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Difference between revisions of "Williams prime PP least"

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m (consistency)
 
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{{DISPLAYTITLE:Williams primes of the form {{Kbn|+|(b+1)|b|n}}, least ''n''-values}}
+
{{DISPLAYTITLE:Williams primes of the form {{Kbn|+|(b+1)|b|n}}, least {{Vn}}-values}}
 
==Description==
 
==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 {{Kbn|+|(b+1)|b|n}}.
+
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}}.
 +
 
 +
Values of bases {{Vb}} ≡ 1 mod 3 are always divisible by 3, so not listed here.
  
 
==History==
 
==History==
 +
*{{HistF|2020-07-19|135981 ([[Williams prime PP 327|b=327]])|(unknown),Conjectures 'R Us|551009}}
 +
*{{HistF|2019-06-15|3615 ([[Williams prime PP 929|b=929]])|Karsten Bonath}}
 +
*{{HistF|2019-06-15|4917 ([[Williams prime PP 912|b=912]])|Karsten Bonath}}
 
*{{HistF|2019-05-21|13418 ([[Williams prime PP 719|b=719]])|Karsten Bonath}}
 
*{{HistF|2019-05-21|13418 ([[Williams prime PP 719|b=719]])|Karsten Bonath}}
 
*{{HistF|2019-05-21|37506 ([[Williams prime PP 717|b=717]])|Karsten Bonath}}
 
*{{HistF|2019-05-21|37506 ([[Williams prime PP 717|b=717]])|Karsten Bonath}}
Line 12: Line 17:
 
*{{HistF|2019-05-14|11229 ([[Williams prime PP 425|b=425]])|Karsten Bonath}}
 
*{{HistF|2019-05-14|11229 ([[Williams prime PP 425|b=425]])|Karsten Bonath}}
  
−
==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">
−
:327 [100000], 813, 863, 912, 929, 947, 962, 983, 1008, 1010, 1017 [250000]
+
{{#dpl:
 +
|debug=1
 +
|namespace=
 +
|category=Williams prime PP without
 +
|include={Williams prime}:WiBase,{Williams prime}:WiBase,{Williams prime}:WiMaxn
 +
|mode=userformat
 +
|format=<ul type="disc">,<li>,</li>,</ul>
 +
|secseparators=[[Williams prime PP ,|,,]],&nbsp;[,]
 +
|order=ascending
 +
|ordermethod=sortkey
 +
|oneresultheader=<b>There is one sequence</b>:
 +
|resultsheader=<b>There are %PAGES% sequences</b>:
 +
|noresultsheader=<b>There are no sequences.</b>
 +
}}</div>
 +
'''Notes:'''
 +
*Base 1017 is sometimes reserved and worked on by [[Conjectures 'R Us]].
  
 
==Data==
 
==Data==
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<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" | {{Vn}}-value {{#for_external_table:<nowiki/>
 
{{!}}-
 
{{!}}-
 
{{!}} style="text-align:right" {{!}} {{{b}}}
 
{{!}} style="text-align:right" {{!}} {{{b}}}
Line 29: Line 49:
 
|}
 
|}
 
</div>
 
</div>
−
==External links==
+
{{Navbox Williams primes}}
−
*see [[Williams prime]]
 
 
[[Category:Williams prime PP| ]]
 
[[Category:Williams prime PP| ]]

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.

Values of bases b ≡ 1 mod 3 are always divisible by 3, so not listed here.

History

Wanted values [searched range]

There are 4 sequences:

Notes:

Data

The data file can be found here.

Base n-value
2 1
3 1
5 1
6 1
8 1
9 2
11 2
12 1
14 1
15 1
17 1
18 9
20 1
21 1
23 2
24 1
26 2
27 1
29 5
30 2
32 5
33 1
35 2
36 3
38 1
39 3
41 1
42 2
44 2
45 2
47 2
48 6
50 1
51 183
53 2
54 1
56 2
57 1
59 1
60 21
62 1
63 185
65 3
66 1
68 2
69 1
71 1
72 120
74 2
75 1
77 1
78 1
80 1
81 8
83 5
84 9
86 2
87 2
89 1
90 1
92 2
93 3
95 9
96 14
98 3
99 1
101 1
102 5
104 5
105 1
107 80
108 398
110 1
111 1
113 3
114 3
116 44
117 1
119 1
120 2
122 2
123 2
125 2
126 5
128 3
129 54
131 1
132 54
134 9
135 17
137 20
138 1
140 2
141 1
143 1
144 3
146 3
147 1
149 9
150 1
152 2
153 1
155 1
156 3
158 141
159 32
161 1
162 1
164 1
165 5
167 1
168 1
170 2
171 1851
173 1
174 14
176 1
177 2
179 2
180 2
182 5
183 3
185 12
186 6
188 1
189 1
191 2
192 1
194 1
195 2
197 18
198 2
200 9
201 31274
203 1
204 3
206 1
207 8
209 1
210 27
212 6
213 447
215 1
216 8
218 1
219 2
221 5
222 52725
224 2
225 30
227 36321
228 5
230 2
231 1
233 6
234 2
236 1
237 30
239 2
240 12
242 9
243 2
245 1
246 1
248 3
249 17
251 11
252 53
254 2
255 2
257 662
258 153
260 9
261 32
263 2
264 2
266 1
267 14
269 1398
270 5
272 1
273 102
275 1911
276 12
278 1
279 1
281 8
282 32
284 2
285 2
287 1
288 1
290 1
291 3
293 1
294 2
296 24
297 2
299 26
300 24
302 1085
303 21
305 6
306 2
308 2
309 1
311 6
312 2
314 1
315 48
317 2
318 30
320 5
321 38
323 2
324 3
326 2
327 135981
329 1
330 6
332 1
333 26
335 2
336 1
338 5
339 1002
341 2
342 1
344 1
345 3
347 320
348 1
350 3
351 1
353 3
354 26
356 5
357 1
359 2
360 8
362 200
363 2
365 2
366 5
368 2
369 1
371 5
372 333
374 3
375 2
377 50
378 1
380 24
381 1
383 1
384 2
386 2
387 8
389 2
390 32
392 1
393 17
395 1
396 24
398 1
399 6
401 26
402 1
404 1
405 1
407 2
408 5
410 3
411 35
413 15
414 1
416 1
417 17
419 5
420 9
422 8
423 6
425 11229
426 1
428 2
429 243
431 18
432 2
434 1
435 1
437 8
438 3
440 2
441 12
443 3
444 12
446 20
447 1
449 696
450 2
452 90
453 1
455 1
456 1
458 3
459 9
461 2
462 14
464 18
465 12
467 2
468 9
470 20
471 2
473 3521
474 5
476 1
477 12
479 3
480 2
482 2
483 3
485 12
486 38
488 3
489 1
491 17
492 26
494 56
495 1
497 5
498 15
500 1
501 8
503 2
504 36
506 6
507 200
509 20
510 3
512 1
513 3
515 6
516 9
518 1
519 38
521 498
522 92
524 20
525 1
527 17
528 2
530 1
531 1
533 1
534 6
536 2
537 1
539 6
540 1
542 1806
543 2
545 11
546 2
548 21
549 8
551 1
552 36
554 1
555 2
557 18
558 11
560 1
561 156
563 3
564 2
566 1
567 1
569 96
570 393
572 1
573 50
575 14
576 5
578 450
579 1
581 11
582 1
584 1
585 32
587 8
588 3
590 2
591 2
593 2
594 3
596 5
597 2
599 36
600 8
602 380
603 1
605 1
606 2
608 9
609 1
611 6
612 1
614 11
615 2
617 338
618 2
620 6
621 1
623 3
624 1
626 1
627 6
629 8
630 2
632 18
633 5246
635 1
636 18
638 11
639 3
641 6
642 1
644 1
645 5
647 504
648 114
650 3
651 2
653 6
654 3
656 2
657 14
659 2
660 261
662 50
663 143
665 5
666 3
668 1
669 32
671 1
672 21
674 2
675 2
677 1
678 215
680 2
681 12
683 6774
684 2
686 1
687 2
689 2
690 39
692 2
693 11
695 3
696 1
698 3
699 23
701 1
702 9
704 8
705 38
707 2
708 2
710 24110
711 3
713 2
714 2
716 78
717 37506
719 13418
720 1
722 8
723 6
725 6
726 1
728 1
729 5
731 3
732 50
734 5
735 1
737 36
738 15
740 2
741 2
743 1
744 3
746 2
747 1
749 2
750 2
752 2
753 2
755 1
756 5
758 2
759 2
761 1
762 1
764 20
765 3
767 2
768 1
770 191
771 2
773 1
774 35
776 51
777 2
779 3
780 6
782 1
783 2
785 1
786 5
788 39
789 248
791 27
792 1
794 30
795 5
797 21
798 1
800 8
801 1
803 2
804 6
806 9
807 5
809 5
810 2
812 1
813
815 2
816 275
818 1
819 1
821 81
822 2
824 8
825 1
827 1
828 3
830 6
831 9
833 17
834 71
836 1
837 2
839 1
840 29
842 69
843 2
845 2
846 1
848 273
849 9
851 9
852 8
854 3
855 1
857 1
858 3749
860 1
861 2
863
864 1
866 2
867 2
869 2
870 3
872 12
873 5
875 1
876 414
878 1
879 11
881 47
882 5
884 5
885 2
887 5
888 1647
890 1
891 816
893 246
894 1
896 8
897 1
899 1
900 2
902 14
903 29
905 6
906 6
908 5
909 164
911 1
912 4917
914 12
915 1
917 2
918 1
920 1
921 137
923 11
924 12
926 6
927 1
929 3615
930 24
932 6
933 2
935 6
936 62
938 17
939 66
941 26
942 5
944 2
945 170
947 2693
948 33
950 1
951 12
953 2
954 2
956 2
957 2
959 1
960 1
962
963 357
965 17
966 6
968 5
969 1
971 2
972 26
974 1
975 2
977 24
978 2
980 17
981 1
983 1875
984 17
986 78
987 1
989 2
990 1
992 1
993 1
995 6
996 416
998 2
999 3761
1001 1
1002 1
1004 2
1005 8
1007 1
1008 2771
1010 3351
1011 1
1013 3
1014 3
1016 1
1017
1019 89
1020 1
1022 1
1023 6
Williams primes
Retrieved from "https://www.rieselprime.de/z/index.php?title=Williams_prime_PP_least&oldid=34645"