[quote=gd_barnes;195848]...with one k left... If proven, Riesel base 22 would have 5 primes of n>25K and Sierp base 17 would have 4. All the rest above would have 3. Sierp base 17 would be the 1st one with 3 primes of n>100K![/quote]
Here's three for Riesel base 61:
[FONT=Arial Narrow]6168*61^29180-1 is 3-PRP! (62.1023s+0.0030s)
1644*61^31715-1 is 3-PRP! (42.4267s+0.0034s)
198*61^41855-1 is 3-PRP! (75.2291s+0.0049s)[/FONT]
and still going (4 k left). This one could /one day/ have 7.

Reserve Riesel base 42
 

Hello

I would like to reserve Riesel base 42 to n=30K for all k's.

[quote=Mathew Steine;195973]Hello

I would like to reserve Riesel base 42 to n=30K for all k's.[/quote]


Hi Mathew. Welcome to Conjectures R Us. If you have any questions, let us know. Everyone is very helpful here.

On your reservation, Riesel base 42 is already at n=25K so you'll be testing n=25K-30K, which is great to get a feel for how long it will take. With 53 k's remaining, I would estimate that you'll find 2-4 primes in the range, although it could be none or many more than that.

I will make a suggestion: Sieving small n-ranges is somewhat inefficient CPU-wise in the long run. You might consider sieving n=25K-50K. What you could do after finishing that is still only test n=25K-30K and if you decide to go no further, just leave the remainder of the file for others. Or you may decide to continue and you'll have a file ready for testing after sieving perhaps only a little more.

I mention this because it should only take ~2.2-2.3 times as long to sieve n=25K-50K to the same depth as n=25K-30K, even though the n-range is 5 times as large.


Gary

Riesel Base 40
 

Reserving Riesel Base 40 (the 4301 k's that are not at n=10k) from n=5k to 10k.

Welcome Mathew :tu:

2906*67^41890-1 is 3-PRP! (122.7303s+0.0085s)
Taking Riesel base 67 to 50K, too, I guess.

[U]Riesel base 88[/U] with conj. k=9702 has 83 k's at 3.5K... and going. Will wrap it at 10K for presentability and will take to 25K.

[U]Sierp. base 93[/U] with conj. k=24394 has ~270 k's left at ~2.5K. Will wrap at 10K.

Taking Sierpinski base 58. It is conjectured at k=43071. It hasn't been started yet. I considered briefly (okay, very briefly) base 51, either Sierpinski or Riesel, but I don't have the resources to tackle those bases. IIRC, those are the only two numbers without any work under base 60.

Riesel base 88
 

at 10.001K, 56 k's remain
[FONT=Arial Narrow]444 464 711 1247 1601 [B]1782[/B] 1932 2010 2013 2258 2417 2471 2493 2538 2744 3114 [B]3168[/B] 3641 3735 3761 [B]3773[/B] 3818 3819 3917 [B]4356[/B] 4538 4572 4967 5027 5112 5121 5307 5517 5606 5892 6101 6329 6332 6353 6393 6498 6759 6876 6945 7386 7667 7842 7911 7968 8667 8810 8990 9326 9344 9647 9678[/FONT]

*some special cases:
1782 = square * base/4
4356 = square
3168 = 36 * base (36 itself was eliminated at n=1; faster search: 36 with odd n)
3773 = 3^3 * 11 (thus, n=3k-1 are algebraic)

Some larger primes
[FONT=Arial Narrow]2382*88^7008-1
9213*88^7322-1
3474*88^7821-1
380*88^8712-1
5322*88^8766-1
3891*88^8957-1
3987*88^9379-1
4451*88^9727-1
6591*88^9909-1
4328*88^[B]10001[/B]-1 (Don't you hate when this happens? :-)
[/FONT]

To the best of my knowledge and from observation, k=3168 should test just as fast as k=36 for Riesel base 88. Just like LLR does for power-of-2 bases, PFGW for non-power-of-2 bases "knows" when a k is a multiple of the base and does an internal conversion to the lower k to make it search at the same speed. So you shouldn't have to do any manual conversion.

As for some of the n-values having algebraic factors for some of the k's that you observed, sr(n)sieve will eliminate a very high percentage of them when sieving. At the lower n-ranges that test in < ~30 secs., I don't bother with removing them because the personal time taken is not worth the hassle to do so.

Sierpinski base 58
 

[QUOTE=rogue;196524]Taking Sierpinski base 58. It is conjectured at k=43071. It hasn't been started yet. I considered briefly (okay, very briefly) base 51, either Sierpinski or Riesel, but I don't have the resources to tackle those bases. IIRC, those are the only two numbers without any work under base 60.[/QUOTE]

There are 196 remaining k at n=10000. Here are the k:
[code]
73*58^n+1
178*58^n+1
222*58^n+1
297*58^n+1
787*58^n+1
886*58^n+1
936*58^n+1
1315*58^n+1
1378*58^n+1
1923*58^n+1
2182*58^n+1
2341*58^n+1
2439*58^n+1
2656*58^n+1
2713*58^n+1
3246*58^n+1
3511*58^n+1
3541*58^n+1
3748*58^n+1
3834*58^n+1
4021*58^n+1
4261*58^n+1
5158*58^n+1
5227*58^n+1
5274*58^n+1
5997*58^n+1
6046*58^n+1
6333*58^n+1
6432*58^n+1
6943*58^n+1
7003*58^n+1
7083*58^n+1
7612*58^n+1
7966*58^n+1
8377*58^n+1
8556*58^n+1
8613*58^n+1
8784*58^n+1
8851*58^n+1
8923*58^n+1
9559*58^n+1
9676*58^n+1
9726*58^n+1
9736*58^n+1
9852*58^n+1
10048*58^n+1
10108*58^n+1
10372*58^n+1
10594*58^n+1
11506*58^n+1
11622*58^n+1
11917*58^n+1
12058*58^n+1
12108*58^n+1
12172*58^n+1
12778*58^n+1
13107*58^n+1
13177*58^n+1
13333*58^n+1
13768*58^n+1
14016*58^n+1
14118*58^n+1
14218*58^n+1
14349*58^n+1
15043*58^n+1
15046*58^n+1
15417*58^n+1
15931*58^n+1
16519*58^n+1
16707*58^n+1
16848*58^n+1
17638*58^n+1
18016*58^n+1
18112*58^n+1
18409*58^n+1
18702*58^n+1
18744*58^n+1
19134*58^n+1
19233*58^n+1
19267*58^n+1
19381*58^n+1
19389*58^n+1
19641*58^n+1
19885*58^n+1
19899*58^n+1
20061*58^n+1
20730*58^n+1
20733*58^n+1
20760*58^n+1
20902*58^n+1
21064*58^n+1
21348*58^n+1
21357*58^n+1
21586*58^n+1
21766*58^n+1
21888*58^n+1
22008*58^n+1
22123*58^n+1
22203*58^n+1
22347*58^n+1
22384*58^n+1
22431*58^n+1
22599*58^n+1
22812*58^n+1
23011*58^n+1
23127*58^n+1
23424*58^n+1
23658*58^n+1
23953*58^n+1
24219*58^n+1
24421*58^n+1
24612*58^n+1
24801*58^n+1
25023*58^n+1
25189*58^n+1
25371*58^n+1
25489*58^n+1
25639*58^n+1
25666*58^n+1
26077*58^n+1
26136*58^n+1
26206*58^n+1
26319*58^n+1
26551*58^n+1
26568*58^n+1
26907*58^n+1
26953*58^n+1
27000*58^n+1
27159*58^n+1
27436*58^n+1
27441*58^n+1
27552*58^n+1
27670*58^n+1
27823*58^n+1
28192*58^n+1
28321*58^n+1
28437*58^n+1
28734*58^n+1
28881*58^n+1
29013*58^n+1
29124*58^n+1
29454*58^n+1
29619*58^n+1
29739*58^n+1
29811*58^n+1
30148*58^n+1
30714*58^n+1
30799*58^n+1
30918*58^n+1
31573*58^n+1
31660*58^n+1
31776*58^n+1
32746*58^n+1
32749*58^n+1
32808*58^n+1
33336*58^n+1
33589*58^n+1
33631*58^n+1
33745*58^n+1
34002*58^n+1
34383*58^n+1
34396*58^n+1
34632*58^n+1
35094*58^n+1
35458*58^n+1
35517*58^n+1
35976*58^n+1
36256*58^n+1
36286*58^n+1
36522*58^n+1
36781*58^n+1
36816*58^n+1
37099*58^n+1
37386*58^n+1
37764*58^n+1
38463*58^n+1
38469*58^n+1
38646*58^n+1
39000*58^n+1
39354*58^n+1
39763*58^n+1
39808*58^n+1
39961*58^n+1
39997*58^n+1
40389*58^n+1
40402*58^n+1
40423*58^n+1
41781*58^n+1
41817*58^n+1
41821*58^n+1
41842*58^n+1
42006*58^n+1
42082*58^n+1
42481*58^n+1
42538*58^n+1
42864*58^n+1
[/code]

I have attached the primes for n < 10000. Now back to Riesel base 58...

Riesel Base 40
 

Riesel Base 40 complete n-5K-10K

1292 primes found and proven (see attached file)

Releasing Base