S143
 

Reserving S143 to n=50K

S225
 

Sierp Base = 225
Conjectured k = 117406
Covering Set = 17, 113, 1489
Trivial Factors = k == 1 mod 2(2)
k == 6 mod 7(7)
Found Primes: 49746k's
Remaining @ n=2500: 433k's
Trivial Factor Eliminations: 8386k's
MOB Eliminations: 137k's
all k's accounted for @ n=2500
PFGW used = 3.4.3 dated 2010/11/04

212 primes found n=2500-10K
221 k's remain @ n=10K

Results emailed - Base released

S143
 

S143 tested n=25K-50K
28 primes found - 138 remain
Results emailed - Base released

R225
 

Riesel Base = 225
Conjectured k = 160032
Covering Set = 17, 113, 1489
Trivial Factors = k == 1 mod 2(2) and k == 1 mod 7(7)
Found Primes: 71000k's
Remaining: 817k's - Tested to n=2.5K
Trivial Factor Eliminations: 12002k's
MOB Eliminations: 196k's
k's in balance @ n=2500
PFGW used = 3.4.3 dated 2010/11/04

337 primes found n=2500-10K
480k's remain @ n=10K

Results emailed - Base released

NOTE: Gary should have a field day eliminating algebraic k's
with this one. I see around 100 of them.

S232
 

Reserving S232 as new to n=10K

[QUOTE=MyDogBuster;382950]<snip>
480k's remain @ n=10K

Results emailed - Base released

NOTE: Gary should have a field day eliminating algebraic k's
with this one. I see around 100 of them.[/QUOTE]

I sure did. :smile: 137 k's are perfect squares and removed. Officially for R225, 343 k's remain at n=10K.

[QUOTE=MyDogBuster;382952]Reserving S232 as new to n=10K[/QUOTE]

Just checking if you have the base correct. This one has a conjecture of 447592.

[QUOTE]Just checking if you have the base correct. This one has a conjecture of 447592. [/QUOTE]

Yup. That's the one.

R226
 

Reserving R226 as new to n=10K

S232
 

Sierp Base = 232
Conjectured k = 447592
Covering Set = 5, 233, 2153
Trivial Factors = k == 2 mod 3(3)
k == 6 mod 7(7)
k == 10 mod 11(11)

Found Primes: 229291k's
Remaining: 2557k's - Tested to n=2.5K
Trivial Factor Eliminations: 215077k's
MOB Eliminations: 663k's
GFN Eliminations: 3ks's
all k's accounted for @ n=2500
PFGW used = 3.4.3 dated 2010/11/04

1324 primes found n=2.5K-10K
1233 remain at n=10k

Results emailed - base released

R226
 

Riesel Base = 226
Conjectured k = 158447
Covering Set = 7, 11, 211, 227, 241
Trivial Factors = k == 1 mod 3(3)
k == 1 mod 5(5)

Found Primes: 82878k's
Remaining: 1384k's - Tested to n=2.5K
Trivial Factor Eliminations: 73942k's
MOB Eliminations: 242k's
k's in balance @ n=2500
PFGW used = 3.4.3 dated 2010/11/04

638 primes found n=2.5K-10K
746 remain at n=10K

Results emailed - Base released

Reserving S231 to n=25K.

R232
 

Reserving R232 to n=10K

Reserving R225 and S225 to n=25K.

S231 is complete to n=25K; 99 primes were found for n=10K-25K shown below; 171 k's remain; base released.

Not bad for CK=251748. :-)

Primes:
[code]
14130*231^10007+1
204148*231^10115+1
112762*231^10229+1
33238*231^10294+1
156050*231^10318+1
130182*231^10330+1
5480*231^10393+1
62530*231^10416+1
59190*231^10536+1
4258*231^10542+1
134202*231^10574+1
178072*231^10699+1
116146*231^10704+1
158658*231^10809+1
237472*231^10889+1
165676*231^10941+1
205820*231^11084+1
122990*231^11328+1
150050*231^11331+1
237886*231^11609+1
237266*231^11689+1
207902*231^11696+1
37440*231^11732+1
221932*231^11921+1
115566*231^11978+1
193112*231^12016+1
16386*231^12176+1
129986*231^12211+1
67900*231^12305+1
112026*231^12349+1
214166*231^12404+1
223526*231^12408+1
147812*231^12425+1
148160*231^12429+1
136908*231^12549+1
100776*231^12616+1
46140*231^12626+1
62378*231^12697+1
42228*231^13068+1
48862*231^13139+1
81808*231^13151+1
208542*231^13247+1
156976*231^13465+1
70456*231^13948+1
21200*231^14416+1
184876*231^14434+1
13116*231^14495+1
92828*231^14519+1
109940*231^14950+1
176060*231^15440+1
72122*231^15487+1
147928*231^15679+1
236740*231^15753+1
79722*231^15756+1
112202*231^16018+1
213706*231^16093+1
85042*231^16180+1
222392*231^16259+1
15668*231^16689+1
200568*231^16821+1
164412*231^16919+1
49910*231^16922+1
225708*231^17154+1
77418*231^17211+1
245488*231^17420+1
176000*231^17465+1
74010*231^17503+1
6176*231^17629+1
165500*231^17669+1
112828*231^17910+1
85000*231^18184+1
217812*231^18249+1
241180*231^18353+1
150712*231^18603+1
185398*231^18720+1
136386*231^18765+1
180640*231^18855+1
6758*231^18922+1
85422*231^18993+1
202216*231^19013+1
193190*231^19509+1
48400*231^19823+1
181600*231^20457+1
216766*231^20490+1
168676*231^20534+1
43690*231^20549+1
204420*231^20829+1
165966*231^21211+1
208668*231^22221+1
176582*231^22312+1
119452*231^23102+1
74848*231^23515+1
132448*231^23565+1
181802*231^23574+1
206626*231^23762+1
177826*231^24113+1
161966*231^24250+1
158310*231^24407+1
245092*231^24566+1
[/code]

S225 is complete to n=25K; 81 primes were found for n=10K-25K shown below; 139 k's remain; base released.

Primes:
[code]
116938*225^10001+1
96766*225^10068+1
88656*225^10125+1
101494*225^10527+1
75934*225^10684+1
83568*225^10888+1
25588*225^11100+1
13160*225^11467+1
82626*225^11587+1
109484*225^11876+1
15250*225^11879+1
20830*225^11969+1
29040*225^12011+1
27524*225^12023+1
58790*225^12046+1
80542*225^12113+1
41918*225^12222+1
39820*225^12413+1
66206*225^12452+1
6816*225^12535+1
62728*225^12740+1
24974*225^12972+1
36044*225^12996+1
30208*225^13087+1
24770*225^13184+1
44074*225^13371+1
101778*225^13427+1
35568*225^13795+1
95212*225^13988+1
102302*225^13992+1
79772*225^14355+1
32704*225^14588+1
114696*225^14612+1
41020*225^14726+1
110538*225^14923+1
23762*225^14930+1
23592*225^15045+1
54742*225^15100+1
68812*225^15101+1
27218*225^15224+1
50674*225^15522+1
44412*225^15658+1
17846*225^15870+1
10592*225^15921+1
115458*225^16005+1
108592*225^16257+1
103138*225^16279+1
92088*225^16383+1
22708*225^16704+1
88098*225^16962+1
50684*225^17041+1
9468*225^17049+1
92044*225^17451+1
41846*225^17464+1
106326*225^17637+1
45644*225^17639+1
12890*225^17830+1
37744*225^18518+1
98700*225^18520+1
74468*225^18856+1
74656*225^19596+1
29104*225^19825+1
58156*225^20322+1
85094*225^20391+1
93968*225^20673+1
48216*225^20839+1
51930*225^21223+1
115950*225^21293+1
100406*225^21296+1
68598*225^21545+1
6134*225^21693+1
51072*225^22363+1
110176*225^22402+1
42280*225^22679+1
117246*225^22849+1
89982*225^22928+1
112898*225^23025+1
84606*225^23104+1
93870*225^23430+1
18138*225^24431+1
98114*225^24602+1
[/code]

R225 is complete to n=25K; 104 primes were found for n=10K-25K shown below; 239 k's remain; base released.

Primes:
[code]
143724*225^10037-1
73720*225^10095-1
163256*225^10128-1
32126*225^10136-1
92082*225^10178-1
49696*225^10418-1
574*225^10620-1
69186*225^10631-1
151792*225^10760-1
75568*225^10819-1
156792*225^10830-1
26360*225^10835-1
98712*225^10905-1
87850*225^10915-1
157654*225^11207-1
44522*225^11297-1
161584*225^11395-1
101446*225^11464-1
142960*225^11556-1
144528*225^11651-1
2648*225^11746-1
104176*225^11773-1
39086*225^11820-1
134848*225^11873-1
24838*225^11958-1
135210*225^11964-1
52994*225^12027-1
74128*225^12045-1
60876*225^12112-1
9278*225^12148-1
44026*225^12168-1
145028*225^12535-1
19122*225^12630-1
143980*225^12668-1
15372*225^12700-1
165938*225^12751-1
77994*225^12788-1
143628*225^12847-1
132944*225^12928-1
113598*225^12938-1
149322*225^12948-1
115906*225^13066-1
124778*225^13076-1
128950*225^13124-1
43944*225^13320-1
89730*225^13340-1
160824*225^13394-1
135938*225^13498-1
15508*225^13750-1
59346*225^13799-1
47074*225^13853-1
157512*225^13956-1
33562*225^13973-1
139554*225^14142-1
102854*225^14590-1
492*225^14824-1
85440*225^14895-1
151532*225^15104-1
128254*225^15208-1
143372*225^15250-1
117556*225^15479-1
160538*225^15593-1
39594*225^15682-1
71980*225^15964-1
115824*225^15966-1
72484*225^16122-1
118702*225^16249-1
155930*225^16265-1
53634*225^16288-1
78306*225^16342-1
61796*225^16513-1
75974*225^16557-1
112264*225^17059-1
72368*225^17175-1
151512*225^17304-1
138424*225^17570-1
78692*225^17815-1
49146*225^18032-1
51698*225^18342-1
11972*225^18520-1
102736*225^18520-1
159714*225^18757-1
154226*225^18813-1
149918*225^18895-1
78808*225^19259-1
137828*225^19347-1
84418*225^19455-1
62230*225^19560-1
115958*225^20271-1
64094*225^20444-1
31568*225^20637-1
83516*225^21195-1
73336*225^21734-1
134874*225^22087-1
131448*225^22760-1
52544*225^22808-1
28950*225^22939-1
113182*225^23232-1
62964*225^23535-1
156664*225^23548-1
157436*225^23695-1
119084*225^23787-1
116420*225^23901-1
56560*225^24935-1
[/code]

R232
 

Riesel Base = 232
Conjectured k = 501417
Covering Set = 5, 7, 13, 31, 61
Trivial Factors = k == 1 mod 3(3) k == 1 mod 7(7) k == 1 mod 11(11)

Found Primes: 256848k's
308025 found composite by partial algebraic factors
Remaining: 2860k's - Tested to n=2.5K
Trivial Factor Eliminations: 240941k's
MOB Eliminations: 766k's
k's in balance @ n=2500
PFGW used = 3.4.3 dated 2010/11/04

1463 primes found n=2500-10K
1397k's remain @ n=10K
Results emailed - Base released

Reserving R121 to n=600K.
Reserving R103, R133, S112, S148 to n=360K.

Batalov finished R121 to n=600K on 11/26. No primes were found for n=250K-600K.

Reserving S155 to n=600K.

Reserving S230 to n=600k.

S117, R117 tested to n=210K

no new primes since
2172*117^180355+1

continuing

Reserving R221 to n=400k.

R190
 

Reserving R190 to n=10K

r193
 

reserving r193 to n=100e3

R190
 

Riesel Base = 190
Conjectured k = 626861
Covering Set = 13, 89, 191, 1753
Trivial Factors = k == 1 mod 3(3) k == 1 mod 7(7)

Found Primes: 355025k's
Remaining: 2020k's - Tested to n=2.5K
Trivial Factor Eliminations: 268655k's
MOB Eliminations: 1160k's

k's in balance @ n=2500
PFGW used = 3.4.3 dated 2010/11/04

1130 primes found n=2.5K-10K
890 k's remain @ n=10K

Results emailed - Base released

Reserving S185 to n=1M for BOINC

[QUOTE=rebirther;391053]Reserving S185 to n=1M for BOINC[/QUOTE]

Be sure and make a note to stop this one if a prime is found. The tests will get extremely long.

This is the type of effort that benefits the most from BOINC.

[QUOTE=gd_barnes;391054]
This is the type of effort that benefits the most from BOINC.[/QUOTE]

Either this or maybe also stuff like R63, n>25k which no individual will take on on their own.

Discussion about Riesel base 3 suggestions, sieving, and testing moved to that thread.

Reserving R138 (8K's remaining)

Sieving for N 100-250K to 500e9

Neo
AtP

[QUOTE=Neo;392696]Reserving R138 (8K's remaining)

Sieving for N 100-250K to 500e9

Neo
AtP[/QUOTE]

Will you be testing or just sieving? You might want to consider a deeper sieve if testing.

[QUOTE=gd_barnes;392736]Will you be testing or just sieving? You might want to consider a deeper sieve if testing.[/QUOTE]

Gary,

It's my intention to LLR.

I'm 84% done bringing the sieve to 500e9 and itching, just itching, to start LLR'ing.. I'm at a 6 seconds/factor removal rate. At least that's what Sr2sieve is reporting. I guess my hope was to hit a prime or two relatively early in the search and then continue sieving once tests started to get longer. I was thinking that Sr2sieve would run faster if it had a few less K's to sieve for, especially because I'm sieving for 8 K's over a wide range of N (100-250K)

I will take your advice though. To what depth should I take it? I am only using one core to sieve; are there any drawbacks/warnings against using the "-t" switch to add some cores?

Neo

[QUOTE=Neo;392769]Gary,

It's my intention to LLR.

I'm 84% done bringing the sieve to 500e9 and itching, just itching, to start LLR'ing.. I'm at a 6 seconds/factor removal rate. At least that's what Sr2sieve is reporting. I guess my hope was to hit a prime or two relatively early in the search and then continue sieving once tests started to get longer. I was thinking that Sr2sieve would run faster if it had a few less K's to sieve for, especially because I'm sieving for 8 K's over a wide range of N (100-250K)

I will take your advice though. To what depth should I take it? I am only using one core to sieve; are there any drawbacks/warnings against using the "-t" switch to add some cores?

Neo[/QUOTE]

An optimal sievedepth using 70% optimal depth, will be approximately:

950 second per test / 6 seconds * 420G = 158.33 * 420G = 66.5 T, you might wanna test the testing time for n=250K for the highest k. However this will be very close to your optimal sievedepth (based on my experienced assumptions, on how long a 1.23M bit test takes).

If you choose in the future to do your own calculations of optimal sievedepth, then this is a pretty good way to calculate the optimal sievedepth.

And yes, you're right, sr2sieve will run faster if a k is removed from the sievefile, but you still have to sieve untill you at least hit the minimum time an LLR test takes at n=100K, else you might not gain as much progress as you desire.

In regards to -t, I honestly have no answer to you, since I never uses the -t function, so someone else has to chime in on this :smile:

KEP

[QUOTE=KEP;392771]
In regards to -t, I honestly have no answer to you, since I never uses the -t function, so someone else has to chime in on this :smile:
KEP[/QUOTE]

From my personal experience you get the maximum performance by adding cores "by hand" i.e. starting several instances of sr2sieve, each searching its own range. If you want to save on the manual labor, I found that up to -t4 the performance drawback is tolerable. For more cores I tend to divide the range I'm sieving. This has been evaluated quite some time back and might not be very accurate any more.

[QUOTE=KEP;392771]An optimal sievedepth using 70% optimal depth, will be approximately:

950 second per test / 6 seconds * 420G = 158.33 * 420G = 66.5 T, you might wanna test the testing time for n=250K for the highest k. However this will be very close to your optimal sievedepth (based on my experienced assumptions, on how long a 1.23M bit test takes).

[/QUOTE]

Thanks KEP and Puzzle Peter for your insights. :)

I ran an LLR on 372*138^100000-1 ... testing time was 210 seconds.
I ran an LLR on 1742*138^250000-1 ... testing time was 1,460 seconds.

SO, once the sieve is finished at 500G, and using the above formula:
210 / 6 = 35 * 500,000,000,000 = 17.5T ???

Second question for you guys:

I'm almost done (97% to 500e9) on the sieve.
I've found 12,755 factors.

Is there a benefit to using srfile to remove the composite K's (factors.txt) from the .abcd sieve file?
Will the removal of the 12,755 K candidates speed up sr2sieve?

If so, what command line do I use to remove composite K's from the abcd file while preserving the abcd file for further sieving?
(Edited) srfile -k --known-factors factors.txt ?

I thank you advance for your assistance. There are tons of threads and messages dating back to 2009... it's hard to keep all this information in my brain, but I have honestly tried hard by re-reading all the sr README's, threads, etc., ;)

srfile -k factors.txt sr_138.abcd --G

-G if you like to have a prpfile
-a if you like to have a abcd file
Lennart

[QUOTE=Neo;392777]Thanks KEP and Puzzle Peter for your insights. :)

I ran an LLR on 372*138^100000-1 ... testing time was 210 seconds.
I ran an LLR on 1742*138^250000-1 ... testing time was 1,460 seconds.

SO, once the sieve is finished at 500G, and using the above formula:
210 / 6 = 35 * 500,000,000,000 = 17.5T ???

Second question for you guys:

I'm almost done (97% to 500e9) on the sieve.
I've found 12,755 factors.

Is there a benefit to using srfile to remove the composite K's (factors.txt) from the .abcd sieve file?
Will the removal of the 12,755 K candidates speed up sr2sieve?

If so, what command line do I use to remove composite K's from the abcd file while preserving the abcd file for further sieving?
(Edited) srfile -k --known-factors factors.txt ?

I thank you advance for your assistance. There are tons of threads and messages dating back to 2009... it's hard to keep all this information in my brain, but I have honestly tried hard by re-reading all the sr README's, threads, etc., ;)[/QUOTE]

1. Your optimal sievedepth is correct for 100% sieve for n=100K (but you can most likely sieve to 12.25T for 70% optimal sievedepth)

2. You will most definently benefit from using "srfile -k factors.txt srsieve.out" and then "srfile -a srsieve.out" since removing factors will be speeding up your sieving. There is no use, for CRUS and other primesearching projects, to keep finding factors for k's already been proven composite as result of sieving, since we don't need factors, only primes.

My own addition:

optimal sievedepth for the entire range n>100K to n<=250K is 1460 / 6 * 500G = 243,33 * 500 = 121.66T (85.17T for 70% sievedepth)

Please notice, that 70% is in many instances a desired sievedepth and can due to the removal of candidates from primed k's, to some extent be justified as optimal sievedepth, for the kind of searching that CRUS does :smile:

Thanks KEP!

I srfile'd -k -a factors.txt base138.abcd

Restarted sieving and P jumped significantly... from 5.4 million to 9.6 million per second!

Despite reading the help file and trying to get some other cores thrown in on the action, (sr2sieve readme file says to just add -t 2)
I couldn't get it to work.

I then did a sr2sieve -h and there was no mention of the -t switch to add child threads.

The readme file says the feature was implemented for versions 1.7 and higher..
I'm using sr2sieve 1.8.11

Anyways... Looks as if I'll just start sieving a different p range in a different directory to speed things up.

Good stuff.

Neo

The 70% rule of thumb is to time LLR for a candidate exponent 70% of the way from min to max of the exponents in your sieve. That gives the average test time. If you were planning to LLR the entire sieve file, it would be most efficient to sieve until the removal rate is equal to that testing rate.

However, as you point out, you do not plan to test the entire file- you plan to find a prime! Finding a prime does two things to alter the "what is the perfect sieve amount" calculation: (1) It removes tests you no longer need to complete, and (2) it speeds the sieve by about sqrt(8/7). Rather than try to calculate the odds of a prime or the expected value where you'll find your first prime, it's wise to just sieve to something deeper than the rate for the initial LLR tests, and alternate LLR with more sieving.

Also, the factors rate will not rise perfectly linearly- the estimate this far in advance is accurate perhaps only within 20%. So, somewhere in the 12 to 15T range would be a reasonable minimum to move to LLR for the first block of tests. Once LLR time jumps substantially, remove the tested candidates from the sieve, and sieve a few more T. The sieve will speed up by the sqrt of the fraction of the number of candidates you removed (just like it does when you prime a k and remove it). So, if you remove 10% of the tests, the sieve will run about sqrt (1.1) faster in T/day.

Edit: Finding a prime is likely to be for one of the heavier k's first, which would remove more than 1/8th of the tests from the sieve. So, the sieve would speed up by more than sqrt (8/7).

I want to thank [B]EVERYONE[/B] for their input and advice.

I now have two separate sr2 sieves going on the same base (R138) with different P ranges...

I have reconfigured my BIOS and have it computing at 4 ghz. (I had my i-5 downclocked to 3.2ghz due to AVX heat concerns). Now running at 4 ghz with a WRgenfer(OCL) task running on my 770gtx, and two sr2sieves.... temps stable at 68 degrees.

Now getting 12.3 million P per second per CORE!

I'm going to crush this R138 base! :)

Neo

[QUOTE=Neo;392786]
I'm going to crush this R138 base! :)
[/QUOTE]

Good plan! :smile:

372*138^103160-1 is prime! (220753 decimal digits, P = 11) Time : 665.765 sec.

1K down, 7K to go!

Neo

S130
 

Sierp Base = 130
Conjectured k = 1021537
Covering Set = 7, 31, 131, 541
Trivial Factors = k == 2 mod 3(3) and k == 42 mod 43(43)

Found Primes: 656253k's
Remaining: 5491k's - Tested to n=2.5K
Trivial Factor Eliminations: 356350k's
MOB Eliminations: 3439k's
GFN Eliminations: 3k's
k's in balance @ n=2.5K
PFGW used = 3.4.3 dated 2010/11/04
2944 primes found 2.5K-10K
2547k's remain @ n=10K

Results emailed - Base released

Reserving R121 to n=1M

S185 tested to n=1M (250k-1M)

nothing found

Results emailed - Base released

R147
 

R147 reserved to n=50K

reserving R123 and R160
n=250000 to 400000

R160
 

status update
R160, n=250000 - 300000 done
no prime
continuing
results emailed

[QUOTE=lalera;396251]status update
R160, n=250000 - 300000 done
no prime
continuing
results emailed[/QUOTE]

I did not get the results on this.

Reserving S118, S122, S173 and S174 to n=400K (and probably higher)

Time to get back to proving conjectures.

[QUOTE=gd_barnes;396263]I did not get the results on this.[/QUOTE]

i sent the results to
[email]gary@noprimeleftbehind.net[/email]
is the email adress correct?
i sent now a second time

[QUOTE=lalera;396420]i sent the results to
[EMAIL="gary@noprimeleftbehind.net"]gary@noprimeleftbehind.net[/EMAIL]
is the email adress correct?
i sent now a second time[/QUOTE]

I still did not get them. There seems to be a problem with forwarding on that address. Please Email me at:

gbarnes017 at gmail dot com

Sorry about the problem.

Edit note: I have updated the main project page at [URL]http://www.noprimeleftbehind.net/crus/[/URL]. (You might have to refresh your browser.) If anyone knows anywhere else that it needs to be updated, let me know.

[QUOTE=gd_barnes;396426]I still did not get them. There seems to be a problem with forwarding on that address. Please Email me at:

gbarnes017 at gmail dot com

Sorry about the problem.

Edit note: I have updated the main project page at [URL]http://www.noprimeleftbehind.net/crus/[/URL]. (You might have to refresh your browser.) If anyone knows anywhere else that it needs to be updated, let me know.[/QUOTE]

hi,
i sent now the results to your new email adress
(R160; n=250t-300t)

R123 and R160
reservation canceled

S117, R117 all ks at n=235K

1 prime
1082*117^235482+1

Continuing to n=250K

S200 completed to n=1M. Results attached.

status r193
 

r193 at n=66e3 ; 106 primes

continuing

R147
 

R147 tested n=25K-50K

52 primes found - 213 remain

Results emailed - Base released

S118-S122-S174
 

Extending reservations for S118 - S122 - S174 to n=600K

R123
 

reserving R123
n=250000 to ?

R123
 

R123;n=250K-300K done - no prime
results emailed
base released

R109
 

reserving R109
n=250K-300K

R121
 

Here are the full results for R121 up to the first prime.

R109
 

R109;n=250K-300K done - no prime
results emailed
base released

Reserving S198 to n=100k (50-100k) for BOINC

S198 tested to n=100k (50-100k)

8 primes found, 36 remain

621*198^53839+1
2253*198^54740+1
706*198^55247+1
2084*198^56478+1
2864*198^62462+1
4014*198^73851+1
2976*198^78439+1
1074*198^86150+1

Results emailed - Base released

Reserving R136 to n=100k (50-100k) for BOINC

R136 tested to n=100k (50-100k)

13 primes found, 51 remain

4688*136^50072-1
13280*136^52153-1
73668*136^53179-1
66993*136^53958-1
83900*136^58077-1
34662*136^60921-1
63293*136^63646-1
9848*136^74282-1
88254*136^76152-1
14715*136^79844-1
12605*136^84371-1
17948*136^93193-1
64028*136^97970-1

Results emailed - Base released

Reserving S155

...a lot of time will be wasted!
 

S155 sieve is the prime example of how bad can algebraic get you.

Who sieved this?!
It contains ~19% patently composite values! :gah::gah::gah:

4*155[SUP]4m[/SUP] + 1 = (2*155[SUP]2m[/SUP] - 2*155[SUP]m[/SUP] + 1) * (2*155[SUP]2m[/SUP] + 2*155[SUP]m[/SUP] + 1)

Can you post me sieve with removed composite?
Thanks

Sure.

Something is very fishy with this sieve

Original sieve contains 5600 candidates, when you removed composite it has 4551 candidates.

But when I make test sieve got this

Read [COLOR=Magenta]7027[/COLOR] terms for 4*155^n+1 from NewPGen file `155.txt'.
Split 1 base 155 sequence into 45 base 155^120 subsequences.
Recognised Generalised Fermat sequence A^2+1
Using 4 Kb for the baby-steps giant-steps hashtable, maximum density 0.15.
Baby step method gen/4, giant step method new/4.
Using 128Kb for the Sieve of Eratosthenes bitmap.
Expecting to find factors for about [COLOR=Magenta]1138.47 terms.[/COLOR]
sr1sieve 1.4.5 started: 750036 <= n <= 999992, 110000000000 <= p <= 15000000000000
110173104133 | 4*155^905128+1
110259397681 | 4*155^967174+1
p=110259523441, 29853266 p/sec, 2 factors, 0.0% done, 1 sec/factor, ETA 17 Jul 23:09
sr1sieve 1.4.5 stopped: at p=110278915793 because SIGINT was received.
Found factors for 2 terms in 9.368 sec. (expected about 0.70)

7027 - 1138 ( to be at 15000000000000 as original sieve) = 5889
Can expected number of candidates be so different ? 5889 compared to 5600 (289)

[QUOTE=pepi37;405685]Something is very fishy with this sieve

Original sieve contains 5600 candidates, when you removed composite it has 4551 candidates.

But when I make test sieve got this

Read [COLOR=Magenta]7027[/COLOR] terms for 4*155^n+1 from NewPGen file `155.txt'.
Split 1 base 155 sequence into 45 base 155^120 subsequences.
Recognised Generalised Fermat sequence A^2+1
Using 4 Kb for the baby-steps giant-steps hashtable, maximum density 0.15.
Baby step method gen/4, giant step method new/4.
Using 128Kb for the Sieve of Eratosthenes bitmap.
Expecting to find factors for about [COLOR=Magenta]1138.47 terms.[/COLOR]
sr1sieve 1.4.5 started: 750036 <= n <= 999992, 110000000000 <= p <= 15000000000000
110173104133 | 4*155^905128+1
110259397681 | 4*155^967174+1
p=110259523441, 29853266 p/sec, 2 factors, 0.0% done, 1 sec/factor, ETA 17 Jul 23:09
sr1sieve 1.4.5 stopped: at p=110278915793 because SIGINT was received.
Found factors for 2 terms in 9.368 sec. (expected about 0.70)

7027 - 1138 ( to be at 15000000000000 as original sieve) = 5889
Can expected number of candidates be so different ? 5889 compared to 5600 (289)[/QUOTE]
file `155.txt' is your own file, so if anything is fishy it could be with that file.
[QUOTE=pepi37;405685]Can [U]expected[/U] number of candidates be so different ? 5889 compared to 5600 (289)[/QUOTE]
Of course it can. That's why the word "[U]expected[/U]" is used. The "[U]expected[/U]" number of candidates can be way off epecially because the estimate is for a irreducible form, while this form is algebraically reducible for a fraction of candidates.

I like that srsieve [B]does [/B]recognize the GFN form and [B]can [/B]as a result sieve faster (this is based on the fact that only primes of form 4k+1 can divide a A^2+1 form). On the other hand, srsieve does [B]not [/B]recognize Aurifeillian fraction and does not remove it - but as the closing line from 'Some Like It Hot' goes, "No one is perfect".

Thanks Batalov, so lets LLR-ing start :)
And thanks for reduce LLR time for about 60 days!

[QUOTE=Batalov;405687]I like that srsieve [B]does [/B]recognize the GFN form and [B]can [/B]as a result sieve faster (this is based on the fact that only primes of form 4k+1 can divide a A^2+1 form). On the other hand, srsieve does [B]not [/B]recognize Aurifeillian fraction and does not remove it - but as the closing line from 'Some Like It Hot' goes, "No one is perfect".[/QUOTE]

If you have a code change that I can apply to srsieve...

[QUOTE=pepi37;405688]Thanks Batalov, so lets LLR-ing start :)
And thanks for reduce LLR time for about 60 days![/QUOTE]
I ran sr1sieve for a bit to check the estimates and removed two more candidates for you:
[CODE]15189078811981 | 4*155^968110+1
[STRIKE]15239240636801 | 4*155^943524+1[/STRIKE] (already removed, because it is 4*A^4+1)
15316822815461 | 4*155^761998+1
[/CODE]

[QUOTE=rogue;405691]If you have a code change that I can apply to srsieve...[/QUOTE]
As my granddad used to say, "Це діло треба розжувати." (Got to ruminate on this one.)
Could we make some small steps?

The 4*A^4+1 recognition can be added precisely where "Recognised Generalised Fermat sequence A^2+1" is emited. Right?
At this point all n divisible by 4 should be eliminated.
This goes for other k :: (k/4) = m^4; that is, k=4, 64, ...2500...

One other simple case is when b=m^2, and k :: (k/4) = m^4; here, all even n should be eliminated. This was the case for S100 (k=64).

But to do is right, we also need to recognize cases where small factors of b can "leak" from the base power. For that, the isPower script is the prototype for many patterns. I don't remember where it was posted, so I attached a copy of it here:
[CODE]#!/usr/bin/perl -w

use Math::BigInt;

line: while(<>) { # this is a pl_remain.txt file; it has k*b^n+c lines only
next unless /^\s*(\d+)\*(\d+)\^(n|\d+)([+-])1/ && $1 && $2;
$k = Math::BigInt->new($1);
$a = Math::BigInt->new($2);
my @powers = ($4 eq '+') ? qw(3 5 7 11) : qw(2 3 5 7 11);

if($4 eq '+') {
print "Mod 0|4 Aur\t$_"
if($k==4 || $k==64 || $k==324 || $k==1024 || $k==2500 || $k==5184);
# $b = $k->copy()->bmul($a);
# print "1|4 Aur\t$_"
# if($b==4 || $b==64 || $b==324 || $b==1024 || $b==2500 || $b==5184);
# $b->bmul($a);
# print "2|4 Aur\t$_"
# if($b==4 || $b==64 || $b==324 || $b==1024 || $b==2500 || $b==5184);
# $b->bmul($a);
# print "3|4 Aur\t$_"
# if($b==4 || $b==64 || $b==324 || $b==1024 || $b==2500 || $b==5184);
}
foreach $m (@powers) {
$b = $k->copy()->broot($m);
if ($b->copy()->bpow($m) == $k) {
if ($a->copy()->broot($m)->bpow($m) == $a) {
print "* x^$m\t$_";
next line;
}
print "Mod 0($m) $b^$m\t$_";
}
}
for ($n=1; $n<$powers[$#powers]; $n++) {
$k->bmul($a);
foreach $m (@powers) {
next if $n>=$m;
$b = $k->copy()->broot($m);
print "Mod $n($m) $b^$m\t$_" if ($b->copy()->bpow($m) == $k);
}
}
}
[/CODE]
I don't know how easy it would be to implement the same rules in sr*sieve.

[QUOTE=Batalov;405722]I ran sr1sieve for a bit to check the estimates and removed two more candidates for you:
[CODE]15189078811981 | 4*155^968110+1
[STRIKE]15239240636801 | 4*155^943524+1[/STRIKE] (already removed, because it is 4*A^4+1)
15316822815461 | 4*155^761998+1
[/CODE][/QUOTE]

Thanks 2.5 hours less :)
What is removal rate if I may ask?

[QUOTE=pepi37;405725]Thanks [B]2.5 hours less[/B] :)
What is removal rate if I may ask?[/QUOTE]
It is slow, about the same as LLR. I'd say this sieve depth is just right.

I sieved on 4 cores, 0.1P interval each (that's from 15.0P to 15.4P); each took ~1.1 hour. And as you can see, 2 factors were removed (we don't count the third, because you can assume that it is [B]not [/B]in the sieve, already; I simply left n divisible by 4 in the input file).
That's 1 factor / [B]2.2 hours[/B]. So just proceed with LLR.

[QUOTE=Batalov;405726]It is slow, about the same as LLR. I'd say this sieve depth is just right.

I sieved on 4 cores, 0.1P interval each (that's from 15.0P to 15.4P); each took ~1.1 hour. And as you can see, 2 factors were removed (we don't count the third, because you can assume that it is [B]not [/B]in the sieve, already; I simply left n divisible by 4 in the input file).
That's 1 factor / [B]2.2 hours[/B]. So just proceed with LLR.[/QUOTE]

Yes, 34 candidates is already done :)
Small step for humankind, huge step for me :)

S212
 

I do some test on k=64 b=212, Sierp

k=64 from 100K-200K no new primes
results attached
base released

R196
 

I'll take R196 to n=10k; with CK of 2730222, this looks like a real barrel of laughs.

Reserving S212 to n=200k (100-200k) for BOINC

Reserving S228 to n=200k (100-200k) for BOINC

Reserving R241 to n=100k (50-100k) for BOINC

Without objection, I'd like to take a whack at starting R201 using k=1 to the CK given. Not sure what n I'll take it up to yet. Let's lowball and say n=1k for right now with the possibility of going higher.

R196
 

R196 is done to n=25k. 1992 k remain. Base is released. Results are emailed.

Reserving these 1-kers:
R109, R123, R181, R332, R492, R493, R636,
[STRIKE]S183[/STRIKE], S257, [STRIKE]S386[/STRIKE], S402, S406, S414, S416, S417, S436, S678, S834, S864.

They will be run together, sorted by decimal size, so I will copy this message in all reservation threads.

S212 tested to n=200k (100-200k)

nothing found

Results emailed - Base released

S212
 

Take K4 and K64 from S212 n>200K

S228 tested to n=200k (100-200k)

1 prime found, 3k left

196*228^156032+1

Results emailed - Base released

Reserving S103 to n=100k (50-100k) for BOINC

Reserving R231 to n=100k (25-100k) for BOINC

R241 tested to n=100k (50-100k)

4 primes found, 27k left

13454*241^57963-1
4038*241^59359-1
13452*241^96546-1
12542*241^96665-1

Results emailed - Base released

R277 tested to n=100k (50-100k)

4 primes found, 25 remain

6008*277^50658-1
6918*277^59328-1
5882*277^74049-1
2538*277^85188-1

Results emailed - Base released