View Single Post
Old 2020-07-04, 16:15   #859
sweety439
 
sweety439's Avatar
 
Nov 2016

2·11·103 Posts
Default

These Sierpinski bases (up to 1024) cannot be proven with current knowledge and technology, since they have either GFN (for even bases) or half GFN (odd bases) remain: (half GFN is much worse, since for these (probable) primes, the divisor gcd(k+-1,b-1) is not 1 (it is 2), and when n is large (for all numbers of the form (k*b^n+-1)/gcd(k+-1,b-1) whose gcd(k+-1,b-1) is not 1) the known primality tests for such a number are too inefficient to run. In this case one must resort to a probable primality test such as a Miller–Rabin test, unless a divisor of the number can be found)

Code:
b     k
2     65536
6     1296
10     100
12     12
15     225
18     18
22     22
31     1
32     4
36     1296
37     37
38     1
40     1600
42     42
50     1
52     52
55     1
58     58
60     60
62     1
63     1
66     4356
67     1
68     1
70     70
72     72
77     1
78     78
83     1
86     1
89     1
91     1
92     1
93     93
97     1
98     1
99     1
104     1
107     1
108     108
109     1
117     117
122     1
123     1
124     15376
126     15876
127     1
128     16
135     1
136     136
137     1
138     138
143     1
144     1
147     1
148     148
149     1
151     1
155     1
161     1
166     166
168     1
178     178
179     1
180     1049760000
182     1
183     1
186     1
189     1
192     192
193     193
196     196
197     1
200     1
202     1
207     1
210     1944810000
211     1
212     1
214     1
215     1
216     36
217     217
218     1
222     222
223     1
225     225
226     226
227     1
232     232
233     1
235     1
241     1
243     27
244     1
246     1
247     1
249     1
252     1
255     1
257     1
258     1
262     262
263     1
265     1
268     268
269     1
273     273
280     78400
281     1
282     282
283     1
285     1
286     1
287     1
291     1
293     1
294     1
298     1
302     1
303     1
304     1
307     1
308     1
310     310
311     1
316     316
319     1
322     1
324     1
327     1
336     336
338     1
343     49
344     1
346     346
347     1
351     1
354     1
355     1
356     1
357     357
358     358
359     1
361     361
362     1
366     366
367     1
368     1
369     1
372     372
377     1
380     1
381     381
383     1
385     385
387     1
388     388
389     1
390     1
393     393
394     1
397     397
398     1
401     1
402     1
404     1
407     1
408     408
410     1
411     1
413     1
416     1
417     1
418     418
420     176400
422     1
423     1
424     1
437     1
438     438
439     1
443     1
446     1
447     1
450     1
454     1
457     457
458     1
460     460
462     462
465     465
467     1
468     1
469     1
473     1
475     1
480     1
481     481
482     1
483     1
484     1
486     486
489     1
493     1
495     1
497     1
500     1
509     1
511     1
512     2, 4, 16
514     1
515     1
518     1
522     522
524     1
528     1
530     1
533     1
534     1
538     1
541     541
546     546
547     1
549     1
552     1
555     1
558     1
563     1
564     1
570     324900
572     1
574     1
578     1
580     1
586     586
590     1
591     1
593     1
597     1
600     129600000000
601     1
602     1
603     1
604     1
606     606
608     1
611     1
612     612
615     1
618     618
619     1
620     1
621     621
622     1
626     1
627     1
629     1
630     630
632     1
633     633
635     1
637     1
638     1
645     1
647     1
648     1
650     1
651     1
652     652
653     1
655     1
658     658
659     1
660     660
662     1
663     1
666     1
667     1
668     1
670     1
671     1
672     672
675     1
678     1
679     1
683     1
684     1
687     1
691     1
692     1
694     1
698     1
706     1
707     1
708     708
709     1
712     1
717     717
720     1
722     1
724     1
731     1
734     1
735     1
737     1
741     1
743     1
744     1
746     1
749     1
752     1
753     1
754     1
755     1
756     756
759     1
762     1
765     765
766     1
767     1
770     1
771     1
773     1
775     1
777     777
783     1
785     1
787     1
792     1
793     793
794     1
796     796
797     1
801     801
802     1
806     1
807     1
809     1
812     1
813     1
814     1
817     817
818     1
820     820
822     822
823     1
825     1
836     1
838     838
840     1
842     1
844     1
848     1
849     1
851     1
852     852
853     1
854     1
858     858
865     865
867     1
868     1
870     1
872     1
873     1
878     1
880     880
882     882
886     886
887     1
888     1
889     1
893     1
896     1
897     897
899     1
902     1
903     1
904     1
907     1
908     1
910     828100
911     1
915     1
922     1
923     1
924     1
926     1
927     1
932     1
933     933
937     1
938     1
939     1
941     1
942     1
943     1
944     1
945     1
947     1
948     1
953     1
954     1
958     1
961     1
964     1
966     870780120336
967     1
968     1
970     970
974     1
975     1
977     1
978     1
980     1
983     1
987     1
988     1
993     1
994     1
998     1
999     1
1000     10
1002     1
1003     1
1005     1005
1006     1
1008     1008
1009     1
1012     1012
1014     1
1016     1
1017     1017
1020     1020
1024     4, 16

Last fiddled with by sweety439 on 2020-07-10 at 06:28
sweety439 is offline   Reply With Quote