Thread: k=1 thru k=12 View Single Post
2008-11-03, 04:49   #7
gd_barnes

May 2007
Kansas; USA

32·5·229 Posts

Quote:
 Originally Posted by robert44444uk This k was generated from looking at (x^2)^n-1 factorisations -covering set is 3,5,17,257,641,65537,6700417 which I think is 32-cover. I do not think anyone has claimed it is the smallest k, it just comes from the smallest-cover.

OK, very good. I asked because I'm undertaking an effort on 2 slow cores to see which small bases do not yield an easy prime for k=2. I started with the Riesel side and am testing bases 2 to 1024.

Here are the 20 Riesel bases <= 1024 remaining that do NOT have a prime of the form 2*b^n-1 at n=10K:
Code:
 b
107
170
278
303
383
515
522
578
581
590
647
662
698
704
845
938
969
989
992
1019
Here are the primes for n>=1000 found for the effort:
Code:
  b   (n)
785 (9670)
233 (8620)
618 (8610)
627 (7176)
872 (6036)
716 (4870)
298 (4202)
572 (3804)
380 (3786)
254 (2866)
669 (2787)
551 (2718)
276 (2484)
382 (2324)
968 (1750)
550 (1380)
434 (1166)
1013 (1116)
734 (1082)
215 (1072)

I'm going to take it up to n=10K and then work on the Sierp side to the same depth. The hard part about the effort is that each base has to be sieved individually. AFAIK sr(x)sieve will not sieve more than one base at a time.

Obviously PROVING that the lowest base that has a Sierp k=2 would not be possible using the brute force approach such as this but it would be quite possible for higher values of k.

If anyone else has any input or info. for searches done like this with a fixed k and variable base, please post it here.

I will edit this post with additional primes found and update the search limit as I progress.

Admin edit: Effort has now been completed to n=10K. 20 bases remain.

Gary

Last fiddled with by gd_barnes on 2008-11-11 at 07:06 Reason: add additional primes