[quote=kar_bon;146770]perhaps these info can help, too:
i tested in a few minutes my scripts with Riesel base 37 and got these info:

all 3885 even values for k=2 to 7770 tested
n=1: 688 primes found (3197 remain)
k==1 mod 3: 1295 deleted (1902 remain)
n=2: 414 primes (1488 remain)
3: 277 (1211)
4: 162 (1049)
5: 106 (943)
6: 91 (852)
7: 77 (775)
8: 65 (710)
9: 36 (674)
10: 42 (632)
11: 48 (584)
12: 35 (549)
13: 21 (528)
14: 23 (505)
15: 17 (488)
16: 20 (468)
17: 20 (448)
18: 20 (428)
19: 13 (415)
20: 13 (402)
and further PRPs found:
10,10,14,9,6,2,8,7,7,15,6,10,5,6,5,3,6,6,8,4,4,5,6,2,5,0,2,3,5,3
220 k's remain after n=50 tested
202 after n=60
182 after n=70
169 after n=80
159 after n=90
151 after n=100
116 after n=200
102 after n=300
85 after n=400
79 after n=500
74 after n=600
71 after n=700
64 after n=800
63 after n=900
62 after n=1000

i will try to modify my scripts, because the log file with candidates left / primes/PRP's found isn't looking good![/quote]


Very interesting info. Karsten. We should be able to do an accurate analysis of future k's remaining based on this info.


Gary

Riesel Base 45
 

I am going to reserve Riesel Base 45 k=24 to n=50k, if I am happy with this computer I might add more k's later.

Riesel Base 35
 

new PRP's
[code]
98114 7140
186752 7160
26522 7162
193960 7171
141602 7180
187898 7216
170470 7219
81038 7222
141144 7239
154090 7261
229660 7263
197416 7267
125242 7269
216830 7302
204914 7342
65864 7346
86624 7366
215398 7379
28010 7382
167314 7387
197042 7390
97942 7391[/code]

4.89M pairs left upto n=7420

Riesel Base 35
 

new PRPs
30304 7423
233318 7426
239534 7438
240080 7450
7478 7452

n=7454

Riesel Base 35
 

267464 7464
95720 7478
63878 7482
82414 7497
53192 7542
25888 7545
11738 7558
162698 7566
230324 7572
72454 7591
258004 7609
111230 7638
259240 7657
53290 7659
9716 7684
122840 7698
209296 7713
93154 7723
198856 7733
163276 7749

at n=7765

Riesel base 35
 

new PRP's

205298 7772
188126 7776
184432 7813
156122 7830
62312 7856
70648 7875
190930 7879
96422 7882
63388 7887
205214 7896
180190 7899
75238 7903
10808 7912
132392 7926
134092 7937
140084 7966
113006 7984
46874 7996
134240 8010

now at n=8024 with 4.675M candidates left

does anyone have any suggestions on what bases it would be easiest to prove

You don't know if a conjecture will easely be proven before you actually start to prove it (just look at sierp base 17 and 18 for example).
I can give you a list of bases with a relatively low conjectured k (<1000).
The first number is the base and the number between brackets is the conjectured k.

Conjectured k for bases 51 to 100:

Sierp: 54 (21), 56 (20), 59 (4), 62 (8), 64 (51), 65 (10), 68 (22), 69 (6), 72 (731), 74 (4), 76 (43), 77 (14), 83 (8), 84 (16), 86 (28), 89 (4), 90 (27), 92 (32), 94 (39), 98 (10), 99 (684)

Riesel: 54 (21), 56 (20), 57 (144), 59 (4), 62 (8), 64 (14), 65 (10), 68 (22), 69 (6), 72 (293), 73 (408), 74 (4), 77 (14), 80 (253), 81 (74), 83 (8), 84 (16), 86 (28), 89 (4), 90 (27), 92 (32), 93 (612), 94 (39), 98 (10), 99 (144), 100 (750)

You can also for example go for Briers ([URL]http://www.mersenneforum.org/showthread.php?t=10930[/URL]) or try to prove the first, second, third, ... conjectured k for one specific base with a lot of small conjectured k (Riesel base 68 for example has a conjectured k at k=22, 43, 142, 185, 783, 1394, 3051)

If you need more info, just ask. I have a lot more interesting things you can do with conjectures :)

I've recently been working on a # of the easier unreserved Riesel bases 50 thru 125. The Sierp side is open for bases > 50 although we have some info. already from Prof. Caldwell for bases 50-100.

I'm going to post the results of some of my searches later tonight. Some were very easily proven and a few others have just a few k's left and could be proven by others at some point.

There is a thread that has all of the conjectured values for all bases on both sides up to 1024. That would be a good starting point.


Gary

[quote=MrOzzy;150940] prove the first, second, third, ... conjectured k for one specific base with a lot of small conjectured k (Riesel base 68 for example has a conjectured k at k=22, 43, 142, 185, 783, 1394, 3051)
[/quote]

This is a very interesting idea that I have toyed around with at different times but never stuck with it very long. Riesel and Sierp base 8 would be interesting bases to attack to prove the 2nd/3rd/etc. conjectured k's since their 1st one is so low and was already easily proven. Also, since base 8 is a power of 2, LLRing would be fast.


Gary

Riesel update
 

Hi Gary,

I am comparing my results with your excellent pages. Here is the difference:

Riesel base 49: I searched until n = 116,000, sieved until n = 200,000.
Riesel base 36: I reached the end of my reservation at n = 25,000. These primes are not yet listed on the pages:
107819*36^24637-1
94152*36^24621-1
114403*36^24366-1
61040*36^24332-1
43215*36^23692-1
100937*36^23147-1
80733*36^22504-1

Cheers, Willem.