Riesel 727
 

Reserving Riesel 727 as new to n=25k

[B]R986: proven, CK=8[/B]
Trivial k's: 1, 6
No MOB's, GFNs
Primes:
2*986^22-1
3*986^1-1
4*986^1-1
5*986^5580-1
7*986^12505-1

Sierp base 900, CK=12.
Primes:
2*900^1+1
3*900^3+1
4*900^3+1
5*900^3+1
6*900^47+1
7*900^1+1
9*900^1+1
10*900^1+1
11*900^1+1
8*900^2270+1

Base proven.

Riesel 727
 

Riesel Base 727
Conjectured k = 246
Covering Set = 7, 13
Trivial Factors k == 1 mod 2(2) and k == 1 mod 3(3) and k == 1 mod 11(11)

Found Primes: 70k's - File attached

Remaining k's: 4k's - Tested to n=25K
8*727^n-1
48*727^n-1
156*727^n-1
194*727^n-1

Trivial Factor Eliminations: 48k's

Base Released

Reserving

S869 to n=75K

Riesel 603
 

Continuing with the experimentation of the new-bases script, I'm going to have a go with Riesel 603. According to the untested bases thread, it has a conjectured k=11324. (I'm crazy with these large k-values, no?) ;]

Arghh, I'm getting _lots_ of these errors:

[CODE]Error occuring in PFGW at Wed May 12 19:58:24 2010
Expr = 8594*603^361-1
Detected in MAXERR>0.45 (round off check) in prp_using_gwnum
Iteration: 94/3347 ERROR: ROUND OFF 0.46094>0.45
PFGW will automatically rerun the test with -a1
-----------------------------------------------------------------------
[/CODE]

They kicked in at ... 4090*603^2467-1 and continued all the way to 11318*603^520-1

I have updated my version of pfgw (I was using whatever was in the CRUS package, which is now woefully out of date), and re-running the script. Is this the sort of error, Gary, that were running into recently?

Advice, comments, platitudes? Iced biscuits?

[QUOTE=paleseptember;214986]Continuing with the experimentation of the new-bases script, I'm going to have a go with Riesel 603. According to the untested bases thread, it has a conjectured k=11324. (I'm crazy with these large k-values, no?) ;]

Arghh, I'm getting _lots_ of these errors:

[CODE]Error occuring in PFGW at Wed May 12 19:58:24 2010
Expr = 8594*603^361-1
Detected in MAXERR>0.45 (round off check) in prp_using_gwnum
Iteration: 94/3347 ERROR: ROUND OFF 0.46094>0.45
PFGW will automatically rerun the test with -a1
-----------------------------------------------------------------------
[/CODE]

They kicked in at ... 4090*603^2467-1 and continued all the way to 11318*603^520-1

I have updated my version of pfgw (I was using whatever was in the CRUS package, which is now woefully out of date), and re-running the script. Is this the sort of error, Gary, that were running into recently?

Advice, comments, platitudes? Iced biscuits?[/QUOTE]

This is due to the version of PFGW you were using. Most (if not all) of these should go away with 3.3.3/3.3.4. With the version you are using, there is no immediate problem since PFGW detected the error and corrected itself.

Am getting the errors again (running with PFGW 3.3.4 now) for the same k/n pairs.

Since it's re-running with the -a1 switch (again), I'm going to assume that pfgw is taking care of it, but just in case, I've attached the pfgw_err.log for brighter minds if they're interested.

Sierp base 800, CK=88.
Primes attached.

k's remain:
26*800^n+1
61*800^n+1
82*800^n+1

Base completed to 25K and released.

[QUOTE=paleseptember;214994]Am getting the errors again (running with PFGW 3.3.4 now) for the same k/n pairs.

Since it's re-running with the -a1 switch (again), I'm going to assume that pfgw is taking care of it, but just in case, I've attached the pfgw_err.log for brighter minds if they're interested.[/QUOTE]

I'll see what we can do, but I'm not too concerned about it.

More closet cleaning

R523 CK=132 Primes=40 Remain=2
R597 CK=116 Primes=54 Remain=1 1 algebraic factor
R730 CK=171 Primes=112 Remain=1
R747 CK=120 Primes=54 Remain=4 1 algebraic factor
R753 CK=144 Primes=64 Remain=4 1 algebraic factor

Reserving S596 and R798 as new to n=25K

Sierp base 666, CK=231.

Base proven.

Edit: Gary, I have S369, S444 and S666 pages complete MDB

2*869^49149+1 is prime!

Sierpinski base 869 conjecture proven.

[QUOTE=rogue;215011]I'll see what we can do, but I'm not too concerned about it.[/QUOTE]

Cheers Rogue.

Okay, next strange thing (sorry sorry!) Having ran the new-bases-4.3 script to 2500, I have taken the pl_remain file to be the input for srsieve for the next step. First thing srsieve says is:
[CODE]WARNING: 1600*603^n-1 has algebraic factors.
WARNING: 1600*603^n-1 has algebraic factors.
WARNING: 5476*603^n-1 has algebraic factors.
WARNING: 5476*603^n-1 has algebraic factors.[/CODE]

Do I need to do anything about these two k-values?

[QUOTE=paleseptember;215172]Cheers Rogue.

Okay, next strange thing (sorry sorry!) Having ran the new-bases-4.3 script to 2500, I have taken the pl_remain file to be the input for srsieve for the next step. First thing srsieve says is:
[CODE]WARNING: 1600*603^n-1 has algebraic factors.
WARNING: 1600*603^n-1 has algebraic factors.
WARNING: 5476*603^n-1 has algebraic factors.
WARNING: 5476*603^n-1 has algebraic factors.[/CODE]

Do I need to do anything about these two k-values?[/QUOTE]

I'll leave this for someone else to answer. I think the answer is no, but others most likely have better informed opinions

[quote=vmod;215149]2*869^49149+1 is prime!

Sierpinski base 869 conjecture proven.[/quote]

Nice. Good work vmod. This was one of the bases where only k=2 remained. It will now be removed from the 1k and recommended bases threads.

[quote=paleseptember;215172]Cheers Rogue.

Okay, next strange thing (sorry sorry!) Having ran the new-bases-4.3 script to 2500, I have taken the pl_remain file to be the input for srsieve for the next step. First thing srsieve says is:
[code]WARNING: 1600*603^n-1 has algebraic factors.
WARNING: 1600*603^n-1 has algebraic factors.
WARNING: 5476*603^n-1 has algebraic factors.
WARNING: 5476*603^n-1 has algebraic factors.[/code]

Do I need to do anything about these two k-values?[/quote]

No, nothing NEEDS to be done. One optional thing that you could do is remove all of the even n-values for those k's from the sieve file to save a little bit of testing time. There won't be very many of them but they will be there.

As an explanation: Because those 2 k's are perfect squares, the even n-values will always be composite due to algebraic factors but sr(x)sieve does not know to automatically remove them. It is because x^2-1 factors as (x-1)*(x+1). As a specific example here, when n is even as in 1600*603^(2n)-1, it factors to (40*603^n-1)*(40*603^n+1).


Gary

Reserving S529 and R696 and S696 as new to n=25K

Per an Email from Mathew, he is at n=18.5K on R703. 24 k's are remaining. Continuing to n=25K.

Riesel 696
 

Riesel Base 696
Conjectured k = 288
Covering Set = 17, 41
Trivial Factors k == 1 mod 5(5) and k == 1 mod 39(139)

Found Primes: 224k's - File emailed

Remaining: 2k's - Tested to n=25K
152*696^n-1
225*696^n-1

k=169 proven composite by partial algebraic factors2

Trivial Factor Eliminations: 59k's

Base Released

Sierp 677
 

Sierp Base 677
Conjectured k = 112
Covering Set = 3, 113
Trivial Factors k == 1 mod 2(2) and k == 12 mod 13(13)

Found Primes: 50k's - File emailed

Remaining: 3k's - Tested to n=25K
34*677^n+1

Trivial Factor Eliminations: 4k's

Base Released

HTML created

Reserving several bases with CK<100 to n=25K from my former k=2 search, all that have only 1 or 2 k's remaining at n=10K, as follows:

R581
R845
R968
S626
S695
S752
S758
S917

Many are extremely low weight and only one has a CK>50. All should complete to n=25K in ~2-3 days running on 2 cores. Hopefully I'll prove 1 or 2 of them.

This should add a few bases to the 1k thread. :-)

Ian, I'll take care of showing these on the pages so that we aren't sending files back and forth.


Gary

Reserving the remaining five CK=10 and 12 Sierp bases (1 is b<500 shown in b=251-500 thread) to n=25K:

S563
S593
S714
S828

This is the last of my testing small conjectured bases for an extended period. The small Sierp bases are beginning to catch up with the Riesel bases now.

The lowest CK on either side is now 14.

ETA is < 2 days on 1 core.

Reserving Riesel 543 as new to n=25K

[quote=gd_barnes;215483]Reserving several bases with CK<100 to n=25K from my former k=2 search, all that have only 1 or 2 k's remaining at n=10K, as follows:

R581
R845
R968
S626
S695
S752
S758
S917

Gary[/quote]


All 8 bases from this former k=2 search that had 1 or 2 k's remaining are complete to n=25K. All are released.

Not a single base was proven! Primes for n=5K-25K:

2*758^8309+1
58*581^16145-1

Both were 2k bases so 1k still remains. :-( Final status:

[code]
k(s)
base CK remain highest prime
R581 98 2 58*581^16145-1
R845 46 2 22*845^593-1
R968 16 4 2*968^1750-1
S626 10 2 5*626^2069+1
S695 28 2,8 26*695^1771+1
S752 16 2 15*752^1128+1
S758 10 8 2*758^8309+1
S917 16 2 8*917^53+1
[/code]

7 more bases for the 1k thread! More to follow with the CK=10 & CK=12 finishing effort...

R702 is complete to n=25
CK=75
k=36 is removed by algebraic factorizations

1k remains k=32

Sorry Gary another base to the 1k thread

Attached are the results.

[quote=gd_barnes;215595]Reserving the remaining five CK=10 and 12 Sierp bases (1 is b<500 shown in b=251-500 thread) to n=25K:

S563
S593
S714
S828
[/quote]

All of the remaining Sierp CK=10 and 12 bases are complete to n=25K. All are released. 2 were proven, 2 had 1k remaining (1 of them in the b<=500 thread), and 1 had 2k remaining.

Final status:
[code]
k(s)
base CK remain highest prime
S563 12 proven 4*563^3958+1
S593 10 2,8 6*593^1+1 (pitiful!)
S714 12 proven 10*714^7839+1
S828 12 8 5*828^6+1
[/code]

2 more bases for a total of 9 for the 1k thread over the last 2 days!

Reserving S999 to n=25K.

Riesel Base 798
Conjectured k = 339
Covering Set = 5, 13, 17
Trivial Factors k == 1 mod 797(797)

Found Primes: 328k's - File emailed

Remaining: 7k's - File emailed - Tested to n=25K
188*798^n-1
279*798^n-1
283*798^n-1
302*798^n-1
307*798^n-1
317*798^n-1
322*798^n-1

k=16, 169 proven composite by partial algebraic factors

Base Released

Sierp Base 596
Conjectured k = 200
Covering Set = 3, 199
Trivial Factors k == 4 mod 5(5)
k == 6 mod 7(7)
k == 16 mod 17(17)

Found Primes: 122k's - File emailed

Remaining: 5k's - Tested to n=25K
8*596^n+1
71*596^n+1
121*596^n+1
136*596^n+1
151*596^n+1

Trivial Factor Eliminations: 71k's

Base Released

Reserving the folllowing "1ker's" to n=50K.

30*514^n-1
22*900^n-1
8*908^n-1
74*947^n-1
4*968^n-1

[quote=MyDogBuster;216462]Reserving the folllowing "1ker's" to n=50K.

30*514^n-1
22*900^n-1
8*908^n-1
74*947^n-1
4*968^n-1[/quote]

22*900^n-1 was done to n=100K by me.

[QUOTE]22*900^n-1 was done to n=100K by me.[/QUOTE]

I can't find a post for R900 to n=100K. I see you did S900 as proven. Would you still have the files for R900?

I was going to post results for R900 together with R888 and R800 which also has reserved. They will be ready in 2-3 days.
I like "round" bases :smile:

[quote=unconnected;216495]I was going to post results for R900 together with R888 and R800 which also has reserved. They will be ready in 2-3 days.
I like "round" bases :smile:[/quote]

Yeah, I noticed you like the round ones...100, 200, 300, etc. :-)

If you have a reservation for R900, I must have missed it. Until you report the official status/results, I'll show it at n=25K and reserved by you to n=100K.

S928
 

Update on S928: complete to 12K

The following are primes:
[CODE]14128*928^11074+1
11518*928^11143+1
23712*928^11280+1
3484*928^11445+1
5547*928^11446+1
5799*928^11475+1
5253*928^11527+1
3934*928^11553+1
25203*928^11671+1
26503*928^11675+1
23113*928^11791+1
7828*928^11795+1
11493*928^11840+1
20523*928^11848+1
18808*928^11968+1
12156*928^11071+1
[/CODE]

16 primes, takes down to 648k-values remaining. Woo.

Continuing.

Riesel base 928 update
 

I have been going a little further on this range with my testing of PRPNet 3.3.0. I have found these primes:

27882*928^17164-1
8958*928^17378-1
24201*928^17447-1
11003*928^17454-1
12245*928^17484-1
21576*928^17495-1
8474*928^17505-1
15051*928^17510-1

I'm continuing on.

R1016 is proven

CK=112

Largest prime

7*1016^23335-1

Attached are the results

R1013 is proven

CK=14

Largest prime

10*1013^2627-1

Attached are the results

[quote=rogue;216667]I have been going a little further on this range with my testing of PRPNet 3.3.0. I have found these primes:

27882*928^17164-1
8958*928^17378-1
24201*928^17447-1
11003*928^17454-1
12245*928^17484-1
21576*928^17495-1
8474*928^17505-1
15051*928^17510-1

I'm continuing on.[/quote]


OK, since you're continuing, I should say this: Before posting the sieve file on the web pages, I found something like 5-10 k's in the file that you sent me from last time that already had primes for them so I used srfile to remove them before posting it.

Therefore if you are not using the file that I posted on the pages and did not remove any additional k's from the file since the last time you stopped, you can save some CPU time by using my file and removing the k's where you found primes here.

2 things I always do before posting sieve files on the pages is check the # of k's in them and their sieve depth, if that depth is either not available or looks unusual.


Gary

[QUOTE=gd_barnes;216751]OK, since you're continuing, I should say this: Before posting the sieve file on the web pages, I found something like 5-10 k's in the file that you sent me from last time that already had primes for them so I used srfile to remove them before posting it.

Therefore if you are not using the file that I posted on the pages and did not remove any additional k's from the file since the last time you stopped, you can save some CPU time by using my file and removing the k's where you found primes here.

2 things I always do before posting sieve files on the pages is check the # of k's in them and their sieve depth, if that depth is either not available or looks unusual.[/QUOTE]

I'll take a look and remove the k's that I had not removed from the server.

Sierp Base 529
 

Sierp Base 529
Conjectured k = 972
Covering Set = 7, 13, 79
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 10 mod 11(11)

Found Primes: 282k's - File emailed

Remaining k's: 12k's - File emailed - Tested to n=25K

Trivial Factor Eliminations: 191k's

Base Released

Riesel 543
 

Riesel Base 543
Conjectured k = 2500
Covering Set = 7, 13, 17, 19
Trivial Factors k == 1 mod 2(2) and k == 1 mod 271(271)

Found Primes: 1192k's - File emailed

Remaining: 47k's - File emailed - Tested to n=25K

k=16, 900, 1444 proven composite by partial algebraic factors

Trivial Factor Eliminations: 5k's

MOB Eliminations: 2k's - File Emailed
1086
2172

Base Released

Riesel 514
 

Riesel 514 the last k (30*514-n-1) tested n=25K-50K. Nothing found

Results attached Base released

R590 is complete to n=25K
CK=196

5k's remaining
38
67
98
109
152

Results will be emailed

Sierpinksi Base 662
 

Conjectured k = 14. Reserving.

Riesel 968
 

Riesel 968 the last k (4*968-n-1) tested n=25K-50K. Nothing found

Results attached - Base released

Reserving the following "1ker's" to n=50K

122*516^n+1
20*605^n+1
2*626^n+1
4*650^n+1
34*677^n+1

Completed the following to n=25K

R677 ck=112 primes=44 remain=7
R720 ck=104 primes=97 remain=5
R920 ck=103 primes=92 remain=9
R926 ck=104 primes=71 remain=9
R962 ck=106 primes=92 remain=9
R980 ck=110 primes=93 remain=5

Sierpinksi Base 662
 

Primes found:

[code]
2*662^183+1
3*662^1+1
4*662^2+1
5*662^13389+1
6*662^2839+1
7*662^2+1
8*662^1+1
9*662^6+1
10*662^154+1
11*662^1+1
12*662^83+1
13*662^2+1
[/code]

With a conjectured k of 14, this conjecture is proven.

Sierpinski bases 935 and 1013
 

These are the last three with a conjectured k of 14. I'm reserving them.

Oops, I just realized that I put this in the wrong thread. Could someone please move this to the correct thread.

Edit: Moved

[QUOTE] These are the last three with a conjectured k of 14. I'm reserving them.[/QUOTE]

You only listed 2, so I'm assuming you meant S740, S935 and S1013.

[QUOTE=MyDogBuster;217581]You only listed 2, so I'm assuming you meant S740, S935 and S1013.[/QUOTE]

I'm only doing two today and the other will be for tomorrow (if someone doesn't beat me to it). I don't want to break the rules. :smile:

[quote=rogue;217591]I'm only doing two today and the other will be for tomorrow (if someone doesn't beat me to it). I don't want to break the rules. :smile:[/quote]

The rules state that you can do as many as you want each day for bases with a conjectured k of <= 200. That's why I enlisted Ian. :smile:

[QUOTE=gd_barnes;217592]The rules state that you can do as many as you want each day for bases with a conjectured k of <= 200. That's why I enlisted Ian. :smile:[/QUOTE]

For some odd reason I was thinking bases <= 200.

In that case I will take Sierpinski base 740 too.

Sierpinski bases 548, 679, 812, 866, 934, and 968
 

All of these have a conjectured k of 16. I'm reserving them.

Sierpinski bases 872 and 908
 

Reserving.

Sierpinski bases 683, 930, 604, 620, 643 and 878
 

Reserving

Sierpinski bases 574, 919, 636, and 898
 

Reserving

rogue,

Hilarious.

[quote=Mathew Steine;217759]rogue,

Hilarious.[/quote]

Hum, well...I think he is serious. (unless there is some inside joke that I am missing) :smile:

He's doing a bunch of the small ones.

Here we go with some more from my former k=2 effort. There are a total of 9 but 2 are in the bases 251-500 thread. These are most of the bases from the k=2 search that had from 2 to 5 k's remaining at n=5K when I originally did the search a couple of years ago.

The following bases have been searched to n=25K and are released. None were proven but we have 3 more for the 1k remaining thread (including one with only k=2 remaining) and 3 more with k=2 remaining. Details to be shown on the pages.

R551; CK=22; k=10 & 14 remain; highest prime 2*551^2718-1
R662; CK=14; only k=7 remains; highest prime 2*662^16590-1
R785; CK=130; k=16 & 28 remain; highest prime 94*785^23033-1

S635 CK=52; only k=28 remains; highest prime 32*635^17309+1
S836 CK=32; only k=2 remains; highest prime 7*836^5700+1
S878 CK=23; k=2, 11, 13, & 17 remain; highest prime 10*878^972+1
S947 CK=80; k=2, 34, & 68 remain; highest prime 22*947^870+1


Collective primes for n=5K-25K:
11*662^13306-1
2*662^16590-1
2*785^9670-1
94*785^23033-1
4*635^11722+1
32*635^17309+1
7*836^5700+1


I checked others recent and older reservations and saw that just one overlapped with these: S878. I'll let Mark know separately.

Ian, all of these (plus the 2 for bases <= 500) have CK<=200 but I'll show these on the pages myself like before so that we aren't sending files back and forth.


Gary

Gary,

I know he is serious about the reservations.

How does a low CK help in the time it takes? R596 with a CK=200 took me <24 hrs to prove whereas R332 with a CK=38 (started only seconds apart, on the same machine) took me almost 2 weeks to get to n=25K. Is there some foresight that I am unaware of?

Also the joke (not inside) is that rogue thought the policy was 2 bases a day. After realizing this was not the case his mindset changed. Which, I find hilarious.

[quote=Mathew Steine;217762]Gary,

I know he is serious about the reservations.

How does a low CK help in the time it takes? R596 with a CK=200 took me <24 hrs to prove whereas R332 with a CK=38 (started only seconds apart, on the same machine) took me almost 2 weeks to get to n=25K. Is there some foresight that I am unaware of?

Also the joke (not inside) is that rogue thought the policy was 2 bases a day. After realizing this was not the case his mindset changed. Which, I find hilarious.[/quote]

I admit it is a bit funny. But I can say that since Ian is doing the HTML for them all as well as updating the untested and 1k threads. :smile:

As a general rule, the lower conjectures will take less time. Of course as you found, there are exceptions. But the fact is, if you choose a base with a CK of 10,000 and one with a CK of 10 or 100, the latter is likely to take much less time but there can be a wide variance in that time. S36 is the most glaring example of this. With a CK of 1886, it was proven almost instantly with a highest prime of n=1571. It is the highest conjecture proven at CRUS but what was the most amazing thing is that it was proven at such a low n. The second highest is S11 with CK=1490 but it did not fall until n=300544 so is not nearly as remarkable as S36!

So...if you choose a base with a CK of > 2000, it's highly unlikely that you will prove it. We do have one base with a CK of 9175 (S10) that has only one k remaining and is being searched at n=470K right now. But S10, S11, and S36 are all fairly small bases relative to the project as a whole. With the bases that are remaining untested now, it's unlikely that any one person will prove any one of those with a CK of > 1000.

I can offer up little in the way of telling ahead-of-time what base will be easy to prove. I know that bases where b==(1 mod 30) and where b=2^q-1 are relatively prime for their size but all of the smaller CK's from those have been searched already. The best thing to do is simply search a base to n=1000 or n=2500 and see what remains relative to the size of the conjecture. I say that because 3 k's remaining for a conjecture of k=1000 is much better than for a conjecture of k=100. The former likely has k's that are much heavier weight than the latter and so will likely be proven more easily.

Reference the weight of individual k's: If you have a k that has < 2% of its candidates remaining on a sieve to P=1G, that would be low weight. One with > 4% would be decent and with > 5% would definitely be high weight. If you have a k with > 5% of candidates remaining and it has been unlucky enough to not have a prime at n=2500 or n=10K or whatever, the chances are pretty good that a prime can be found with a continued search.


Gary

[quote=rogue;217740]Reserving[/quote]

Mark,

I just finished S878 to n=25K. See my recent post. If you've started on it, feel free to doublecheck it though.


Gary

[QUOTE=gd_barnes;217766]Mark,

I just finished S878 to n=25K. See my recent post. If you've started on it, feel free to doublecheck it though.[/QUOTE]

I haven't started it yet, so I'll get rid of it.

In case people are curious, I am dumping all of these into a PRPNet server trying to keep two computers "fed" through the next week as I will be on vacation. Right now I have about six days of work queued up, but if k fall, then that six days gets reduced. I'm only reserving whenever I have the time to sieve. I've been taking conjectures on the Sierspinski side because it hasn't had as much "love" as the Riesel side. There will be (unfortunately) an number of new single k conjectures when I'm done.

And speaking of such, I'll reserve S702, conjectured k of 75.

Sierpinski results
 

Base 548

[code]
2*548^1+1
3*548^6+1
4*548^2+1
5*548^1+1
6*548^115+1
7*548^4+1
8*548^5311+1
9*548^1+1
10*548^12+1
11*548^1+1
12*548^1+1
13*548^22+1
14*548^1+1
15*548^1+1
[/code]

Conjecture proven.

Base 679

[code]
6*679^4+1
10*679^1+1
12*679^10+1
[/code]

k=4 remains at n=25000. Releasing.

Base 740

[code]
2*740^1+1
3*740^1+1
5*740^1+1
6*740^1+1
7*740^2+1
8*740^83+1
9*740^1+1
10*740^12+1
12*740^5+1
[/code]

k=4, 11, and 13 remain at n=25000. Releasing.

Base 812

[code]
2*812^1003+1
3*812^1+1
4*812^26+1
5*812^5+1
6*812^19+1
7*812^2+1
8*812^3461+1
9*812^1+1
10*812^18+1
11*812^1+1
12*812^6+1
13*812^2+1
14*812^1+1
15*812^31+1
[/code]

Conjecture proven.

Base 866

[code]
2*866^1+1
3*866^7+1
5*866^5+1
6*866^1+1
7*866^2+1
10*866^2+1
11*866^35+1
12*866^531+1
13*866^1492+1
15*866^8+1
[/code]

k=8 remains at n=25000. Releasing.

Sierpinski results
 

Base 934

[code]
3*934^1+1
6*934^4+1
7*934^6+1
9*934^429+1
10*934^1+1
12*934^44+1
13*934^1+1
15*934^1+1
[/code]

k=4 remains at n=25000. Releasing.

Base 935

[code]
2*935^1+1
4*935^2+1
6*935^8+1
8*935^1+1
12*935^3+1
[/code]

k=10 remains at n=25000. Releasing.

Base 968

[code]
2*968^917+1
3*968^2+1
4*968^90+1
5*968^3+1
6*968^40+1
7*968^8+1
8*968^7+1
9*968^1+1
10*968^162+1
12*968^1+1
13*968^2+1
14*968^1+1
15*968^20+1
[/code]

k=11 remains at n=25000. Releasing.

Base 1013

[code]
2*1013^1+1
4*1013^2+1
6*1013^1+1
12*1013^1+1
[/code]

k=8 remains at n=25000. Releasing.

Note that any other k that appear to be "missing" have trivial factors.

Sierpinski Bases 542, 743, 747, and 893
 

Reserving

Sierpinski Bases 879, 924, 993, and 846
 

Reserving

R788 is proven
CK=14

Largest prime

7*788^1663-1

k=9 is removed by algebraic factors

attached are the results

[quote]k=9 is removed by algebraic factors[/quote]Factor 3 can never eliminate k's due to algebraic factors. Gary will have to explain the math. k=9 will have to be tested. Ian

[quote=Mathew Steine;217873]R788 is proven
CK=14

Largest prime

7*788^1663-1

k=9 is removed by algebraic factors

attached are the results[/quote]

Algebraic factors only remove the even n. There is no common factor for the odd n. As Ian said, you'll need to test k=9. If there was a common factor for the odd n, then you could make the statement: k=9 is removed by [I]partial [/I]algebraic factors. You could never make the statement that k=9 is removed by algebraic factors unless the base was also a perfect square. In that case, k's that are perfect squares are removed by (full) algebraic factors because the algebraic factors occur on [I]all[/I] n; not just the [I]even[/I] n.

To determine which common factor(s) for the odd n that there could be for a k that is a perfect square on a base, prime factor the base + 1 and only consider factors (f) that are f==(1 mod 4). Here:

789 = 3 * 263

Since 3 and 263 are both f==(3 mod 4), there can be no common factor for any odd n on squared k's for base 788. Therefore all squared k's must be tested unless they are eliminated by trivial factors, which the script would do automatically.

We'll wait to show this on the pages until you let us know that you've tested k=9.


Gary

Round 2
 

R788 is proven

9*788^11325-1 is 3-PRP! (44.1679s+0.0027s)
Primality testing 9*788^11325-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling Brillhart-Lehmer-Selfridge with factored part 79.21%
9*788^11325-1 is prime! (458.7986s+0.0052s)

Edit: Thanks Mathew

Riesel 908
 

Riesel 908 the last k (8*908-n-1) tested n=25K-50K. Nothing found

Results attached - Base released

74*947*n-1 removed - Prime at 74*947^27996-1

Finally movement in the other direction.

[QUOTE=MyDogBuster;217946]74*947*n-1 removed - Prime at 74*947^27996-1

Finally movement in the other direction.[/QUOTE]

That was easy. Unfortunately, most are not that easy.

[QUOTE]That was easy. Unfortunately, most are not that easy. [/QUOTE]

I've tested 4 bases so far in this scenario and R947 was by far the lowest weight of the 4. Go figure. LOL

Sierpinksi Base 908
 

Primes found:

[code]
3*908^6+1
4*908^2+1
5*908^5+1
6*908^1+1
7*908^10+1
9*908^1069+1
10*908^6+1
11*908^9855+1
12*908^4+1
13*908^10+1
14*908^1+1
15*908^2+1
16*908^5320+1
17*908^5+1
18*908^6+1
19*908^6+1
20*908^215+1
21*908^1+1
22*908^6+1
23*908^67+1
24*908^3+1
25*908^2+1
26*908^1+1
27*908^1+1
28*908^20+1
29*908^1471+1
30*908^1+1
31*908^360+1
33*908^27+1
35*908^3+1
37*908^2+1
38*908^11+1
39*908^2+1
40*908^84+1
41*908^23083+1
42*908^4+1
43*908^24+1
44*908^1+1
45*908^2+1
46*908^100+1
47*908^1+1
48*908^3+1
50*908^119+1
51*908^1+1
52*908^20+1
53*908^15+1
55*908^23710+1
54*908^1+1
56*908^1+1
57*908^4+1
58*908^4+1
59*908^3+1
60*908^4+1
61*908^16+1
62*908^921+1
63*908^3876+1
64*908^10+1
65*908^1+1
66*908^1+1
67*908^4+1
68*908^8091+1
69*908^1+1
70*908^26+1
72*908^10+1
73*908^6+1
74*908^125+1
75*908^3+1
78*908^378+1
80*908^5+1
81*908^3+1
82*908^36+1
83*908^251+1
84*908^6+1
85*908^2+1
86*908^3+1
87*908^25+1
88*908^4+1
89*908^69+1
90*908^3+1
91*908^24+1
92*908^1+1
93*908^3+1
95*908^3+1
96*908^5+1
97*908^70+1
98*908^2731+1
99*908^185+1
[/code]

k=2,8,32,34,36,49,71,76,77,79,94 remain at n=25000. Releasing.

With a conjectured k of 100, this base still has 11 k remaining at n=25000. I thought it was going to be 13 until those two showed up today. I don't know of any bases (not including those with very small conjectures) that have had such a large percentage of k remaining.

[quote=unconnected;216495]I was going to post results for R900 together with R888 and R800 which also has reserved. They will be ready in 2-3 days.
I like "round" bases :smile:[/quote]

Unconnected,

Are you now done with these 3 bases? Just thought I'd check.

Sierpinski bases 665, 887, 948, 998
 

Reserving.

Riesel bases 668 and 815
 

Reserving

Riesel bases 620, 695, 782, 836
 

Reserving.

R703 is complete to n=25K I am releasing

1 more prime was found

4310*703^20265-1

Results will be emailed

P.S. since rogue is creeping up to it I would like mention that I am working on R998 currently n~= 20.5K

Reserving S518, S578, and S647 to n=25K from my former k=2 effort.

Sierpinski base 872
 

Primes found:

[code]
2*872^7+1
3*872^1+1
4*872^14+1
5*872^15+1
6*872^1+1
7*872^10+1
8*872^1+1
9*872^3+1
10*872^78+1
11*872^5+1
14*872^5+1
15*872^2+1
16*872^8+1
17*872^3+1
18*872^17+1
20*872^13+1
21*872^1+1
22*872^2+1
23*872^6793+1
24*872^1+1
27*872^7438+1
28*872^58+1
29*872^29+1
30*872^1+1
31*872^4+1
32*872^4203+1
33*872^1581+1
34*872^2+1
35*872^21+1
36*872^1+1
37*872^328+1
39*872^3+1
40*872^14+1
41*872^1+1
42*872^2+1
43*872^2+1
44*872^4367+1
45*872^1+1
47*872^107+1
48*872^2+1
49*872^86+1
50*872^15+1
52*872^6+1
53*872^33+1
54*872^18+1
55*872^4+1
56*872^5+1
57*872^4+1
58*872^2+1
59*872^1+1
60*872^1+1
61*872^48+1
62*872^5987+1
63*872^10+1
65*872^1+1
67*872^44+1
69*872^1+1
70*872^64+1
71*872^37+1
72*872^30+1
73*872^10+1
74*872^3+1
75*872^2+1
76*872^28+1
78*872^2+1
79*872^6794+1
80*872^1+1
81*872^60+1
82*872^2+1
83*872^25+1
84*872^89+1
85*872^2+1
86*872^3+1
87*872^3+1
88*872^58+1
89*872^27+1
91*872^4+1
92*872^63+1
93*872^1+1
95*872^7+1
96*872^3+1
97*872^2+1
[/code]

k=13, 19, 26, 46, 68, and 94 remain at n=25000. Released.

Sierpinski base 604
 

Primes found:

[code]
3*604^2+1
4*604^1+1
6*604^4+1
7*604^1+1
9*604^1+1
10*604^3+1
12*604^17370+1
13*604^1+1
15*604^19+1
16*604^124+1
18*604^3+1
19*604^49+1
[/code]

Conjecture proven.

R800, R888 and R900 completed to n=100K.
There is only one prime: 4*800^33837-1
Results attached, bases released.

Sierp 516
 

Sierp 516 the last k (122*516-n-1) tested n=25K-50K. Nothing found

Results attached - Base released

Results
 

Sierpinski base 542 primes found:

[code]

3*542^1+1
4*542^15982+1
5*542^1+1
6*542^1+1
7*542^8+1
8*542^1+1
9*542^51+1
10*542^12+1
11*542^4909+1
12*542^20+1
14*542^1+1
15*542^109+1
16*542^364+1
17*542^3+1
18*542^69+1
19*542^18950+1
20*542^5+1
21*542^1+1
22*542^98+1
23*542^89+1
24*542^1+1
25*542^116+1
26*542^3+1
27*542^334+1
28*542^34+1
29*542^859+1
30*542^156+1
31*542^4+1
[/code]

k =2 and 13 remain at n=25000. Released.

Sierpinki base 574 primes found:

[code]
3*574^1+1
4*574^1+1
6*574^2+1
7*574^1+1
9*574^1+1
10*574^1+1
12*574^3+1
13*574^6+1
15*574^110+1
18*574^1+1
19*574^3+1
21*574^2+1
22*574^3+1
[/code]

k=16 remains at n=25000. Released.

Riesel base 620 primes found:

[code]

2*620^2-1
3*620^2-1
4*620^1773-1
5*620^4-1
6*620^1-1
7*620^1-1
8*620^10-1
9*620^9-1
10*620^1-1
11*620^1434-1
12*620^6-1
13*620^1-1
14*620^2-1
15*620^562-1
16*620^11-1
17*620^2-1
18*620^1-1
19*620^1-1
21*620^39-1
[/code]

k=20 remains at n=25000. Released.

Sierpinski base 620 primes found:

[code]

2*620^13+1
3*620^1+1
4*620^18+1
5*620^41+1
6*620^4+1
7*620^6+1
8*620^5+1
9*620^1+1
10*620^138+1
11*620^53+1
14*620^1+1
15*620^3+1
16*620^54+1
17*620^91+1
18*620^1+1
19*620^12+1
20*620^1+1
21*620^3+1
[/code]

k=12 and 13 remain at n=25000. Released.

Results
 

Sierpinski base 636 primes found:

[code]

2*636^2+1
3*636^141+1
5*636^1+1
6*636^3+1
7*636^11+1
8*636^8+1
10*636^1+1
11*636^1+1
12*636^3+1
13*636^1+1
15*636^9850+1
16*636^1+1
17*636^2+1
18*636^5+1
20*636^1+1
21*636^8+1
22*636^2+1
23*636^1+1
25*636^1+1
26*636^4+1
[/code]

Proven.

Sierpinski base 643 primes found:

[code]
4*643^5+1
10*643^42+1
12*643^1+1
16*643^1+1
18*643^3+1
[/code]

k=6 remains at n=25000. Released.

Sierpinski base 665 primes found:

[code]

2*665^45+1
4*665^1334+1
6*665^2+1
8*665^5+1
10*665^6+1
12*665^2+1
14*665^1+1
16*665^4+1
18*665^1+1
20*665^61+1
22*665^28+1
24*665^2+1
26*665^1+1
28*665^6+1
30*665^2+1
32*665^33+1
34*665^4+1
36*665^5749+1
[/code]

Proven.

Riesel base 668 primes found:

[code]

2*668^486-1
3*668^1-1
4*668^1-1
5*668^330-1
6*668^1-1
7*668^67-1
8*668^4-1
9*668^1-1
10*668^1-1
12*668^59-1
13*668^41-1
[/code]

k=11 remains at n=25000. Released.

Sierpinski base 683 primes found:

[code]
2*683^1+1
4*683^2+1
6*683^1+1
8*683^91+1
12*683^5+1
14*683^25+1
16*683^84+1
[/code]

k=18 remains at n=25000. Released.

Riesel base 695 primes found:

[code]
2*695^10-1
4*695^149-1
6*695^384-1
8*695^4-1
10*695^1-1
12*695^7-1
14*695^9970-1
16*695^1-1
18*695^2-1
20*695^8-1
22*695^1-1
24*695^2-1
[/code]

k=26 remains at n=25000. Released

Results
 

Sierpinski base 702 primes found:

[code]

2*702^3+1
3*702^2+1
4*702^9+1
5*702^1+1
6*702^1228+1
7*702^87+1
8*702^4+1
9*702^2+1
10*702^8+1
11*702^1+1
12*702^12+1
13*702^1+1
14*702^1+1
15*702^1+1
16*702^4+1
17*702^8+1
18*702^1+1
19*702^1+1
20*702^2+1
21*702^21+1
22*702^8+1
23*702^2+1
24*702^2+1
25*702^1+1
26*702^1+1
27*702^2+1
28*702^2+1
29*702^1+1
30*702^1+1
31*702^33+1
32*702^68+1
33*702^1+1
34*702^1+1
35*702^1+1
36*702^3+1
37*702^63+1
38*702^2+1
40*702^1+1
41*702^4+1
42*702^62+1
43*702^1+1
44*702^2+1
45*702^2+1
46*702^8+1
47*702^1422+1
48*702^2+1
49*702^15+1
50*702^13+1
51*702^1+1
52*702^3+1
53*702^25+1
54*702^307+1
55*702^1+1
56*702^1+1
57*702^72+1
58*702^2+1
59*702^17+1
60*702^2+1
61*702^408+1
62*702^1087+1
63*702^4+1
64*702^5+1
65*702^1+1
66*702^5+1
67*702^8+1
68*702^1+1
69*702^5+1
70*702^13+1
71*702^1+1
72*702^388+1
73*702^5+1
74*702^1+1
[/code]

k=39 remains at n=25000. Released

Sierpinski base 743 primes found:

[code]
2*743^1+1
4*743^246+1
8*743^71+1
12*743^2+1
14*743^10449+1
16*743^4+1
18*743^6+1
22*743^12+1
24*743^42+1
26*743^1+1
28*743^2+1
30*743^1+1
[/code]

k=10 remains at n=25000. Released.

Sierpinski base 747 primes found:

[code]
2*747^4+1
4*747^2+1
6*747^1+1
8*747^2+1
10*747^13+1
12*747^118+1
14*747^1+1
16*747^1+1
18*747^4+1
20*747^2+1
22*747^3560+1
24*747^1+1
26*747^1+1
28*747^2+1
30*747^2+1
[/code]

Proven.

Riesel base 782 primes found:

[code]
2*782^4-1
3*782^3-1
4*782^3-1
5*782^2-1
6*782^1-1
7*782^1685-1
8*782^8-1
9*782^3-1
10*782^3-1
11*782^2-1
13*782^11-1
15*782^7-1
16*782^1-1
17*782^4-1
18*782^510-1
19*782^3-1
20*782^16-1
21*782^1-1
22*782^1-1
24*782^3-1
25*782^3-1
26*782^2-1
27*782^4-1
[/code]

k=14 remains at n=25000. Released.

Results
 

Riesel base 815 primes found:

[code]
2*815^2-1
4*815^1-1
6*815^1-1
10*815^3-1
14*815^470-1
[/code]

k=8 remains at n=25000. Released.

Riesel base 836 primes found:

[code]
2*836^330-1
3*836^2-1
4*836^1-1
5*836^56-1
7*836^1-1
9*836^1-1
10*836^21-1
12*836^11-1
13*836^1-1
14*836^2-1
15*836^1-1
17*836^10-1
18*836^214-1
19*836^3-1
20*836^38-1
22*836^5-1
23*836^350-1
24*836^1-1
25*836^1-1
27*836^1-1
28*836^213-1
29*836^2-1
30*836^8-1
[/code]

k=8 remains at n=25000. Released.

Sierpinski base 846 primes found:

[code]
2*846^1+1
3*846^1+1
5*846^1+1
6*846^1+1
7*846^1+1
8*846^2+1
10*846^1+1
11*846^88+1
13*846^3+1
15*846^408+1
16*846^1+1
17*846^5+1
18*846^13+1
20*846^1+1
21*846^13+1
22*846^8+1
23*846^6+1
26*846^1+1
27*846^3371+1
28*846^1+1
30*846^2+1
31*846^1+1
32*846^1+1
33*846^1+1
35*846^1+1
36*846^2+1
37*846^3+1
40*846^2+1
41*846^1+1
42*846^1+1
[/code]

Proven.

Sierpinski base 879 primes found:

[code]
2*879^1+1
4*879^1+1
6*879^2+1
8*879^4+1
12*879^2+1
14*879^167+1
16*879^2+1
18*879^1+1
20*879^1+1
22*879^6+1
24*879^1183+1
26*879^24+1
28*879^4+1
30*879^1+1
32*879^4617+1
[/code]

k=10 remains at n=25000. Released.

Results
 

Sierspinki base 893 primes found:

[code]
2*893^1+1
4*893^10+1
6*893^7+1
10*893^12+1
12*893^8+1
14*893^1+1
16*893^20+1
18*893^2+1
22*893^2+1
24*893^1+1
26*893^519+1
28*893^2+1
30*893^7+1
[/code]

k=8 and 20 remain at n=25000. Released.

Sierpinski base 898 primes found:

[code]
3*898^6+1
4*898^1+1
6*898^29+1
7*898^1+1
9*898^15+1
10*898^2+1
13*898^35+1
15*898^3+1
16*898^1+1
18*898^2+1
19*898^165+1
21*898^1+1
24*898^30+1
27*898^1+1
[/code]

k=28 remains at n=25000. Released.

Sierpinski base 919 primes found:

[code]
4*919^1+1
6*919^5092+1
10*919^8+1
18*919^386+1
22*919^1+1
[/code]

k=12 remains at n=25000. Released.

Sierpinski base 924 primes found:

[code]
2*924^4+1
3*924^3+1
4*924^1+1
5*924^1+1
6*924^10+1
7*924^1+1
8*924^1+1
9*924^1+1
10*924^1+1
11*924^2+1
13*924^9+1
14*924^8031+1
15*924^2+1
16*924^386+1
17*924^2+1
18*924^1+1
19*924^19+1
20*924^1+1
21*924^10+1
22*924^4+1
23*924^43+1
24*924^49+1
26*924^14+1
27*924^5+1
28*924^1+1
29*924^15+1
30*924^4+1
31*924^4+1
32*924^1+1
33*924^1+1
34*924^7+1
35*924^1+1
[/code]

Proven.

Sierpinski base 930 primes found:

[code]
2*930^1+1
3*930^1+1
4*930^2+1
5*930^1+1
6*930^1+1
7*930^217+1
9*930^24+1
10*930^2+1
11*930^7+1
12*930^1+1
13*930^207+1
14*930^7+1
15*930^12+1
16*930^3+1
17*930^2+1
18*930^1+1
19*930^3+1
[/code]

k=8 remains at n=25000. Released.

Sierpinski base 993 primes found:

[code]
2*993^1+1
4*993^39+1
10*993^1+1
12*993^2+1
14*993^1+1
16*993^1+1
18*993^3+1
20*993^1+1
22*993^8+1
24*993^1+1
26*993^1+1
28*993^104+1
32*993^13+1
[/code]

k=6, 8, and 34 remain at n=25000. Released.

If I've kept track of my reservations correctly, I only have S887, S948, and S998 remaining for these small conjectures.

Nice work rogue! I'm in awe at the work that you're putting in. You're putting my efforts with R603 (currently at ~19K) and S928 (at 12.8K) to shame!

[QUOTE]If I've kept track of my reservations correctly, I only have S887, S948, and S998 remaining for these small conjectures. [/QUOTE]

That's what I show also. I did get an extra one in S702. I didn't see a reservation for it but it may be there. I'll process it.