Bases 6-32 reservations/statuses/primes

[gd_barnes]

Status report in an Email from Mathew on March 1st for Riesel base 30:

225 (127K)
239 (138K)
249 (130K)
659 (129K)
774 (126K)
1024 (140K) complete
1580 (124K)
1642 (127K)
1936 (115K)
2293 (114K)
2538 (113K)
2916 (114K)
3256 (110K)
3719 (110K)
4372 (110K)
4897 (110K)


No primes.

He is searching all k's to n=140K so k=1024 is now released. It is very low weight. < 1% of n-values remain on a sieve to an optimal depth.

[Siemelink]

I'd like to reserve from Riesel base 28 k = 233 and k = 4871 until 200,000.

Regards, Willem.

[Xentar]

sierp-b19: 934 k remaining, n = 40k

[Xentar]

Primes for the range
s19, n=34K - 40K

310306*19^34004+1
297474*19^34069+1
327916*19^34078+1
143776*19^34304+1
252166*19^34402+1
452226*19^34420+1
232536*19^34550+1
504516*19^34576+1
705946*19^34596+1
325366*19^34646+1
476304*19^34675+1
656914*19^34991+1
557436*19^35046+1
662236*19^35046+1
560634*19^35103+1
413586*19^35200+1
623776*19^35516+1
398586*19^35548+1
306426*19^35664+1
82854*19^35979+1
46516*19^35990+1
295054*19^36231+1
457896*19^36498+1
560464*19^36523+1
675186*19^36548+1
145536*19^36604+1
191416*19^36760+1
129216*19^36764+1
667726*19^36926+1
29484*19^37113+1
89026*19^37126+1
710644*19^37433+1
742794*19^37527+1
519514*19^37735+1
282004*19^37773+1
732676*19^37832+1
223854*19^37867+1
521784*19^37869+1
654456*19^37950+1
19464*19^38111+1
185854*19^38199+1
728766*19^38240+1
238624*19^38371+1
572604*19^38373+1
536944*19^38571+1
254046*19^38734+1
446166*19^38880+1
148636*19^39252+1
61216*19^39334+1
431566*19^39716+1
597126*19^39742+1
146514*19^39791+1
738504*19^39929+1

[Mathew]

I will be sieving Riesel base 19 to optimal depth

[Batalov]

Originally Posted by Flatlander

R base 30 tested to 110k. Sieve to 140k attached, P=3T.

/sigh/ It is a little disheartening to see 225*30^n-1 (and k=1936, 2916) with even n's in that file, as well as n|5 for k=1024. The pfgw with internal algebraic factorization patch could help these cases automagically, if Mark bites on my pitch in the other thread.

I'll take the unreserved k=1024 R30 to 200K.
And k=225,1936,2916 from 140K to 200K, can I?

[gd_barnes]

Originally Posted by Batalov

/sigh/ It is a little disheartening to see 225*30^n-1 (and k=1936, 2916) with even n's in that file, as well as n|5 for k=1024. The pfgw with internal algebraic factorization patch could help these cases automagically, if Mark bites on my pitch in the other thread.

I'll take the unreserved k=1024 R30 to 200K.
And k=225,1936,2916 from 140K to 200K, can I?

I must admit that all I do when I post those sieve files left by others is to verify that the sieve depth is what is shown in the file and remove any k's where primes have already been found. Unfortunately I don't quite have the time to check everything such as removing even n's on k's that are perfect squares and higher n-modulos for k's that are higher powers. It's good to have people checking things like that.

Yes, you may take k=225, 1024, 1936, and 2916 from n=140K-200K. This is somewhat unusual but we have done it before. I just show both of you as having the k's reserved for different n-ranges.

Mathew, if you happen to see this, your k=225, 1936, and 2916 are not being poached. Serge will be searching above your range. If he finds a prime for one of them before you do, we'd still ask that you continue searching and possibly find a smaller prime. CRUS (which means me in this case ) likes to find the smallest prime for each k, if that is reasonably possible. We certainly won't argue if 2 different people find 2 different top-5000 primes for the same k. It happened once before when Max and I found primes a few days apart on the same k for base 16. It is the smallest prime for each k that gets shown on the pages.

Also, if you want to mess with it, as Serge pointed out, you could remove all even n-values for k=225, 1936, and 2916 from the sieve file because the k's are perfect squares. But if you don't, it won't hurt too much. It's usually only 1-5% of all remaining candidates for each k.

With the last prime at n=~50K, I'm wondering when we are finally going to find one on this base. Searching all to n=140K and 5 others to n=200K will hopefully finally yield a large prime for it.


Gary

[Mathew]

I didn't catch that 1936 and 2916 were squares. I used mini-geek's perl code and have removed n's for 225 (15^2) 169 n's, 1024 (2^5) 20 n's, 1936 (44^2) 217 n's, 2916 (54^2) 77 n's. I guess I have to brush up on my squares.

I attached the new out file. I also told Batalov to go right ahead with taking these k's to 200k.

Mathew

[Batalov]

Ah, wait, the 110-140K interval was always yours and never was intended to be trespassed. Nothing like that crossed my mind. Your PM and this last message were still ambiguous, and I want to clarify - you are keeping them for 110-140K, right?

I am only trying n=140-200K for these four k's (sieiving, mostly, and prescreening to get the timing estimates).

In fact, it went down like this: I saw that k=1024 was free, I liked it (2¹⁰, lots of fun eliminations, but even bases actually turned out to be eliminated by a small factor). Then I checked - were there other squares? and there were. (And I've misread the status how far the were, I thought they were at ~138K done, but I looked at a different line, apparently.) Then I've grabbed the sieve file just to see that they only had odd n's and was surprised that - not. Sorry, Chris,... could have happened to myself just as easily; no criticism intended.
...and only then I edited my message which was originally only about k=1024 (and 225).

Peace!

[Mathew]

Originally Posted by Batalov

Ah, wait, the 110-140K interval was always yours and never was intended to be trespassed. Nothing like that crossed my mind. Your PM and this last message were still ambiguous, and I want to clarify - you are keeping them for 110-140K, right?

That is correct I will continue to 140k for all the k's. I think Gary marked it well on this page Reservations

Hopefully that clears up all ambiguity.

Also Gary I sent you completions of k= 239,249,and 659

[gd_barnes]

Glad you guys got that straight on base 30. It looks like everything is in order. I actually think it's an excellent idea for the "math type" of people to take "weird" k's like ones that are squared, cubed, or have higher powers to a higher search limit. The math folks know exactly what to look for in eliminating n's that don't need to be searched and as is the case with Serge, frequently eliminating entire k's that don't need to be searched.

I remember doing a very detailed look way-back-when on base 30 due to the large # of perfect squared k's remaining. I did find the unusual partial algebraic factorization for k=1369, which allowed its removal, where the odd n's actually have 3 factors to eliminate them. I mention this because I can virtually guarantee that none of the k's remaining can be eliminated due to an unusual combination of numeric/algebraic factors. They all should have a prime at some point, even if that prime is n>1T! That said, I didn't do a detailed look at the sieve file; hence you found the even n's and n|5's that could be removed on the squared k's and the 5th-power k.

In the mean time, here is a status:

Sierp base 9 is at n=600K. Max and I are continuing on to n=750K, although there exists the possibility that I/we might stop closer to n=700K. The tests are well over 2 hours now; already a little beyond my tolerance level.


Gary