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Difference between revisions of "Williams prime PP remaining"
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*The highest ''n''-value for all listed bases is ''n'' = 1000, otherwise the search range is given in brackets. | *The highest ''n''-value for all listed bases is ''n'' = 1000, otherwise the search range is given in brackets. | ||
− | The data file can be found [[:File:Williams_prime_PP_remaining.csv|here]]. | + | The data file can be found [[:File:Williams_prime_PP_remaining.csv|here]]. |
− | {{#get_web_data:url=https://www.rieselprime.de/z/images/ | + | {{#get_web_data:url=https://www.rieselprime.de/z/images/2/2e/Williams_prime_PP_remaining.csv|format=csv with header|delimiter=;|data=b=Base,n=n-values}} |
− | <div style="width: | + | <div style="width: 28em; height:50em; overflow:auto;"> |
{| class="wikitable sortable" style="height: 200px" | {| class="wikitable sortable" style="height: 200px" | ||
! data-sort-type="number" class="fixhead" | Base | ! data-sort-type="number" class="fixhead" | Base | ||
Line 15: | Line 15: | ||
{{!}} style="text-align:left" {{!}} {{{n}}} | {{!}} style="text-align:left" {{!}} {{{n}}} | ||
}} | }} | ||
− | |}</div> | + | |}</div> |
+ | {{Navbox Williams primes}} | ||
[[Category:Williams prime PP| ]] | [[Category:Williams prime PP| ]] |
Latest revision as of 10:26, 26 August 2024
Description
Here are all remaining data given not yet available as separate page for Williams primes of the form (b+1)•bn+1 for b < 1025.
- The highest n-value for all listed bases is n = 1000, otherwise the search range is given in brackets.
The data file can be found here.
Base | n-value |
---|---|
111 | 1, 2, 5, 14, 71, 159 |
114 | 3, 9, 11, 71, 89, 192 |
116 | 44, 53, 71, 126, 161, 876 |
117 | 1, 14 |
119 | 1, 18 |
120 | 2, 9, 30, 39, 56, 72, 101, 104, 126, 488 |
122 | 2, 8, 72, 128 |
123 | 2, 389 |
125 | 2, 45, 62, 92, 860 |
126 | 5, 6, 93, 465 |
129 | 54, 134, 552 |
131 | 1, 968 |
132 | 54, 168, 488 |
134 | 9, 36, 206, 501, 846 |
135 | 17, 146, 219, 815 |
137 | 20 |
138 | 1, 23, 159, 794 |
140 | 2, 6, 27, 38, 39, 45, 165, 180, 291, 389, 584 |
141 | 1, 29, 32, 38, 77, 224, 464, 873 |
143 | 1, 2, 962 |
144 | 3, 12, 219, 278, 429 |
146 | 3, 17, 99, 197 |
147 | 1, 2, 5, 6, 24, 33, 936 |
149 | 9, 27, 53, 189, 221 |
150 | 1, 3, 507 |
152 | 2, 8, 9, 68 |
153 | 1, 3, 201, 321 |
155 | 1, 5, 15, 180, 251, 459, 476 |
156 | 3, 6, 83, 168, 362, 720 |
159 | 32, 356, 975 |
161 | 1, 408, 822 |
162 | 1, 8, 312 |
164 | 1, 132, 186, 249, 267, 291 |
165 | 5, 311 |
167 | 1, 872 |
168 | 1, 14, 546, 569 |
170 | 2, 6, 8, 17, 30, 51 |
174 | 14, 21, 63, 71, 443 |
176 | 1, 18, 170 |
177 | 2, 9, 821 |
180 | 2, 3, 51 |
182 | 5, 9, 30, 33 |
183 | 3, 11, 14, 75, 93 |
185 | 12, 21, 156 |
186 | 6, 12, 21, 39, 126, 132, 186 |
188 | 1, 14, 147 |
189 | 1, 8, 68, 198, 284, 332, 651 |
191 | 2, 56, 297 |
192 | 1, 2, 42, 866 |
194 | 1, 38, 227, 251, 512 |
195 | 2, 5, 8, 11, 14 |
197 | 18, 120, 581 |
198 | 2, 5, 14, 105, 198, 323 |
200 | 9, 35, 65, 140 |
203 | 1, 2, 6, 207, 747 |
204 | 3, 9, 21, 24, 51 |
206 | 1, 6 |
207 | 8, 17, 33, 326, 497 |
209 | 1, 2, 23, 120, 414 |
210 | 27, 56, 116, 119, 258 |
212 | 6, 8, 14, 38 |
213 | 447, 674 |
215 | 1, 8, 998 |
216 | 8, 39 |
218 | 1, 54, 366 |
219 | 2, 6, 9, 14, 15, 38, 50, 51, 110, 140 |
221 | 5, 8, 14, 27, 32, 47, 413 |
224 | 2, 23 |
225 | 30 |
228 | 5, 14, 71 |
230 | 2, 3, 24, 41, 54, 156, 221, 303, 534 |
231 | 1, 6, 9, 18, 26, 62, 144, 309 |
233 | 6 |
234 | 2, 6, 12, 15, 141, 471, 633 |
236 | 1, 3, 5, 17, 201 |
237 | 30 |
239 | 2, 128, 272 |
240 | 12, 198, 768 |
242 | 9, 14 |
243 | 2, 201, 353 |
245 | 1, 2, 3, 5, 32 |
246 | 1, 2, 8, 35, 81 |
248 | 3, 6, 230 |
249 | 17, 647 |
251 | 11, 24, 53, 414 |
252 | 53, 108, 216, 908 |
254 | 2, 24, 39, 78, 159, 363 |
255 | 2, 8, 24, 110, 140, 531 |
257 | 662, 788 |
258 | 153 |
260 | 9, 27, 39, 87, 752 |
261 | 32, 56, 327, 492, 561, 945 |
263 | 2 |
264 | 2, 35, 224, 915 |
266 | 1, 2, 3, 80, 278 |
267 | 14, 56, 146, 569 |
270 | 5, 6, 23, 26, 134, 213, 261, 497 |
272 | 1, 2, 12, 105 |
273 | 102, 222 |
276 | 12, 27, 44, 45 |
278 | 1, 14 |
279 | 1, 2, 8, 9, 17, 29, 357 |
281 | 8, 14, 26, 170, 206, 404 |
282 | 32, 42 |
284 | 2, 11 |
285 | 2, 9, 39, 992 |
287 | 1, 18, 38, 150 |
288 | 1, 5, 11, 294 |
290 | 1, 27, 32, 386 |
291 | 3, 12, 26, 33, 41, 612, 920 |
293 | 1, 11, 38, 39 |
294 | 2, 6, 14 |
296 | 24, 30, 36, 210, 303, 584 |
297 | 2, 6, 18, 74, 200, 513, 525 |
299 | 26, 225 |
300 | 24 |
303 | 21 |
305 | 6, 72, 144, 294, 386, 989 |
306 | 2, 3, 23, 51, 62 |
308 | 2, 6, 23, 89 |
309 | 1, 5, 36 |
311 | 6, 9, 68 |
312 | 2, 6, 480, 824 |
314 | 1, 5, 6, 773 |
315 | 48, 110, 378, 734 |
317 | 2, 288, 708 |
318 | 30, 75, 171 |
320 | 5, 29, 230 |
321 | 38, 122 |
323 | 2, 15, 29, 230, 578 |
324 | 3, 26, 480 |
326 | 2, 24 |
329 | 1, 2, 96, 648 |
330 | 6, 27 |
332 | 1, 38, 126, 192 |
333 | 26, 29 |
335 | 2, 3, 200 |
336 | 1, 11, 15, 201, 234 |
338 | 5, 15, 345 |
341 | 2, 8, 9 |
342 | 1, 188 |
344 | 1, 2, 9, 44, 329 |
345 | 3, 6, 8, 18, 24, 54, 83, 312, 654 |
347 | 320, 564 |
348 | 1, 53, 131, 249, 731 |
350 | 3, 12, 21, 227 |
351 | 1 |
353 | 3, 18 |
354 | 26, 63, 125, 128, 249 |
356 | 5, 8, 81, 314, 521 |
357 | 1, 2, 8, 62, 585, 641 |
359 | 2, 5, 8, 11, 59, 120, 492 |
360 | 8, 62, 978 |
362 | 200, 369 |
363 | 2, 219 |
365 | 2, 84, 339, 654 |
366 | 5, 6, 18, 41, 77, 483 |
368 | 2, 18, 113, 338 |
369 | 1, 3, 45 |
371 | 5, 42, 155 |
372 | 333, 674 |
374 | 3, 21, 51, 54, 672, 936 |
375 | 2, 3, 116 |
377 | 50, 294 |
378 | 1, 2, 6, 41, 129, 227 |
380 | 24, 74, 239 |
381 | 1, 2, 14, 30, 219, 468 |
383 | 1, 3, 69 |
384 | 2, 5, 8, 128 |
386 | 2, 60, 200, 525 |
387 | 8, 45, 242, 281 |
389 | 2, 5, 27, 345 |
390 | 32, 320 |
392 | 1, 8, 54, 744 |
393 | 17, 57 |
395 | 1, 2, 378 |
396 | 24, 132, 140, 183, 774 |
398 | 1, 2, 3, 179, 278 |
399 | 6, 8, 11, 12 |
401 | 26, 62 |
402 | 1, 6, 20, 44 |
404 | 1, 8, 9, 29, 194, 215, 245 |
405 | 1, 9, 12, 44, 231 |
407 | 2, 54, 81, 168, 173, 981 |
408 | 5, 15, 30 |
410 | 3, 8, 483 |
411 | 35 |
413 | 15 |
414 | 1, 8, 29, 80, 174 |
416 | 1, 44 |
417 | 17, 66, 68, 134, 264 |
419 | 5, 69, 102, 530 |
420 | 9 |
422 | 8, 77, 93, 842 |
423 | 6 |
426 | 1, 15, 21, 27, 356, 861, 866 |
428 | 2 |
429 | 243 |
431 | 18, 71, 810 |
432 | 2 |
434 | 1, 5, 11, 402 |
435 | 1, 125 |
437 | 8, 26, 30 |
438 | 3 |
440 | 2, 3, 9, 21, 99, 387, 893 |
441 | 12, 51, 102, 486 |
443 | 3, 9, 11, 18, 23, 65, 74, 138, 165, 435 |
444 | 12 |
446 | 20, 327 |
447 | 1, 662 |
449 | 696 |
450 | 2, 6, 20, 144, 201, 456 |
452 | 90 |
453 | 1, 2, 33 |
455 | 1, 3, 6, 21, 54 |
456 | 1, 15, 20, 53, 221 |
458 | 3, 15, 434 |
459 | 9, 14 |
461 | 2, 3, 195, 422, 507, 989 |
462 | 14, 30 |
464 | 18, 210, 903 |
465 | 12, 20, 39 |
467 | 2, 542 |
468 | 9, 51, 227, 335 |
470 | 20, 32, 72, 417, 977 |
471 | 2, 309 |
474 | 5, 333 |
476 | 1, 2, 104, 315 |
477 | 12, 41, 558 |
479 | 3 |
480 | 2, 3, 5, 33 |
482 | 2, 17, 62, 488, 504 |
483 | 3, 6, 179 |
485 | 12, 44, 158 |
486 | 38, 476, 612 |
488 | 3, 14 |
489 | 1, 3, 42, 81 |
491 | 17, 20, 21, 41, 195 |
492 | 26 |
494 | 56, 126, 212 |
495 | 1, 2, 17, 29, 899 |
497 | 5, 9, 18 |
498 | 15, 62, 131, 591 |
500 | 1, 63, 86 |
501 | 8, 36, 171, 180 |
503 | 2 |
504 | 36 |
506 | 6, 11, 198, 270, 554, 620 |
507 | 200, 528 |
509 | 20, 101, 200 |
510 | 3, 5, 9, 68, 260 |
513 | 3, 9, 69, 137, 774 |
515 | 6, 8, 27, 249 |
516 | 9, 44, 80, 219, 603 |
518 | 1, 2, 3, 150, 165 |
519 | 38, 479 |
521 | 498 |
522 | 92 |
524 | 20, 170 |
525 | 1, 9, 87 |
527 | 17, 48, 420 |
528 | 2 |
530 | 1, 2, 86, 95, 98, 345, 735 |
531 | 1, 65, 155, 377, 387, 639, 942 |
533 | 1, 255 |
534 | 6, 63, 270, 846 |
536 | 2, 260 |
537 | 1 |
539 | 6, 51 |
540 | 1, 2 |
543 | 2, 5, 41, 42, 75, 101, 837 |
545 | 11, 20 |
546 | 2, 15, 114, 200 |
548 | 21 |
549 | 8, 30 |
551 | 1, 2, 3, 140 |
552 | 36, 110, 138 |
554 | 1, 3, 5, 54, 305, 377, 974 |
555 | 2, 3, 677, 830 |
557 | 18, 270 |
558 | 11 |
560 | 1, 14, 36, 851 |
561 | 156, 455, 753 |
563 | 3, 15, 273 |
564 | 2, 14, 690 |
566 | 1, 15, 51, 68 |
567 | 1, 45, 50 |
569 | 96, 411 |
570 | 393 |
572 | 1, 41 |
573 | 50, 186 |
575 | 14, 120, 170, 347, 870 |
576 | 5, 68, 297 |
578 | 450 |
579 | 1, 15 |
581 | 11 |
582 | 1, 12, 30 |
584 | 1, 2, 6, 81 |
585 | 32, 39, 65, 390, 779, 828 |
587 | 8, 213 |
588 | 3, 53 |
590 | 2, 3, 14, 878 |
591 | 2, 36, 267, 474 |
593 | 2, 27 |
594 | 3, 45, 177 |
596 | 5, 11, 54 |
597 | 2, 29, 278, 876 |
599 | 36, 90, 110, 152, 740 |
600 | 8, 201 |
602 | 380 |
603 | 1, 161, 734 |
605 | 1, 2, 36, 360 |
606 | 2, 3 |
608 | 9, 17 |
609 | 1, 3, 6, 8, 213 |
611 | 6, 956 |
612 | 1, 9 |
614 | 11, 14, 423, 602 |
615 | 2, 41, 975 |
617 | 338, 588 |
618 | 2 |
620 | 6, 8, 12, 69, 621 |
621 | 1, 3, 5, 15, 650 |
623 | 3, 131 |
624 | 1, 6, 8, 72, 81, 92, 390, 540 |
626 | 1, 9, 20, 27, 45 |
627 | 6, 14, 161 |
629 | 8, 78, 764 |
630 | 2, 6 |
632 | 18, 48 |
635 | 1, 8 |
636 | 18, 47 |
638 | 11, 30, 65, 741 |
639 | 3, 5, 77 |
641 | 6 |
642 | 1, 21, 149, 189 |
644 | 1 |
645 | 5, 17, 77 |
647 | 504 |
648 | 114, 254, 257 |
650 | 3, 5, 41, 131, 204, 537, 575 |
651 | 2, 3, 63, 110 |
653 | 6, 50, 111 |
654 | 3, 62, 236 |
656 | 2, 17, 45, 425, 605 |
657 | 14 |
659 | 2, 23, 26, 120, 212, 408 |
660 | 261 |
662 | 50, 110, 365 |
663 | 143, 257, 573 |
665 | 5, 20, 426 |
666 | 3 |
668 | 1, 9, 14, 126 |
669 | 32 |
671 | 1, 3, 312, 608 |
672 | 21, 366 |
674 | 2 |
675 | 2, 117 |
677 | 1, 26 |
678 | 215, 438 |
680 | 2, 6, 18, 29, 41 |
681 | 12, 29, 326 |
684 | 2, 32, 95 |
686 | 1, 89, 489 |
687 | 2, 41, 98 |
689 | 2, 8 |
690 | 39, 104, 120 |
692 | 2, 528 |
693 | 11, 15, 23, 126, 698, 815 |
695 | 3, 6, 51, 438 |
696 | 1, 6, 8 |
698 | 3 |
699 | 23 |
701 | 1, 318, 392 |
702 | 9, 29, 113 |
704 | 8, 33, 320 |
705 | 38, 101, 153 |
707 | 2, 56, 197, 285 |
708 | 2, 50 |
711 | 3, 9, 224 |
713 | 2, 23, 78, 123 |
714 | 2, 24, 293, 380 |
716 | 78 |
720 | 1, 15, 282 |
722 | 8 |
723 | 6, 9, 17, 107 |
725 | 6, 12, 18 |
726 | 1, 8 |
728 | 1 |
729 | 5, 33, 54, 101, 663, 689 |
731 | 3, 15, 60, 650 |
732 | 50 |
734 | 5, 6, 18, 48, 96, 98 |
735 | 1, 8, 423 |
737 | 36, 62, 338 |
738 | 15, 87, 422, 675 |
740 | 2, 35, 177, 467, 891 |
741 | 2, 5, 86, 242, 359, 948 |
743 | 1, 5, 6, 197, 569 |
744 | 3, 11 |
746 | 2, 17 |
747 | 1, 8, 14 |
749 | 2, 14, 128, 270, 669 |
750 | 2, 869 |
752 | 2, 18, 186, 194, 393 |
753 | 2, 122 |
755 | 1, 2, 3, 12, 50, 852 |
756 | 5, 8, 69, 369 |
758 | 2, 3, 5, 6, 114 |
759 | 2, 26 |
761 | 1, 2, 15, 155, 482 |
762 | 1, 5, 8, 17 |
764 | 20, 156 |
765 | 3, 5, 110, 113, 293, 410, 890, 998 |
767 | 2, 9, 41, 516 |
768 | 1, 39, 669 |
770 | 191, 584 |
771 | 2, 6, 44, 176, 218, 494 |
773 | 1, 3 |
774 | 35, 95 |
776 | 51, 74, 527 |
777 | 2, 21, 197 |
779 | 3, 21 |
780 | 6, 21, 354 |
782 | 1, 32, 57, 188 |
783 | 2, 5 |
785 | 1, 6, 11, 27, 303 |
786 | 5, 77, 357 |
788 | 39, 42 |
789 | 248, 249 |
791 | 27, 162 |
792 | 1, 18, 86 |
794 | 30, 38, 312, 615 |
795 | 5, 23, 30, 56, 296, 915 |
797 | 21, 861 |
798 | 1, 3, 77, 165 |
800 | 8, 38, 221, 228 |
801 | 1, 39, 687 |
803 | 2, 3, 17, 303 |
804 | 6, 86 |
806 | 9, 462, 485 |
807 | 5, 156 |
809 | 5 |
810 | 2, 14, 101 |
812 | 1, 8, 176, 461 |
815 | 2, 590, 717 |
816 | 275 |
818 | 1, 2, 6, 74, 141, 245 |
819 | 1, 8, 350 |
821 | 81, 120 |
822 | 2, 6, 26, 80, 168, 360 |
824 | 8, 221 |
825 | 1, 9, 14, 492, 594, 663 |
827 | 1, 54, 56, 188, 198, 228, 353 |
828 | 3, 9 |
830 | 6, 8, 23, 458, 608 |
831 | 9, 59, 63, 716 |
833 | 17, 354, 987 |
834 | 71, 263 |
836 | 1, 2, 9, 675 |
837 | 2, 6, 54, 84, 249 |
839 | 1, 5, 23 |
840 | 29 |
842 | 69, 194 |
843 | 2, 3, 21, 30, 362 |
845 | 2 |
846 | 1, 20, 125 |
848 | 273, 569 |
849 | 9, 35, 134, 192, 581, 642 |
851 | 9, 36, 53, 284 |
852 | 8, 158, 257, 260 |
854 | 3, 14, 24, 587 |
855 | 1, 14, 431 |
857 | 1, 8, 18, 78, 188 |
860 | 1, 54, 119, 632, 732 |
861 | 2, 27, 38, 138 |
864 | 1, 6 |
866 | 2, 8, 51 |
867 | 2, 32 |
869 | 2, 11 |
870 | 3, 6, 20, 21, 41, 803 |
872 | 12, 26, 29, 138 |
873 | 5, 15, 107, 437 |
875 | 1, 6, 20, 74 |
876 | 414, 455 |
878 | 1 |
879 | 11, 177, 597, 815 |
881 | 47, 134, 171 |
882 | 5, 14 |
884 | 5, 51, 138 |
885 | 2, 138 |
887 | 5, 8, 557 |
890 | 1, 12, 14, 30, 449, 752 |
891 | 816 |
893 | 246, 273 |
894 | 1, 3 |
896 | 8, 48, 281, 488 |
897 | 1, 38 |
899 | 1, 9, 75, 174 |
900 | 2, 18, 503, 971 |
902 | 14, 24, 510, 654 |
903 | 29 |
905 | 6, 39, 204 |
906 | 6, 104 |
908 | 5 |
909 | 164, 401 |
911 | 1, 62, 84 |
914 | 12, 164 |
915 | 1, 93 |
917 | 2, 6, 8, 74, 326 |
918 | 1, 246 |
920 | 1, 9 |
921 | 137, 869 |
923 | 11, 41, 239, 413, 473 |
924 | 12, 152, 752 |
926 | 6, 9, 11, 26 |
927 | 1 |
930 | 24 |
932 | 6, 30, 281 |
933 | 2, 798, 963 |
935 | 6, 231, 269 |
936 | 62, 86, 791 |
938 | 17 |
939 | 66 |
941 | 26, 128 |
942 | 5, 14, 948 |
944 | 2, 6 |
945 | 170, 357 |
948 | 33, 75, 138 |
950 | 1 |
951 | 12, 21, 23, 36, 312 |
953 | 2, 5, 15, 63 |
954 | 2, 14, 71, 392 |
956 | 2, 3, 12, 891 |
957 | 2, 830 |
959 | 1, 3, 15, 672 |
960 | 1, 5, 162 |
963 | 357 |
965 | 17 |
966 | 6, 27 |
968 | 5, 29, 69 |
969 | 1, 8, 116, 543 |
971 | 2, 3, 9, 17 |
972 | 26, 42, 56, 89 |
974 | 1, 26, 171, 209, 611 |
975 | 2, 5, 18 |
977 | 24 |
978 | 2, 3, 41 |
980 | 17, 23 |
981 | 1, 6, 12, 18, 819 |
984 | 17 |
986 | 78, 597, 647 |
987 | 1, 2, 5, 12 |
989 | 2, 11, 15, 26, 84, 95 |
990 | 1, 3, 15 |
992 | 1, 2, 21, 278 |
993 | 1, 6, 47, 51, 113 |
995 | 6, 36, 48, 83 |
996 | 416 |
998 | 2, 6, 41 |
1001 | 1, 2, 11, 429 |
1002 | 1, 5, 176, 222, 266 |
1004 | 2, 62 |
1005 | 8, 11, 23, 44, 224, 302, 494 |
1007 | 1 |
1011 | 1, 2, 6, 27, 32, 810 |
1013 | 3, 5, 15, 38 |
1014 | 3, 6 |
1016 | 1, 201 |
1019 | 89, 627, 855 |
1020 | 1, 2, 26, 320 |
1022 | 1, 57, 672 |
1023 | 6, 59 |
Williams primes
Main |
Type MM: (b-1)•bn-1 |
Type MP: (b-1)•bn+1 |
Type PM: (b+1)•bn-1 |
Type PP: (b+1)•bn+1 |