
494	2, 13, 19
495	3, 5, 11
496	2, 31
497	7, 71
498	2, 3, 83
499	499
500	2, 5
501	3, 167

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