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Difference between revisions of "Williams prime PM least"
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− | {{DISPLAYTITLE:Williams primes of the form {{Kbn|(b+1)|b|n}}, least | + | {{DISPLAYTITLE:Williams primes of the form {{Kbn|(b+1)|b|n}}, least {{Vn}}-values}} |
==Description== | ==Description== | ||
− | Here are shown the least | + | Here are shown the least {{Vn}}-value ≥ 1 for any base {{Vb}} with 2 ≤ {{Vb}} ≤ 1024 which generates a [[Williams prime]] of the form {{Kbn|(b+1)|b|n}}. |
==History== | ==History== | ||
*Any new found value will be displayed here. | *Any new found value will be displayed here. | ||
− | ==Wanted values== | + | ==Wanted values [searched range]== |
− | + | <b>There is one sequence</b>: | |
− | + | *[[Williams prime PM 575|575]] [{{GP|Williams prime PM 575|WiMaxn}}] | |
==Data== | ==Data== | ||
Line 15: | Line 15: | ||
<div style="width: 12em; height:50em; overflow:auto;"> | <div style="width: 12em; height:50em; overflow:auto;"> | ||
{| class="wikitable sortable" style="height: 200px" | {| class="wikitable sortable" style="height: 200px" | ||
− | ! Base | + | ! data-sort-type="number" class="fixhead" | Base |
− | ! | + | ! data-sort-type="number" class="fixhead" | {{Vn}}-value {{#for_external_table:<nowiki/> |
{{!}}- | {{!}}- | ||
{{!}} style="text-align:right" {{!}} {{{b}}} | {{!}} style="text-align:right" {{!}} {{{b}}} | ||
Line 23: | Line 23: | ||
|} | |} | ||
</div> | </div> | ||
− | + | {{Navbox Williams primes}} | |
− | |||
[[Category:Williams prime PM| ]] | [[Category:Williams prime PM| ]] |
Latest revision as of 00:47, 8 September 2024
Description
Here are shown the least n-value ≥ 1 for any base b with 2 ≤ b ≤ 1024 which generates a Williams prime of the form (b+1)•bn-1.
History
- Any new found value will be displayed here.
Wanted values [searched range]
There is one sequence:
- 575 [458000]
Data
The data file can be found here.
Base | n-value |
---|---|
2 | 1 |
3 | 1 |
4 | 1 |
5 | 1 |
6 | 1 |
7 | 4 |
8 | 1 |
9 | 1 |
10 | 1 |
11 | 1 |
12 | 2 |
13 | 1 |
14 | 2 |
15 | 1 |
16 | 1 |
17 | 4 |
18 | 3 |
19 | 1 |
20 | 1 |
21 | 1 |
22 | 2 |
23 | 7 |
24 | 1 |
25 | 2 |
26 | 1 |
27 | 2 |
28 | 1 |
29 | 2 |
30 | 1 |
31 | 1 |
32 | 2 |
33 | 4 |
34 | 2 |
35 | 1 |
36 | 2 |
37 | 2 |
38 | 1 |
39 | 1 |
40 | 2 |
41 | 1 |
42 | 8 |
43 | 3 |
44 | 1 |
45 | 1 |
46 | 1 |
47 | 2 |
48 | 1 |
49 | 2 |
50 | 1 |
51 | 5 |
52 | 3 |
53 | 1 |
54 | 1 |
55 | 1 |
56 | 1 |
57 | 3 |
58 | 3 |
59 | 1 |
60 | 1 |
61 | 5 |
62 | 2 |
63 | 1483 |
64 | 1 |
65 | 1 |
66 | 1 |
67 | 24 |
68 | 1 |
69 | 2 |
70 | 1 |
71 | 2 |
72 | 6 |
73 | 3 |
74 | 3 |
75 | 36 |
76 | 1 |
77 | 10 |
78 | 8 |
79 | 3 |
80 | 7 |
81 | 2 |
82 | 2 |
83 | 1 |
84 | 2 |
85 | 1 |
86 | 1 |
87 | 7 |
88 | 1704 |
89 | 1 |
90 | 3 |
91 | 9 |
92 | 4 |
93 | 1 |
94 | 1 |
95 | 2 |
96 | 1 |
97 | 2 |
98 | 24 |
99 | 25 |
100 | 1 |
101 | 1 |
102 | 3 |
103 | 1 |
104 | 3 |
105 | 6 |
106 | 2 |
107 | 2 |
108 | 39 |
109 | 4 |
110 | 13 |
111 | 8 |
112 | 36 |
113 | 3 |
114 | 1 |
115 | 1 |
116 | 3 |
117 | 136 |
118 | 9 |
119 | 2 |
120 | 1 |
121 | 2 |
122 | 3 |
123 | 3 |
124 | 20 |
125 | 1 |
126 | 1 |
127 | 2 |
128 | 4 |
129 | 4 |
130 | 1 |
131 | 1 |
132 | 2 |
133 | 20 |
134 | 1 |
135 | 3 |
136 | 52 |
137 | 8 |
138 | 1 |
139 | 2 |
140 | 1 |
141 | 1 |
142 | 7 |
143 | 921 |
144 | 1 |
145 | 1 |
146 | 7 |
147 | 2 |
148 | 1 |
149 | 1 |
150 | 12 |
151 | 6 |
152 | 110 |
153 | 1 |
154 | 1 |
155 | 1 |
156 | 6 |
157 | 23 |
158 | 1 |
159 | 1 |
160 | 1 |
161 | 2 |
162 | 4 |
163 | 1 |
164 | 1 |
165 | 2 |
166 | 6 |
167 | 4 |
168 | 25 |
169 | 1 |
170 | 5 |
171 | 1 |
172 | 2 |
173 | 53 |
174 | 1 |
175 | 11 |
176 | 1 |
177 | 38 |
178 | 5 |
179 | 2 |
180 | 1 |
181 | 1 |
182 | 4 |
183 | 3 |
184 | 1 |
185 | 9 |
186 | 1 |
187 | 18 |
188 | 1 |
189 | 7 |
190 | 2 |
191 | 1 |
192 | 4 |
193 | 1 |
194 | 6 |
195 | 1 |
196 | 1 |
197 | 4 |
198 | 11 |
199 | 1 |
200 | 320 |
201 | 2 |
202 | 22 |
203 | 1 |
204 | 2 |
205 | 6 |
206 | 1 |
207 | 2 |
208 | 26680 |
209 | 1 |
210 | 25 |
211 | 4 |
212 | 2 |
213 | 17 |
214 | 10 |
215 | 1 |
216 | 2 |
217 | 40 |
218 | 1 |
219 | 1 |
220 | 1 |
221 | 4 |
222 | 23 |
223 | 3 |
224 | 35 |
225 | 1 |
226 | 2 |
227 | 7 |
228 | 4 |
229 | 4 |
230 | 1 |
231 | 1 |
232 | 468 |
233 | 1 |
234 | 3 |
235 | 2 |
236 | 1 |
237 | 12 |
238 | 5 |
239 | 73 |
240 | 1 |
241 | 1 |
242 | 6 |
243 | 4 |
244 | 1 |
245 | 12 |
246 | 1 |
247 | 3 |
248 | 1 |
249 | 4 |
250 | 2 |
251 | 4 |
252 | 4 |
253 | 7 |
254 | 2 |
255 | 17 |
256 | 2 |
257 | 44 |
258 | 1 |
259 | 1 |
260 | 5 |
261 | 3 |
262 | 7 |
263 | 1 |
264 | 1 |
265 | 1 |
266 | 6 |
267 | 2 |
268 | 1 |
269 | 7 |
270 | 13 |
271 | 38 |
272 | 3 |
273 | 3 |
274 | 2 |
275 | 2 |
276 | 6 |
277 | 3 |
278 | 4 |
279 | 9 |
280 | 2 |
281 | 1 |
282 | 778 |
283 | 12 |
284 | 72 |
285 | 1 |
286 | 3 |
287 | 2 |
288 | 1 |
289 | 2 |
290 | 1 |
291 | 2 |
292 | 496 |
293 | 17 |
294 | 1 |
295 | 9 |
296 | 1 |
297 | 12 |
298 | 1 |
299 | 16 |
300 | 7 |
301 | 1 |
302 | 12 |
303 | 1 |
304 | 7 |
305 | 1 |
306 | 1 |
307 | 30 |
308 | 4 |
309 | 1 |
310 | 5 |
311 | 5 |
312 | 2 |
313 | 19 |
314 | 1 |
315 | 2 |
316 | 1492 |
317 | 2 |
318 | 2175 |
319 | 1 |
320 | 215 |
321 | 199 |
322 | 2 |
323 | 1 |
324 | 42 |
325 | 53 |
326 | 2 |
327 | 2 |
328 | 84 |
329 | 3 |
330 | 1 |
331 | 1 |
332 | 4 |
333 | 49 |
334 | 2 |
335 | 1 |
336 | 8 |
337 | 2 |
338 | 3 |
339 | 1 |
340 | 11 |
341 | 2 |
342 | 26 |
343 | 1 |
344 | 2 |
345 | 19 |
346 | 3 |
347 | 4 |
348 | 13 |
349 | 1 |
350 | 1 |
351 | 1 |
352 | 4 |
353 | 69 |
354 | 1 |
355 | 137 |
356 | 9 |
357 | 3 |
358 | 1 |
359 | 35 |
360 | 1 |
361 | 1 |
362 | 2 |
363 | 7 |
364 | 1 |
365 | 13 |
366 | 3 |
367 | 7 |
368 | 28 |
369 | 23 |
370 | 2 |
371 | 6 |
372 | 2 |
373 | 1 |
374 | 1 |
375 | 5 |
376 | 20 |
377 | 50 |
378 | 1 |
379 | 2 |
380 | 1 |
381 | 90 |
382 | 12 |
383 | 19 |
384 | 2 |
385 | 1 |
386 | 1 |
387 | 6 |
388 | 3 |
389 | 14 |
390 | 7 |
391 | 1 |
392 | 7 |
393 | 1 |
394 | 2 |
395 | 1 |
396 | 1 |
397 | 2 |
398 | 3 |
399 | 15 |
400 | 6 |
401 | 1 |
402 | 6 |
403 | 4 |
404 | 5 |
405 | 1 |
406 | 5 |
407 | 2 |
408 | 1 |
409 | 4 |
410 | 2 |
411 | 2 |
412 | 380 |
413 | 3 |
414 | 3 |
415 | 3 |
416 | 10 |
417 | 2 |
418 | 1 |
419 | 1 |
420 | 1 |
421 | 19 |
422 | 6 |
423 | 1 |
424 | 2 |
425 | 12 |
426 | 13 |
427 | 4 |
428 | 1 |
429 | 5 |
430 | 3 |
431 | 1 |
432 | 8 |
433 | 1 |
434 | 3 |
435 | 2 |
436 | 2 |
437 | 4 |
438 | 13 |
439 | 6 |
440 | 17 |
441 | 3 |
442 | 3 |
443 | 3 |
444 | 885 |
445 | 1 |
446 | 26 |
447 | 2 |
448 | 1 |
449 | 1 |
450 | 1 |
451 | 3 |
452 | 4 |
453 | 1 |
454 | 3 |
455 | 1 |
456 | 1 |
457 | 3 |
458 | 24 |
459 | 2 |
460 | 23 |
461 | 1 |
462 | 10 |
463 | 1 |
464 | 5 |
465 | 37 |
466 | 20 |
467 | 6 |
468 | 1 |
469 | 8 |
470 | 2 |
471 | 1 |
472 | 12 |
473 | 1 |
474 | 1 |
475 | 1 |
476 | 18 |
477 | 2 |
478 | 1 |
479 | 5 |
480 | 18 |
481 | 1 |
482 | 10 |
483 | 145 |
484 | 5 |
485 | 5 |
486 | 1 |
487 | 7 |
488 | 1085 |
489 | 3 |
490 | 1 |
491 | 7 |
492 | 14 |
493 | 3 |
494 | 1 |
495 | 1 |
496 | 1 |
497 | 56 |
498 | 44 |
499 | 1 |
500 | 1 |
501 | 1 |
502 | 2 |
503 | 2292 |
504 | 1 |
505 | 4 |
506 | 1 |
507 | 15 |
508 | 7 |
509 | 2 |
510 | 1 |
511 | 1 |
512 | 2 |
513 | 3 |
514 | 4 |
515 | 1 |
516 | 2 |
517 | 38 |
518 | 1 |
519 | 1 |
520 | 24 |
521 | 7 |
522 | 67 |
523 | 5 |
524 | 3 |
525 | 3 |
526 | 2 |
527 | 90 |
528 | 1 |
529 | 3 |
530 | 1 |
531 | 2 |
532 | 2 |
533 | 29 |
534 | 11 |
535 | 5 |
536 | 15 |
537 | 548 |
538 | 4 |
539 | 4 |
540 | 7 |
541 | 1 |
542 | 18 |
543 | 4 |
544 | 1 |
545 | 5 |
546 | 3 |
547 | 6 |
548 | 1 |
549 | 1 |
550 | 1 |
551 | 1 |
552 | 44 |
553 | 13 |
554 | 2 |
555 | 7 |
556 | 6 |
557 | 3 |
558 | 76 |
559 | 41 |
560 | 1 |
561 | 1 |
562 | 15 |
563 | 5 |
564 | 10 |
565 | 31 |
566 | 8 |
567 | 15 |
568 | 4 |
569 | 1 |
570 | 11 |
571 | 1 |
572 | 6 |
573 | 1 |
574 | 4 |
575 | |
576 | 2 |
577 | 4620 |
578 | 1 |
579 | 2 |
580 | 2 |
581 | 1 |
582 | 3 |
583 | 9 |
584 | 4 |
585 | 6 |
586 | 4 |
587 | 70 |
588 | 1 |
589 | 1 |
590 | 4 |
591 | 1 |
592 | 2 |
593 | 13 |
594 | 1 |
595 | 1 |
596 | 1 |
597 | 3 |
598 | 1 |
599 | 7 |
600 | 2 |
601 | 6 |
602 | 7 |
603 | 5 |
604 | 1 |
605 | 12 |
606 | 1 |
607 | 11030 |
608 | 3 |
609 | 2 |
610 | 1 |
611 | 2 |
612 | 3 |
613 | 55 |
614 | 2 |
615 | 17 |
616 | 1 |
617 | 2 |
618 | 1 |
619 | 9 |
620 | 5 |
621 | 8 |
622 | 215 |
623 | 7 |
624 | 1 |
625 | 1 |
626 | 12 |
627 | 503 |
628 | 19 |
629 | 1 |
630 | 12 |
631 | 1112 |
632 | 3 |
633 | 1 |
634 | 4 |
635 | 2 |
636 | 5 |
637 | 18 |
638 | 15 |
639 | 1 |
640 | 1 |
641 | 23 |
642 | 10 |
643 | 7 |
644 | 1 |
645 | 2 |
646 | 1 |
647 | 22 |
648 | 1 |
649 | 32 |
650 | 2 |
651 | 1 |
652 | 38 |
653 | 7 |
654 | 1 |
655 | 1 |
656 | 16 |
657 | 116 |
658 | 4 |
659 | 1 |
660 | 11 |
661 | 3 |
662 | 6 |
663 | 4 |
664 | 5 |
665 | 5 |
666 | 3 |
667 | 2 |
668 | 1 |
669 | 128 |
670 | 1 |
671 | 98 |
672 | 2 |
673 | 1 |
674 | 19 |
675 | 7 |
676 | 1 |
677 | 2 |
678 | 3 |
679 | 10 |
680 | 2 |
681 | 5 |
682 | 16 |
683 | 1 |
684 | 5 |
685 | 3 |
686 | 1 |
687 | 7 |
688 | 25 |
689 | 3 |
690 | 2 |
691 | 1 |
692 | 8 |
693 | 1 |
694 | 5 |
695 | 1 |
696 | 90 |
697 | 11 |
698 | 8 |
699 | 1 |
700 | 10 |
701 | 4 |
702 | 3 |
703 | 5 |
704 | 3 |
705 | 1 |
706 | 1 |
707 | 8 |
708 | 1 |
709 | 1 |
710 | 22 |
711 | 3 |
712 | 80 |
713 | 11 |
714 | 2 |
715 | 1 |
716 | 1 |
717 | 3 |
718 | 3 |
719 | 4 |
720 | 1 |
721 | 4 |
722 | 7 |
723 | 3 |
724 | 1 |
725 | 13 |
726 | 22 |
727 | 14 |
728 | 1 |
729 | 13 |
730 | 6 |
731 | 7 |
732 | 6 |
733 | 7 |
734 | 2 |
735 | 6 |
736 | 2 |
737 | 2 |
738 | 16 |
739 | 1 |
740 | 2 |
741 | 5 |
742 | 2 |
743 | 1 |
744 | 6 |
745 | 3 |
746 | 1 |
747 | 588 |
748 | 35 |
749 | 6 |
750 | 1 |
751 | 7 |
752 | 11 |
753 | 1 |
754 | 1 |
755 | 26 |
756 | 2 |
757 | 7 |
758 | 37 |
759 | 3 |
760 | 303 |
761 | 1 |
762 | 4 |
763 | 1 |
764 | 36 |
765 | 1 |
766 | 18 |
767 | 3 |
768 | 11 |
769 | 1 |
770 | 4 |
771 | 3 |
772 | 8 |
773 | 4 |
774 | 67 |
775 | 8 |
776 | 1 |
777 | 6 |
778 | 3 |
779 | 1 |
780 | 1 |
781 | 1 |
782 | 47 |
783 | 3 |
784 | 4 |
785 | 5 |
786 | 1 |
787 | 11 |
788 | 149 |
789 | 4 |
790 | 23 |
791 | 2 |
792 | 2 |
793 | 7 |
794 | 1 |
795 | 7 |
796 | 2 |
797 | 30 |
798 | 1 |
799 | 12 |
800 | 91 |
801 | 11 |
802 | 2 |
803 | 1 |
804 | 1 |
805 | 79 |
806 | 9 |
807 | 10 |
808 | 4 |
809 | 1 |
810 | 6 |
811 | 4 |
812 | 3 |
813 | 8 |
814 | 1 |
815 | 1 |
816 | 1 |
817 | 79 |
818 | 156 |
819 | 10 |
820 | 5 |
821 | 7 |
822 | 3 |
823 | 4 |
824 | 2 |
825 | 1 |
826 | 2 |
827 | 3 |
828 | 19657 |
829 | 11 |
830 | 15 |
831 | 58 |
832 | 2 |
833 | 1 |
834 | 15 |
835 | 6 |
836 | 11 |
837 | 2 |
838 | 1 |
839 | 2 |
840 | 27 |
841 | 6 |
842 | 2 |
843 | 55 |
844 | 2 |
845 | 1 |
846 | 7 |
847 | 3 |
848 | 1 |
849 | 5 |
850 | 7 |
851 | 2 |
852 | 1026 |
853 | 53 |
854 | 3 |
855 | 5 |
856 | 1 |
857 | 19 |
858 | 8 |
859 | 86 |
860 | 73 |
861 | 2 |
862 | 4 |
863 | 1 |
864 | 3 |
865 | 35 |
866 | 2 |
867 | 2 |
868 | 4 |
869 | 24 |
870 | 11 |
871 | 3 |
872 | 2 |
873 | 1 |
874 | 4 |
875 | 8 |
876 | 16 |
877 | 2 |
878 | 17 |
879 | 20 |
880 | 4 |
881 | 1 |
882 | 3 |
883 | 1179 |
884 | 1 |
885 | 1 |
886 | 11 |
887 | 2 |
888 | 3 |
889 | 1 |
890 | 1 |
891 | 6 |
892 | 4 |
893 | 3 |
894 | 2 |
895 | 25 |
896 | 5 |
897 | 2 |
898 | 4 |
899 | 835 |
900 | 3 |
901 | 1 |
902 | 2 |
903 | 23 |
904 | 7 |
905 | 3 |
906 | 1 |
907 | 2 |
908 | 31 |
909 | 4 |
910 | 2 |
911 | 5 |
912 | 2 |
913 | 121 |
914 | 2 |
915 | 1 |
916 | 3 |
917 | 24 |
918 | 5 |
919 | 5 |
920 | 4 |
921 | 1 |
922 | 2 |
923 | 1 |
924 | 2 |
925 | 1 |
926 | 10 |
927 | 15 |
928 | 12 |
929 | 14 |
930 | 1 |
931 | 6 |
932 | 47 |
933 | 3 |
934 | 747 |
935 | 16 |
936 | 2 |
937 | 16 |
938 | 7 |
939 | 1 |
940 | 32 |
941 | 1 |
942 | 78 |
943 | 52 |
944 | 1 |
945 | 5 |
946 | 1 |
947 | 4 |
948 | 11 |
949 | 2 |
950 | 1 |
951 | 126 |
952 | 3 |
953 | 5580 |
954 | 3 |
955 | 1 |
956 | 1 |
957 | 2 |
958 | 7 |
959 | 9 |
960 | 15 |
961 | 2 |
962 | 40 |
963 | 1 |
964 | 146 |
965 | 1 |
966 | 1 |
967 | 3 |
968 | 1 |
969 | 7 |
970 | 3 |
971 | 98 |
972 | 6 |
973 | 3 |
974 | 1 |
975 | 3 |
976 | 1 |
977 | 7 |
978 | 17 |
979 | 160 |
980 | 2 |
981 | 1 |
982 | 18 |
983 | 16 |
984 | 1 |
985 | 24 |
986 | 5 |
987 | 122 |
988 | 3 |
989 | 1 |
990 | 24 |
991 | 7 |
992 | 6 |
993 | 263 |
994 | 1 |
995 | 2 |
996 | 1 |
997 | 3 |
998 | 1 |
999 | 2 |
1000 | 1 |
1001 | 1 |
1002 | 302 |
1003 | 4 |
1004 | 4 |
1005 | 1 |
1006 | 1 |
1007 | 83 |
1008 | 47 |
1009 | 62 |
1010 | 7 |
1011 | 4 |
1012 | 2 |
1013 | 1 |
1014 | 1 |
1015 | 3 |
1016 | 1 |
1017 | 2 |
1018 | 19 |
1019 | 4 |
1020 | 395 |
1021 | 2 |
1022 | 3 |
1023 | 1 |
1024 | 1 |
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 |