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Difference between revisions of "Williams prime MP least"

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(950)
(b=634)
(6 intermediate revisions by the same user not shown)
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==History==
 
==History==
 +
<div style="width: 35em; height:20em; overflow:auto;">
 +
{{HistF|2019-08-06|84822 ([[Williams prime MP 634|b=634]])|Karsten Bonath}}
 +
{{HistF|2019-06-20|60994 ([[Williams prime MP 953|b=953]])|Karsten Bonath}}
 +
{{HistF|2019-06-15|29684 ([[Williams prime MP 1004|b=1004]])|Karsten Bonath}}
 +
{{HistF|2019-06-14|1622 ([[Williams prime MP 974|b=974]])|Karsten Bonath}}
 +
{{HistF|2019-06-13|4470 ([[Williams prime MP 923|b=923]])|Karsten Bonath}}
 
{{HistF|2019-06-11|5956 ([[Williams prime MP 950|b=950]])|Karsten Bonath}}
 
{{HistF|2019-06-11|5956 ([[Williams prime MP 950|b=950]])|Karsten Bonath}}
 
{{HistF|2019-06-09|37376 ([[Williams prime MP 890|b=890]])|Karsten Bonath}}
 
{{HistF|2019-06-09|37376 ([[Williams prime MP 890|b=890]])|Karsten Bonath}}
Line 24: Line 30:
 
{{HistF|2019-05-22|4012 ([[Williams prime MP 497|b=497]])|Karsten Bonath}}
 
{{HistF|2019-05-22|4012 ([[Williams prime MP 497|b=497]])|Karsten Bonath}}
 
{{HistF|2019-05-13|142876 ([[Williams prime MP 363|b=363]])|Karsten Bonath}}
 
{{HistF|2019-05-13|142876 ([[Williams prime MP 363|b=363]])|Karsten Bonath}}
 +
</div>
  
==Wanted values==
+
==Wanted values [searched range]==
Given here bases and known searched ranges:
+
<div style="column-count:6;-moz-column-count:6;-webkit-column-count:6">
*Searched by [[Conjectures 'R Us]]
+
{{#dpl:
**123 [250000]
+
|debug=1
**342 [100000]
+
|namespace=
**438 [100000]
+
|category=Williams prime MP without
**487 [100000]
+
|include={Williams prime}:WiBase,{Williams prime}:WiBase,{Williams prime}:WiMaxn
**757 [100000]
+
|mode=userformat
**997 [100000]
+
|format=<ul type="disc">,<li>,</li>,</ul>
**1005 [100000]
+
|secseparators=[[Williams prime MP ,|,,]],&nbsp;[,]
*Others
+
|order=ascending
**[[Williams prime MP 362|362]] at {{GP|Williams prime MP 362|WiMaxn}} {{#if:{{GP|Williams prime MP 362|WiReserved}}|<b>RESERVED!</b>}}
+
|ordermethod=sortkey
**[[Williams prime MP 479|479]] at {{GP|Williams prime MP 479|WiMaxn}} {{#if:{{GP|Williams prime MP 479|WiReserved}}|<b>RESERVED!</b>}}
+
|oneresultheader=<b>There is one sequence</b>:
**[[Williams prime MP 422|422]] at {{GP|Williams prime MP 422|WiMaxn}} {{#if:{{GP|Williams prime MP 422|WiReserved}}|<b>RESERVED!</b>}}
+
|resultsheader=<b>There are %PAGES% sequences</b>:
**[[Williams prime MP 512|512]] see [[Proth prime 511]]
+
|noresultsheader=<b>There are no entries.</b>
**542, 602, 634, 767, 817, 830, 872, 893, 923, 932, 953, 974, 992, 1004, 1007
+
}}</div>
 +
'''Notes:'''
 +
*Base 512: [[Proth prime 511|Proth prime {{Kbn|+|511|n}}]] (first n-value divisible by 9)
 +
*Base 817: [[Conjectures 'R Us]] not started yet
 +
*Bases 123, 342, 438, 487, 757, 997, 1005 reserved by [[Conjectures 'R Us]]
  
 
==Data==
 
==Data==
Line 48: Line 59:
 
<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
! ''n''-value {{#for_external_table:<nowiki/>
+
! data-sort-type="number" class="fixhead" | ''n''-value {{#for_external_table:<nowiki/>
 
{{!}}-
 
{{!}}-
 
{{!}} style="text-align:right" {{!}} {{{b}}}
 
{{!}} style="text-align:right" {{!}} {{{b}}}

Revision as of 10:05, 6 August 2019

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

Wanted values [searched range]

There are 21 sequences:

Notes:

Data

The data file can be found here.

Base n-value
2 1
3 1
4 1
5 2
6 1
7 1
8 2
9 1
10 3
11 10
12 3
13 1
14 2
15 1
16 1
17 4
18 1
19 29
20 14
21 1
22 1
23 14
24 2
25 1
26 2
27 4
28 1
29 2
30 4
31 5
32 12
33 2
34 1
35 2
36 2
37 9
38 16
39 1
40 2
41 80
42 1
43 2
44 4
45 2
46 3
47 16
48 2
49 2
50 2
51 1
52 15
53 960
54 15
55 1
56 4
57 3
58 1
59 14
60 1
61 6
62 20
63 1
64 3
65 946
66 6
67 1
68 18
69 10
70 1
71 4
72 1
73 5
74 42
75 4
76 1
77 828
78 1
79 1
80 2
81 1
82 12
83 2
84 6
85 4
86 30
87 3
88 3022
89 2
90 1
91 1
92 8
93 2
94 4
95 4
96 2
97 11
98 8
99 2
100 1
101 2
102 1
103 56
104 2
105 12
106 1
107 4
108 5
109 15
110 2
111 1
112 1
113 4
114 3
115 2
116 16
117 3
118 1
119 46
120 1
121 2
122 6216
123
124 2
125 16
126 4
127 165
128 72
129 5
130 64
131 14
132 1
133 2
134 50
135 2
136 279
137 12
138 2
139 1
140 2
141 6
142 1
143 4
144 1
145 3
146 4
147 4
148 1
149 2
150 14
151 1
152 8
153 4
154 1
155 6
156 1
157 29
158 1620
159 16
160 5
161 2
162 1
163 1
164 20
165 1
166 5
167 24
168 1
169 1
170 2
171 52
172 99
173 2
174 1
175 15
176 4
177 1
178 8
179 46
180 2484
181 2
182 396
183 22
184 3
185 208
186 3
187 8
188 10
189 1
190 1
191 2
192 15
193 1
194 2
195 1
196 60
197 520
198 4
199 8
200 60
201 2
202 46773
203 2
204 1
205 2
206 2
207 1
208 9
209 2
210 1
211 2
212 4
213 4
214 118
215 2
216 1
217 5
218 44
219 1
220 5
221 24
222 3
223 14
224 2
225 5
226 2
227 16
228 24
229 41
230 2
231 4
232 1
233 16
234 10
235 15
236 4
237 1
238 40
239 50
240 3
241 38
242 4
243 6
244 14
245 4
246 1
247 1
248 604
249 1851
250 3
251 102978
252 11
253 2
254 2
255 4
256 4
257 1344
258 2
259 2
260 2
261 5
262 4
263 10
264 5
265 3
266 2
267 1
268 6
269 1436
270 3
271 12
272 16680
273 1
274 2
275 980
276 3
277 24
278 2
279 1
280 1
281 2
282 276
283 14
284 36
285 2
286 2
287 4
288 1
289 1
290 24
291 1
292 5
293 44
294 1
295 6
296 4
297 14313
298 60670
299 4
300 2
301 2
302 16
303 5
304 70
305 52
306 8
307 203
308 8
309 2
310 1
311 2
312 4
313 4
314 12
315 1
316 5
317 128
318 2
319 564
320 2
321 2
322 17
323 2
324 6
325 2
326 64756
327 24
328 1626
329 480
330 1
331 4
332 112
333 1
334 2
335 4
336 2
337 1
338 272
339 10
340 324
341 84
342
343 1
344 2
345 1
346 4
347 69660
348 2
349 1
350 270
351 5
352 1
353 2
354 21
355 2
356 528
357 3
358 1
359 104
360 4
361 6
362
363 142876
364 3
365 2
366 2
367 5
368 36
369 8
370 1
371 22
372 3
373 2
374 52
375 6
376 8
377 16
378 5
379 1
380 2
381 3
382 1
383 4
384 1
385 9
386 2
387 4
388 41
389 70
390 2
391 3
392 4
393 1
394 3
395 2
396 1
397 44
398 56
399 1
400 2
401 16
402 112
403 1
404 2
405 1
406 1
407 500
408 76
409 3
410 42
411 2
412 9
413 4
414 2
415 1
416 180
417 1
418 9
419 4338
420 10
421 9
422
423 2
424 4
425 2
426 3
427 1
428 2
429 6
430 3
431 76
432 99
433 2
434 882
435 1
436 1
437 108
438
439 15
440 4
441 2
442 16
443 4
444 2
445 3
446 2
447 3
448 1
449 14
450 20
451 2
452 71940
453 6
454 1
455 1168
456 1
457 1
458 2
459 3
460 5
461 26
462 80
463 10
464 36
465 2
466 4
467 40
468 18
469 9
470 24
471 263
472 45
473 72
474 2
475 4
476 60
477 1
478 9
479
480 15
481 5
482 4
483 2
484 2
485 20
486 4
487
488 10
489 2
490 1
491 2
492 27
493 5
494 144
495 2
496 1
497 4012
498 1937
499 20
500 2
501 1
502 3
503 892
504 9
505 2
506 2
507 3
508 4
509 194
510 3
511 15
512
513 1
514 2
515 6
516 6
517 8
518 2
519 1
520 24
521 8
522 105
523 2
524 814
525 2
526 1
527 328
528 2
529 6
530 4
531 1
532 1
533 6
534 1
535 45
536 9762
537 56
538 1
539 2
540 12
541 1
542
543 10041
544 10
545 1822
546 131
547 11
548 16
549 23
550 4
551 248
552 1
553 752
554 22
555 1
556 6
557 60
558 32
559 9
560 2
561 1
562 5
563 6
564 38064
565 2
566 2
567 1
568 1
569 148
570 160
571 10
572 1832
573 1
574 17
575 34
576 3
577 3
578 2764
579 2
580 1
581 44
582 4
583 1
584 2
585 1
586 2
587 916
588 106
589 4
590 26
591 10
592 99
593 1660
594 2
595 11
596 370
597 15
598 4
599 1018
600 5
601 17
602
603 9
604 1
605 6
606 1
607 3
608 2
609 5
610 1
611 274
612 5
613 1
614 30
615 3
616 2
617 16
618 18
619 2
620 972
621 3
622 1
623 2
624 18
625 1
626 8
627 1
628 8
629 2
630 5
631 3
632 4
633 5
634 84822
635 74
636 1
637 11
638 6
639 3
640 9
641 4
642 3
643 1
644 14
645 1
646 5
647 24
648 6
649 34
650 22
651 131
652 71
653 6
654 2
655 142
656 236
657 4
658 786
659 4
660 3
661 237
662 28
663 2
664 60
665 70
666 2
667 3
668 58
669 1
670 2
671 12
672 1
673 24
674 6342
675 9
676 3
677 320
678 1
679 2
680 40
681 2
682 616
683 738
684 3
685 6
686 64
687 1
688 172
689 4
690 3
691 314
692 4
693 5
694 227
695 2
696 4
697 1
698 10
699 23
700 23
701 8662
702 1
703 6
704 12
705 197
706 70
707 12
708 6
709 9
710 2
711 21
712 4
713 14
714 2
715 3
716 8
717 59
718 144
719 16
720 3
721 1
722 972
723 2
724 3
725 4
726 6
727 1
728 16
729 1
730 4
731 14
732 1803
733 5
734 2
735 3
736 1
737 12
738 86
739 12
740 766
741 4
742 11
743 238
744 1
745 71
746 40
747 20
748 1
749 6
750 2
751 870
752 4
753 40
754 2
755 2
756 1
757
758 3014
759 802
760 267
761 4
762 1
763 1
764 2
765 2
766 81
767
768 65
769 1
770 116
771 6
772 3
773 2
774 1
775 3
776 6
777 3
778 4
779 1014
780 5
781 4
782 1200
783 1
784 6
785 2
786 1
787 20
788 13540
789 2
790 5
791 26
792 12
793 1
794 962
795 52
796 9
797 5188
798 5
799 1
800 12
801 53
802 1
803 2
804 3
805 16
806 2
807 36
808 2
809 10
810 2440
811 99
812 44
813 1
814 3
815 2
816 6
817
818 2
819 1
820 1
821 14
822 3
823 1089
824 2
825 5
826 1
827 8452
828 1
829 4
830
831 6
832 65
833 18
834 4
835 24
836 1048
837 1
838 104
839 2172
840 1
841 12
842 52
843 4
844 9
845 10
846 18
847 1
848 2
849 3
850 5
851 12
852 45
853 2
854 2
855 2
856 1
857 12
858 1
859 2
860 4
861 1
862 11
863 4
864 322
865 1
866 14
867 65
868 5
869 12288
870 4
871 3
872
873 2
874 3
875 58
876 1
877 4
878 114
879 1
880 2
881 2
882 3
883 2
884 2
885 4
886 33
887 32
888 5
889 3
890 37376
891 1
892 596
893
894 11
895 1
896 4
897 27
898 1
899 2
900 1
901 23
902 16
903 302
904 3
905 4
906 4
907 327
908 2
909 3
910 2
911 4
912 1
913 36
914 18
915 3
916 1
917 44
918 653
919 1
920 142
921 1
922 41
923 4470
924 17
925 2
926 10
927 96
928 1
929 28
930 4
931 3
932
933 4
934 51
935 84
936 26
937 56
938 12
939 15
940 42
941 24
942 243
943 5
944 4
945 36
946 2
947 120
948 36
949 9
950 5956
951 1
952 41
953 60994
954 2
955 173
956 714
957 17
958 10
959 10
960 1
961 1
962 64
963 81
964 50
965 2
966 6
967 12
968 6
969 2
970 1
971 6
972 15
973 30
974 1622
975 1
976 3
977 48
978 26
979 4
980 2
981 118
982 1
983 2
984 33
985 3
986 4
987 8
988 1
989 68
990 3
991 1
992
993 1
994 1
995 110
996 5
997
998 34
999 3
1000 8
1001 28
1002 1
1003 1
1004 29684
1005
1006 3
1007
1008 1
1009 18
1010 4
1011 2
1012 1
1013 6
1014 2
1015 71
1016 14
1017 1
1018 16
1019 444
1020 3
1021 1
1022 6064
1023 1
1024 38

External links