Sierp base 45 is at n=21K; 58 k's remaining; continuing to n=25K.

Sierp base 91 is at n=18K; 39 k's remaining; continuing to n=25K.

Riesel bases 42 and 48 for n=10K-25K to start after these are done.

Riesel Base 39
 

Riesel Base 39

Tested from n=2K-3K. 1899 primes found (see attached file)

8898 k's remaining + the 1 I am not testing = 8899 left

Continuing

Riesel Base 58
 

37256*58^29445-1

24182*58^30234-1
49043*58^30709-1
84998*58^30872-1

84998*58^31553-1
68924*58^31737-1
30818*58^31946-1
60729*58^31965-1

53582*58^32291-1
65046*58^32355-1
61623*58^32433-1
22226*58^32731-1

63719*58^33604-1
4986*58^33903-1

101184*58^34068-1
77037*58^34078-1
92513*58^34093-1
642*58^34348-1
45152*58^34390-1
36054*58^34439-1

Completed to 35000 and continuing. They seem to be getting quite a bit more sparse.

1866*37^48305+1 is prime!
Only 3 more to go on Sierp. base 37. :smile:

[quote=rogue;187476]Completed to 35000 and continuing. They seem to be getting quite a bit more sparse.[/quote]

Yeah, base 58 is definitely a below average prime base. Compare it to Sierp base 91 that I'm near n=22K on. With a conjecture of ~85K (vs. your ~110K), it only has about 35-37 k's remaining. That would be a very prime base! :-) Even taking into account that only 4/15 of all k's are tested (due to trivial factors), that's still > 22000 k's that have a prime already found for them. Having such a small percentage of initial k's remaining for such a high base is very unusual.

A new potential analogy about the conjectures: In addition to bases where b=2^q-1, it appears that bases where b==(1 mod 30) are also quite prime bases. It's interesting that base 31 overlaps both of these and it is definitely one of the more prime bases. Bases 31, 61, and 91 all definitely have fewer k's remaining than the usual bases for their sizes and conjectures. Like above, I'm taking into account the fact that all only have 4/15 of their k's tested due to trivial factors so that doesn't explain their density of primes.

This analogy needs to be extended to base 121, 151, 181, etc. to see if it holds water. A further extension of it might be: Any base where b-1 contains a large # of factors is likely to be a very prime base.

I'd like to make a prediction at this point: Sierp base 31 with a conjecture of k=~6.4M will be easier to prove than Riesel base 58 with a conjecture at k=~110K! I'm taking base 31 to n=25K and I expect to have ~1000 k's remaining at that point. At the rate in which they are being removed and taking into account a lowering of that rate in the future due to lower average weight k's, I expect there to be ~500 k's remaining at n=100K. Although we may not see it in the foreseeable future, I think by the time Riesel base 58 and Sierp base 31 are nearing n=1M, base 31 will have fewer k's remaining!

BTW, I meant to ask you, what caused you to want to take such a difficult base to a higher limit?


Gary

[quote=mdettweiler;187632]1866*37^48305+1 is prime!
Only 3 more to go on Sierp. base 37. :smile:[/quote]

Good one Max!

With me getting multiple bases on the Sierp side up to n=25K now, it will be good to have people follow up behind me and bring many of them to n=50K and 100K, especially on the bases with < ~10-20 k's remaining.

The speedier PFGW has been a boon to this project! :-)

[quote=gd_barnes;187651]A new potential analogy about the conjectures: In addition to bases where b=2^q-1, it appears that bases where b==(1 mod 30) are also quite prime bases. It's interesting that base 31 overlaps both of these and it is definitely one of the more prime bases. Bases 31, 61, and 91 all definitely have fewer k's remaining than the usual bases for their sizes and conjectures. Like above, I'm taking into account the fact that all only have 4/15 of their k's tested due to trivial factors so that doesn't explain their density of primes.

This analogy needs to be extended to base 121, 151, 181, etc. to see if it holds water. A further extension of it might be: Any base where b-1 contains a large # of factors is likely to be a very prime base.

Gary[/quote]
i will be soon looking soon for bases to work on
i might help do some of this research
i can now work out trivial factors and k/base removal
i might need a little help with algebraic factors though

[quote=Siemelink;175292]
I have started on the remains of Riesel base 23. I'll take it from 180,000 to 200,000

Cheers, Willem[/quote]

Oh, the base 49 tests have reached 150,000 and I have run them from 180,000 to 200,000 as well.

Cheers, Willem.

Doing a lot of little stuff:

Reserving:

Riesel Base 80 all k's 25K-100K

Sierp base 45 is complete to n=25K; 53 k's remaining; now unreserved

Sierp base 91 is complete to n=25K; 35 k's remaining; now unreserved

Details to be shown on web pages when I get them updated for all CRUS efforts completed in the last week sometime on Thurs. or Fri.

Riesel bases 42 and 48 for n=10K-25K to start later today.

[quote=Siemelink;188429]Hi friend, I am ahead of you on this base 160. I've taken it to 30,000 already. Aha, I must have mentioned the reservation in the Base < 32 posts.

Willem.[/quote]

I have copied that post over to this thread. See post #467.

Willem, please separate the statuses on bases <= 32 and bases > 32 to avoid any future confusion.

Also, I need the results on this. Without them, it is best that it be double checked.


Thanks,
Gary