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Old 2008-06-24, 07:00   #89
gd_barnes
 
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Quote:
Originally Posted by Siemelink View Post
Just for the heck of it I've sieved 2949008 until n = 100,000. My testing has reached 70,000 but no prime so far.

Continuing, Willem.
Quote:
Originally Posted by kar_bon View Post
Sierp Base 3:
2980832*3^38101+1 is prime.

so only one k < 3M !
Quote:
Originally Posted by Siemelink View Post
I reached 100,000 without a prime for this k. I am not continuing. I have too many choices as it is...

Willem.
Quote:
Originally Posted by kar_bon View Post
just sieving/llring all remaining k's <10M (not k=2949008) upto n=100k.

current n is 32k and PRP's found so far:
3159992 27396
3234118 31235
7969792 25529

45200 candidates left.

Oh, goodness! It's great that we now have only 1 k remaining < 3M! Nice work guys but I must make a request. Please reserve any work before starting on it to avoid any extra double-work. I was about ready to work on the 2 k's remaining for k<3M myself when I saw this.

Karsten, I was planning on starting a team sieve for n=25K-100K for all k<50M after I got back. I think that ~200 k's is a good number of k's for sr2sieve. Since you'll be on vacation for 6-8 weeks, I'll still plan on doing that, which will essentially make it a double-check for n=25K-32K for k<10M. Of course, we'll eliminate the k's that you found a prime for and include the one that Willem didn't find a prime for, which will effectively make it a double-check for n=25K-100K.

We may even make a mini team-drive to LLR all k<50M up to n=100K and later continue it for k=50M-100M, etc. Ultimately, it will make sense to set up LLRnet servers for it, probably for searching n>100K.


Thanks,
Gary
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Old 2008-06-24, 17:37   #90
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That's how this search was 'intended' to be too.

Phase 1) First do some first elimination (to 25k)
Phase 2) then go from 25k to 100k (for some reasonable amount of k's, 200 seems fine)
Phase 3) then go from 100k to 200k... and so on...

just to keep things interesting :)

(Phase 1, 50-100M is at 19.5k now...)
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Old 2008-06-27, 06:35   #91
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I just did another quick double-check of the top-5000 site vs. our list of k's remaining on Sierp base 3. I found that I missed one from my own search of k=10M-30M:

26803256*3^69079+1 is prime


So based on the additional searching by others and this research here, I have eliminated the following 5 k-values, which leaves 204 k's < 50M remaining for sieving and a total of 303 k's remaining for k< 50M and k=100M-120M:

2980832
3159992
3234118
7969792
26803256


Gary

Last fiddled with by gd_barnes on 2008-06-27 at 06:53
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Old 2008-06-27, 06:46   #92
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Quote:
Originally Posted by michaf View Post
That's how this search was 'intended' to be too.

Phase 1) First do some first elimination (to 25k)
Phase 2) then go from 25k to 100k (for some reasonable amount of k's, 200 seems fine)
Phase 3) then go from 100k to 200k... and so on...

just to keep things interesting :)

(Phase 1, 50-100M is at 19.5k now...)

Micha,

Below are some former top-5000 primes in your k-range. They may or may not help you eliminate some k's.

59054564*3^64030+1
66683018*3^98716+1
70260298*3^72927+1


Gary

Last fiddled with by gd_barnes on 2008-06-27 at 06:47
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Old 2008-06-27, 06:52   #93
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Reserving the 204 k's remaining for Sierp base 3 k<50M for n=25K-100K for SIEVING ONLY.

We can decide how we want to distribute the work a little later. Would anyone be interested in helping sieve? If so, I'll get an initial sieved file started up to P=100G or 250G and then we can coordinate.

I figure we can sieve to an optimal depth for n=25K-50K, break off that piece for primality testing and then continue sieving for n=50K-100K while removing k-values from the higher range as we find primes in the lower range.


Gary
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Old 2008-06-27, 07:22   #94
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Quote:
Originally Posted by gd_barnes View Post
Micha,

Below are some former top-5000 primes in your k-range. They may or may not help you eliminate some k's.

59054564*3^64030+1
66683018*3^98716+1
70260298*3^72927+1


Gary
All three were not found (yet) and now deleted, saving quite some CPU-time.

(50-100M search now at n=21814 with 383 sequences remaining, 30448 terms left)

Last fiddled with by michaf on 2008-06-27 at 07:33 Reason: added update
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Old 2008-06-27, 07:29   #95
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Quote:
Originally Posted by michaf View Post
All three were not found (yet) and now deleted, saving quite some CPU-time

It seems that at some point somebody had taken up the Riesel and Sierp base 3 conjectures previously because we have eliminated quite a few k-values with former top-5000 primes...far more than chance alone would dictate.

Since you had not found a prime for them in your search at lower n-values, then they are top-10 primes for the base and will be reflected as such for the time being.


Gary
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Old 2008-06-30, 19:10   #96
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Considering 50-100M base 3 sierpinski:

The following 213 k's are left at n=25k with k mod 3 = 1 or 2 (and thus still need to be searched)
Code:
50219374    1
50222338    1
50287288    1
50449528    1
50541412    1
50620060    1
50877592    1
50921056    1
52186900    1
53109118    1
53314642    1
53593726    1
54315148    1
54503602    1
55055116    1
55075498    1
55193434    1
55703236    1
56148718    1
56171218    1
56524036    1
56581678    1
56882284    1
56905378    1
57254656    1
57336382    1
57557068    1
57675862    1
58437532    1
58871836    1
59763448    1
60209746    1
60703348    1
60935716    1
61270336    1
61429768    1
62499142    1
62531902    1
63016906    1
64341406    1
65507272    1
65554012    1
65595592    1
66255214    1
66557716    1
66928276    1
67852672    1
68093614    1
68155474    1
68526046    1
68558962    1
69187234    1
69487006    1
69897658    1
70143826    1
70260532    1
71647042    1
71825584    1
73225294    1
74803858    1
75465868    1
76479688    1
77475694    1
77519584    1
77554786    1
77976142    1
78702082    1
78703468    1
78967678    1
79190206    1
79473862    1
79545946    1
79714294    1
80078764    1
80763370    1
81095362    1
81540346    1
81903964    1
81956716    1
82085494    1
82386316    1
82436518    1
83880508    1
84469954    1
85310794    1
86000056    1
86850334    1
87173668    1
87252058    1
89478076    1
89824888    1
90473998    1
90784756    1
90978172    1
91233724    1
91293316    1
91379272    1
92793016    1
92894182    1
93364996    1
93409276    1
93711076    1
94591624    1
95450302    1
95489092    1
96026332    1
96746836    1
97418338    1
97696726    1
97826494    1
98043514    1
98392246    1
98926396    1
99613186    1
50357012    2
52898312    2
52912976    2
54282752    2
54320036    2
54332516    2
55196756    2
56092742    2
57703994    2
58007336    2
58537244    2
58680938    2
60260912    2
60581468    2
60650732    2
62109506    2
63362504    2
63973712    2
64133198    2
64877882    2
65719268    2
65924882    2
66048746    2
66431468    2
66600104    2
68203706    2
68204198    2
68232896    2
68268602    2
68426882    2
69005336    2
69026702    2
69563192    2
70009502    2
70258712    2
70668452    2
71192354    2
71440646    2
71445854    2
71448584    2
71744534    2
72086978    2
72880994    2
73308278    2
73440644    2
74374772    2
74481242    2
74927714    2
75065462    2
75734312    2
76020188    2
77057588    2
77304608    2
77357576    2
77574956    2
78373346    2
79379414    2
79822118    2
80114018    2
80126414    2
80292008    2
80382650    2
80598086    2
81106076    2
81278324    2
83873906    2
84187388    2
84215078    2
84481472    2
85867196    2
87080432    2
87593744    2
87706772    2
88091054    2
89106848    2
89665952    2
89813708    2
90269594    2
90733694    2
92297696    2
93455522    2
93882734    2
94389422    2
95532098    2
96103394    2
96259778    2
96693302    2
96839144    2
97016048    2
97132676    2
97688816    2
97963454    2
98486582    2
98762336    2
98841272    2
98997092    2
99170018    2
99341384    2
99434222    2
The following 83 are left at n=25k, but can be left out of the search as they are already searched as their (k mod 3) reduced version:

Code:
50080092    0    16693364    already being searched
50817246    0    16939082    already being searched
51184956    0    17061652    already being searched
51770814    0    17256938    already being searched
52608126    0    17536042    already being searched
53367864    0    17789288    already being searched
53746536    0    17915512    already being searched
54907896    0    18302632    already being searched
57158196    0    19052732    already being searched
57404058    0    19134686    already being searched
58350822    0    19450274    already being searched
58722414    0    19574138    already being searched
59842548    0    19947516    already being searched
60266832    0    20088944    already being searched
60775602    0    20258534    already being searched
60796566    0    20265522    already being searched
60915378    0    20305126    already being searched
60980334    0    20326778    already being searched
61308816    0    20436272    already being searched
61783518    0    20594506    already being searched
62313456    0    20771152    already being searched
62568984    0    20856328    already being searched
62665392    0    20888464    already being searched
63526044    0    21175348    already being searched
63563244    0    21187748    already being searched
64434408    0    21478136    already being searched
64493238    0    21497746    already being searched
66901566    0    22300522    already being searched
69729846    0    23243282    already being searched
69894348    0    23298116    already being searched
71181816    0    23727272    already being searched
71568912    0    23856304    already being searched
71588724    0    23862908    already being searched
71689188    0    23896396    already being searched
72058344    0    24019448    already being searched
74033112    0    24677704    already being searched
74177232    0    24725744    already being searched
74291604    0    24763868    already being searched
74776116    0    24925372    already being searched
74903178    0    24967726    already being searched
75286182    0    25095394    already being searched
75621948    0    25207316    already being searched
76400466    0    25466822    already being searched
76436058    0    25478686    already being searched
76565616    0    25521872    already being searched
78783756    0    26261252    already being searched
79181868    0    26393956    already being searched
79334466    0    26444822    already being searched
80414916    0    26804972    already being searched
81327648    0    27109216    already being searched
81870396    0    27290132    already being searched
83114886    0    27704962    already being searched
84215598    0    28071866    already being searched
84470448    0    28156816    already being searched
85605486    0    28535162    already being searched
86026002    0    28675334    already being searched
86893278    0    28964426    already being searched
87303774    0    29101258    already being searched
87399168    0    29133056    already being searched
87992922    0    29330974    already being searched
88045374    0    29348458    already being searched
88351962    0    29450654    already being searched
88433838    0    29477946    already being searched
88646016    0    29548672    already being searched
88842498    0    29614166    already being searched
89318382    0    29772794    already being searched
90098124    0    30032708    already being searched
90712896    0    30237632    already being searched
91320486    0    30440162    already being searched
91484592    0    30494864    already being searched
91820208    0    30606736    already being searched
93003468    0    31001156    already being searched
93773742    0    31257914    already being searched
95644314    0    31881438    already being searched
95910240    0    31970080    already being searched
97120722    0    32373574    already being searched
97291158    0    32430386    already being searched
97350336    0    32450112    already being searched
97696122    0    32565374    already being searched
98048838    0    32682946    already being searched
98082228    0    32694076    already being searched
99672414    0    33224138    already being searched
99981192    0    33327064    already being searched
The following 6 have (k mod 3^2) = 1 or 2 and cannot be eliminated as they have primes as their reduced form on n=1:

Code:
65943336    0    21981112    1    has a prime at n=1, so this one needs to be searched further 
70848912    0    23616304    1    has a prime at n=1, so this one needs to be searched further 
59343216    0    19781072    2    has a prime at n=1, so this one needs to be searched further 
62837376    0    20945792    2    has a prime at n=1, so this one needs to be searched further 
93040692    0    31013564    2    has a prime at n=1, so this one needs to be searched further 
98555838    0    32851946    2    has a prime at n=1, so this one needs to be searched further
The following 1 has (k mod 3^2) = 1 or 2 and CAN be eliminated because of a prime for the reduced form > n=1:

Code:
80409768    0    26803256    2    has a prime larger then 1, so this one can be eliminated
Of the 40 k's with (k mod 3^2)=0 there are 27 k's already tested as their reduced forms:

Code:
50171796    0    16723932    0    5574644    already being tested
55110546    0    18370182    0    6123394    already being tested
57271356    0    19090452    0    6363484    already being tested
60770772    0    20256924    0    6752308    already being tested
61735626    0    20578542    0    6859514    already being tested
63729054    0    21243018    0    7081006    already being tested
64005894    0    21335298    0    7111766    already being tested
67215438    0    22405146    0    7468382    already being tested
70915608    0    23638536    0    7879512    already being tested
72530982    0    24176994    0    8058998    already being tested
72812178    0    24270726    0    8090242    already being tested
73506276    0    24502092    0    8167364    already being tested
73640844    0    24546948    0    8182316    already being tested
77431176    0    25810392    0    8603464    already being tested
79454106    0    26484702    0    8828234    already being tested
80199324    0    26733108    0    8911036    already being tested
80912142    0    26970714    0    8990238    already being tested
81390438    0    27130146    0    9043382    already being tested
81859392    0    27286464    0    9095488    already being tested
83165814    0    27721938    0    9240646    already being tested
83653866    0    27884622    0    9294874    already being tested
85349196    0    28449732    0    9483244    already being tested
86155632    0    28718544    0    9572848    already being tested
87216516    0    29072172    0    9690724    already being tested
89890272    0    29963424    0    9987808    already being tested
92017494    0    30672498    0    10224166    already being tested
94541724    0    31513908    0    10504636    already being tested
Of the 13 k's remaining, 12 can be eliminated because their reduced versions have a prime > n=2:

Code:
60961302    0    20320434    0    6773478    has a prime > n=2 so can be eliminated
61856352    0    20618784    0    6872928    has a prime > n=2 so can be eliminated
70787142    0    23595714    0    7865238    has a prime > n=2 so can be eliminated
71728128    0    23909376    0    7969792    has a prime > n=2 so can be eliminated
77379462    0    25793154    0    8597718    has a prime > n=2 so can be eliminated
78289416    0    26096472    0    8698824    has a prime > n=2 so can be eliminated
79111458    0    26370486    0    8790162    has a prime > n=2 so can be eliminated
79623216    0    26541072    0    8847024    has a prime > n=2 so can be eliminated
80482464    0    26827488    0    8942496    has a prime > n=2 so can be eliminated
85319784    0    28439928    0    9479976    has a prime > n=2 so can be eliminated
87321186    0    29107062    0    9702354    has a prime > n=2 so can be eliminated
99122256    0    33040752    0    11013584    has a prime > n=2 so can be eliminated
The last k has a prime at n=2, and so needs to be checked further:

Code:
63003672    0    21001224    0    7000408    has a prime at n=2, so original has a prime at n=0, so needs to be checked further
In short: the remaining 220 k's are:

Code:
50219374
50222338
50287288
50449528
50541412
50620060
50877592
50921056
52186900
53109118
53314642
53593726
54315148
54503602
55055116
55075498
55193434
55703236
56148718
56171218
56524036
56581678
56882284
56905378
57254656
57336382
57557068
57675862
58437532
58871836
59763448
60209746
60703348
60935716
61270336
61429768
62499142
62531902
63016906
64341406
65507272
65554012
65595592
66255214
66557716
66928276
67852672
68093614
68155474
68526046
68558962
69187234
69487006
69897658
70143826
70260532
71647042
71825584
73225294
74803858
75465868
76479688
77475694
77519584
77554786
77976142
78702082
78703468
78967678
79190206
79473862
79545946
79714294
80078764
80763370
81095362
81540346
81903964
81956716
82085494
82386316
82436518
83880508
84469954
85310794
86000056
86850334
87173668
87252058
89478076
89824888
90473998
90784756
90978172
91233724
91293316
91379272
92793016
92894182
93364996
93409276
93711076
94591624
95450302
95489092
96026332
96746836
97418338
97696726
97826494
98043514
98392246
98926396
99613186
50357012
52898312
52912976
54282752
54320036
54332516
55196756
56092742
57703994
58007336
58537244
58680938
60260912
60581468
60650732
62109506
63362504
63973712
64133198
64877882
65719268
65924882
66048746
66431468
66600104
68203706
68204198
68232896
68268602
68426882
69005336
69026702
69563192
70009502
70258712
70668452
71192354
71440646
71445854
71448584
71744534
72086978
72880994
73308278
73440644
74374772
74481242
74927714
75065462
75734312
76020188
77057588
77304608
77357576
77574956
78373346
79379414
79822118
80114018
80126414
80292008
80382650
80598086
81106076
81278324
83873906
84187388
84215078
84481472
85867196
87080432
87593744
87706772
88091054
89106848
89665952
89813708
90269594
90733694
92297696
93455522
93882734
94389422
95532098
96103394
96259778
96693302
96839144
97016048
97132676
97688816
97963454
98486582
98762336
98841272
98997092
99170018
99341384
99434222
65943336
70848912
59343216
62837376
93040692
98555838
63003672
PHEW

Gary, would you be kind and check my reasoning? I think I've got it alright now, but a confirmation would be nice.

Last fiddled with by gd_barnes on 2008-07-03 at 05:11 Reason: corrected (k mod 3)=0 to (k mod 3^2)=0
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Old 2008-06-30, 19:15   #97
michaf
 
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Quote:
Originally Posted by gd_barnes View Post
Reserving the 204 k's remaining for Sierp base 3 k<50M for n=25K-100K for SIEVING ONLY.

We can decide how we want to distribute the work a little later. Would anyone be interested in helping sieve? If so, I'll get an initial sieved file started up to P=100G or 250G and then we can coordinate.

I figure we can sieve to an optimal depth for n=25K-50K, break off that piece for primality testing and then continue sieving for n=50K-100K while removing k-values from the higher range as we find primes in the lower range.


Gary
Gary, are you able to sieve this with sr2sieve?
(I am not, at least not on my laptop, I think due to memory shortages...)

For another thing:
How would you feel upon me taking up prp'ing upto 10k with my script, and then report the remaining back to you? Anything beyond 10k takes too long with pfgw, and really needs to be sieved. (which can then be taken on by anyone willing to :) )

50-100M range yielded 808 left-overs upto 10k, so I think it should still be managable file-wise.

I'm aware that the administration would be a bit more complicated (as in, when do you delete the k's that have reduced forms, hosting the files etc, but I think it has the advantage of getting the search started a bit more quickly too

Last fiddled with by michaf on 2008-06-30 at 19:27
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Old 2008-06-30, 20:38   #98
gd_barnes
 
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Quote:
Originally Posted by michaf View Post
Gary, are you able to sieve this with sr2sieve?
(I am not, at least not on my laptop, I think due to memory shortages...)

For another thing:
How would you feel upon me taking up prp'ing upto 10k with my script, and then report the remaining back to you? Anything beyond 10k takes too long with pfgw, and really needs to be sieved. (which can then be taken on by anyone willing to :) )

50-100M range yielded 808 left-overs upto 10k, so I think it should still be managable file-wise.

I'm aware that the administration would be a bit more complicated (as in, when do you delete the k's that have reduced forms, hosting the files etc, but I think it has the advantage of getting the search started a bit more quickly too

It's interesting that you asked. I tried a number of experiments with sr2sieve and srsieve in order to see what I felt was the fastest and least manual-intervention method of sieving.

At first I tried half of the k-values (102) using sr2sieve. Although it took several hours to create the Legendre symbols, that worked fine. I observed that it was using ~480M of memory. My machine has ~1G of memory but the operating system and other things of course use up ~100M (I think).

I decided to push the limit on it and try with all 204 k-values using sr2sieve. Wouldn't you know it, I got a MALLOC error on the 198th k-value and it took over 8 hours (kind-of-slow 1.6 Ghz Athlon) to create the symbols. Unfortunately, even though I told it to save the symbols file, it doesn't do so if it goes down with an error.

I then tried it with 195 k-values and after another ~8 hours to recreate the symbols file, it was working fine. The P-rate was ~170K/sec and the symbols file was 1.6 GB!!

I would then need to run another instance of sr2sieve with the remaining 9 k-values but the P-rates would be so inconsistent that I determined that I should just run 2 instances of sr2sieve, one each for half of the k-values. I did that for the first half of them using the symbols file from my first test above and was getting a ~320K/sec P-rate, about what I would expect (slightly < double the 195 k's rate).

I started to run the second instance of sr2sieve for the second half of the k's and after watching it VERY slowly creating the symbols file, I got sick of waiting.

So, that's when I decided to see how much slower srsieve was for the entire 208 k's. I did an initial sieve to P=4G and then came the real test. I started a sieve from P=4G and the P-rate was ~150K/sec.; only about 10-12% slower than sr2sieve was for 195 k's.

At that point, I just decided that sr2sieve was simply too much of a headache and have been running two instances of srsieve on my dual-core 1.6 Ghz Athlon laptop, each with all of the k's in them for different P-ranges.

I've completed sieving to P=20G as of yesterday and started sieving P=20G-60G but have temporarily suspended it. Right now, I am running PFGW for bases 7 and 25 to get some small primes and balance the k's remaining for Siemlink's efforts on those bases.

I am sieving n=25K-100K. My estimate is that the optimal sieve for breaking off the n=25K-50K piece is P=100G.

If you want to pitch in on sieving, I can send you my ABCD file sieved to P=20G. I'm taking P=20G-60G so if you want to take P=60G-100G, then that should get us to where we need to begin LLRing n=25K-50K. (We'll need to check the removal rate again at that point.) For sieving, we can then remove the n=25K-50K candidates and continue sieving n=50K-100K.

Edit: At the higher n-ranges, the 10-12% savings (minus time needed to create symbols) by using 2 instances of sr2sieve, one each for half of the k-values, would be more significant. We may want to revisit the issue for n=50K-100K or perhaps if we decide to go to a higher n-range with it. My opinion, though, is that we don't go testing above n=100K and that we go on to the next k-range and bring it up to n=100K also, etc. Of course others may prefer to search for higher primes.


Gary

Last fiddled with by gd_barnes on 2008-06-30 at 20:41
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Old 2008-06-30, 20:47   #99
gd_barnes
 
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May 2007
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26·3·53 Posts
Default

Quote:
Originally Posted by michaf View Post
Considering 50-100M base 3 sierpinski:

The following 213 k's are left at n=25k with k mod 3 = 1 or 2 (and thus still need to be searched)
Code:
50219374    1
50222338    1
50287288    1
50449528    1
50541412    1
50620060    1
50877592    1
50921056    1
52186900    1
53109118    1
53314642    1
53593726    1
54315148    1
54503602    1
55055116    1
55075498    1
55193434    1
55703236    1
56148718    1
56171218    1
56524036    1
56581678    1
56882284    1
56905378    1
57254656    1
57336382    1
57557068    1
57675862    1
58437532    1
58871836    1
59763448    1
60209746    1
60703348    1
60935716    1
61270336    1
61429768    1
62499142    1
62531902    1
63016906    1
64341406    1
65507272    1
65554012    1
65595592    1
66255214    1
66557716    1
66928276    1
67852672    1
68093614    1
68155474    1
68526046    1
68558962    1
69187234    1
69487006    1
69897658    1
70143826    1
70260532    1
71647042    1
71825584    1
73225294    1
74803858    1
75465868    1
76479688    1
77475694    1
77519584    1
77554786    1
77976142    1
78702082    1
78703468    1
78967678    1
79190206    1
79473862    1
79545946    1
79714294    1
80078764    1
80763370    1
81095362    1
81540346    1
81903964    1
81956716    1
82085494    1
82386316    1
82436518    1
83880508    1
84469954    1
85310794    1
86000056    1
86850334    1
87173668    1
87252058    1
89478076    1
89824888    1
90473998    1
90784756    1
90978172    1
91233724    1
91293316    1
91379272    1
92793016    1
92894182    1
93364996    1
93409276    1
93711076    1
94591624    1
95450302    1
95489092    1
96026332    1
96746836    1
97418338    1
97696726    1
97826494    1
98043514    1
98392246    1
98926396    1
99613186    1
50357012    2
52898312    2
52912976    2
54282752    2
54320036    2
54332516    2
55196756    2
56092742    2
57703994    2
58007336    2
58537244    2
58680938    2
60260912    2
60581468    2
60650732    2
62109506    2
63362504    2
63973712    2
64133198    2
64877882    2
65719268    2
65924882    2
66048746    2
66431468    2
66600104    2
68203706    2
68204198    2
68232896    2
68268602    2
68426882    2
69005336    2
69026702    2
69563192    2
70009502    2
70258712    2
70668452    2
71192354    2
71440646    2
71445854    2
71448584    2
71744534    2
72086978    2
72880994    2
73308278    2
73440644    2
74374772    2
74481242    2
74927714    2
75065462    2
75734312    2
76020188    2
77057588    2
77304608    2
77357576    2
77574956    2
78373346    2
79379414    2
79822118    2
80114018    2
80126414    2
80292008    2
80382650    2
80598086    2
81106076    2
81278324    2
83873906    2
84187388    2
84215078    2
84481472    2
85867196    2
87080432    2
87593744    2
87706772    2
88091054    2
89106848    2
89665952    2
89813708    2
90269594    2
90733694    2
92297696    2
93455522    2
93882734    2
94389422    2
95532098    2
96103394    2
96259778    2
96693302    2
96839144    2
97016048    2
97132676    2
97688816    2
97963454    2
98486582    2
98762336    2
98841272    2
98997092    2
99170018    2
99341384    2
99434222    2
The following 83 are left at n=25k, but can be left out of the search as they are already searched as their (k mod 3) reduced version:

Code:
50080092    0    16693364    already being searched
50817246    0    16939082    already being searched
51184956    0    17061652    already being searched
51770814    0    17256938    already being searched
52608126    0    17536042    already being searched
53367864    0    17789288    already being searched
53746536    0    17915512    already being searched
54907896    0    18302632    already being searched
57158196    0    19052732    already being searched
57404058    0    19134686    already being searched
58350822    0    19450274    already being searched
58722414    0    19574138    already being searched
59842548    0    19947516    already being searched
60266832    0    20088944    already being searched
60775602    0    20258534    already being searched
60796566    0    20265522    already being searched
60915378    0    20305126    already being searched
60980334    0    20326778    already being searched
61308816    0    20436272    already being searched
61783518    0    20594506    already being searched
62313456    0    20771152    already being searched
62568984    0    20856328    already being searched
62665392    0    20888464    already being searched
63526044    0    21175348    already being searched
63563244    0    21187748    already being searched
64434408    0    21478136    already being searched
64493238    0    21497746    already being searched
66901566    0    22300522    already being searched
69729846    0    23243282    already being searched
69894348    0    23298116    already being searched
71181816    0    23727272    already being searched
71568912    0    23856304    already being searched
71588724    0    23862908    already being searched
71689188    0    23896396    already being searched
72058344    0    24019448    already being searched
74033112    0    24677704    already being searched
74177232    0    24725744    already being searched
74291604    0    24763868    already being searched
74776116    0    24925372    already being searched
74903178    0    24967726    already being searched
75286182    0    25095394    already being searched
75621948    0    25207316    already being searched
76400466    0    25466822    already being searched
76436058    0    25478686    already being searched
76565616    0    25521872    already being searched
78783756    0    26261252    already being searched
79181868    0    26393956    already being searched
79334466    0    26444822    already being searched
80414916    0    26804972    already being searched
81327648    0    27109216    already being searched
81870396    0    27290132    already being searched
83114886    0    27704962    already being searched
84215598    0    28071866    already being searched
84470448    0    28156816    already being searched
85605486    0    28535162    already being searched
86026002    0    28675334    already being searched
86893278    0    28964426    already being searched
87303774    0    29101258    already being searched
87399168    0    29133056    already being searched
87992922    0    29330974    already being searched
88045374    0    29348458    already being searched
88351962    0    29450654    already being searched
88433838    0    29477946    already being searched
88646016    0    29548672    already being searched
88842498    0    29614166    already being searched
89318382    0    29772794    already being searched
90098124    0    30032708    already being searched
90712896    0    30237632    already being searched
91320486    0    30440162    already being searched
91484592    0    30494864    already being searched
91820208    0    30606736    already being searched
93003468    0    31001156    already being searched
93773742    0    31257914    already being searched
95644314    0    31881438    already being searched
95910240    0    31970080    already being searched
97120722    0    32373574    already being searched
97291158    0    32430386    already being searched
97350336    0    32450112    already being searched
97696122    0    32565374    already being searched
98048838    0    32682946    already being searched
98082228    0    32694076    already being searched
99672414    0    33224138    already being searched
99981192    0    33327064    already being searched
The following 6 have (k mod 3^2) = 1 or 2 and cannot be eliminated as they have primes as their reduced form on n=1:

Code:
65943336    0    21981112    1    has a prime at n=1, so this one needs to be searched further 
70848912    0    23616304    1    has a prime at n=1, so this one needs to be searched further 
59343216    0    19781072    2    has a prime at n=1, so this one needs to be searched further 
62837376    0    20945792    2    has a prime at n=1, so this one needs to be searched further 
93040692    0    31013564    2    has a prime at n=1, so this one needs to be searched further 
98555838    0    32851946    2    has a prime at n=1, so this one needs to be searched further
The following 1 has (k mod 3^2) = 1 or 2 and CAN be eliminated because of a prime for the reduced form > n=1:

Code:
80409768    0    26803256    2    has a prime larger then 1, so this one can be eliminated
Of the 40 k's with (k mod 3)=0 there are 27 k's already tested as their reduced forms:

Code:
50171796    0    16723932    0    5574644    already being tested
55110546    0    18370182    0    6123394    already being tested
57271356    0    19090452    0    6363484    already being tested
60770772    0    20256924    0    6752308    already being tested
61735626    0    20578542    0    6859514    already being tested
63729054    0    21243018    0    7081006    already being tested
64005894    0    21335298    0    7111766    already being tested
67215438    0    22405146    0    7468382    already being tested
70915608    0    23638536    0    7879512    already being tested
72530982    0    24176994    0    8058998    already being tested
72812178    0    24270726    0    8090242    already being tested
73506276    0    24502092    0    8167364    already being tested
73640844    0    24546948    0    8182316    already being tested
77431176    0    25810392    0    8603464    already being tested
79454106    0    26484702    0    8828234    already being tested
80199324    0    26733108    0    8911036    already being tested
80912142    0    26970714    0    8990238    already being tested
81390438    0    27130146    0    9043382    already being tested
81859392    0    27286464    0    9095488    already being tested
83165814    0    27721938    0    9240646    already being tested
83653866    0    27884622    0    9294874    already being tested
85349196    0    28449732    0    9483244    already being tested
86155632    0    28718544    0    9572848    already being tested
87216516    0    29072172    0    9690724    already being tested
89890272    0    29963424    0    9987808    already being tested
92017494    0    30672498    0    10224166    already being tested
94541724    0    31513908    0    10504636    already being tested
Of the 13 k's remaining, 12 can be eliminated because their reduced versions have a prime > n=2:

Code:
60961302    0    20320434    0    6773478    has a prime > n=2 so can be eliminated
61856352    0    20618784    0    6872928    has a prime > n=2 so can be eliminated
70787142    0    23595714    0    7865238    has a prime > n=2 so can be eliminated
71728128    0    23909376    0    7969792    has a prime > n=2 so can be eliminated
77379462    0    25793154    0    8597718    has a prime > n=2 so can be eliminated
78289416    0    26096472    0    8698824    has a prime > n=2 so can be eliminated
79111458    0    26370486    0    8790162    has a prime > n=2 so can be eliminated
79623216    0    26541072    0    8847024    has a prime > n=2 so can be eliminated
80482464    0    26827488    0    8942496    has a prime > n=2 so can be eliminated
85319784    0    28439928    0    9479976    has a prime > n=2 so can be eliminated
87321186    0    29107062    0    9702354    has a prime > n=2 so can be eliminated
99122256    0    33040752    0    11013584    has a prime > n=2 so can be eliminated
The last k has a prime at n=2, and so needs to be checked further:

Code:
63003672    0    21001224    0    7000408    has a prime at n=2, so original has a prime at n=0, so needs to be checked further
In short: the remaining 220 k's are:

Code:
50219374
50222338
50287288
50449528
50541412
50620060
50877592
50921056
52186900
53109118
53314642
53593726
54315148
54503602
55055116
55075498
55193434
55703236
56148718
56171218
56524036
56581678
56882284
56905378
57254656
57336382
57557068
57675862
58437532
58871836
59763448
60209746
60703348
60935716
61270336
61429768
62499142
62531902
63016906
64341406
65507272
65554012
65595592
66255214
66557716
66928276
67852672
68093614
68155474
68526046
68558962
69187234
69487006
69897658
70143826
70260532
71647042
71825584
73225294
74803858
75465868
76479688
77475694
77519584
77554786
77976142
78702082
78703468
78967678
79190206
79473862
79545946
79714294
80078764
80763370
81095362
81540346
81903964
81956716
82085494
82386316
82436518
83880508
84469954
85310794
86000056
86850334
87173668
87252058
89478076
89824888
90473998
90784756
90978172
91233724
91293316
91379272
92793016
92894182
93364996
93409276
93711076
94591624
95450302
95489092
96026332
96746836
97418338
97696726
97826494
98043514
98392246
98926396
99613186
50357012
52898312
52912976
54282752
54320036
54332516
55196756
56092742
57703994
58007336
58537244
58680938
60260912
60581468
60650732
62109506
63362504
63973712
64133198
64877882
65719268
65924882
66048746
66431468
66600104
68203706
68204198
68232896
68268602
68426882
69005336
69026702
69563192
70009502
70258712
70668452
71192354
71440646
71445854
71448584
71744534
72086978
72880994
73308278
73440644
74374772
74481242
74927714
75065462
75734312
76020188
77057588
77304608
77357576
77574956
78373346
79379414
79822118
80114018
80126414
80292008
80382650
80598086
81106076
81278324
83873906
84187388
84215078
84481472
85867196
87080432
87593744
87706772
88091054
89106848
89665952
89813708
90269594
90733694
92297696
93455522
93882734
94389422
95532098
96103394
96259778
96693302
96839144
97016048
97132676
97688816
97963454
98486582
98762336
98841272
98997092
99170018
99341384
99434222
65943336
70848912
59343216
62837376
93040692
98555838
63003672
PHEW

Gary, would you be kind and check my reasoning? I think I've got it alright now, but a confirmation would be nice.

Wow, it looks like great work! Nice job! Thanks for providing all of the detail. It'll make the review far easier. It'll probably be tomorrow or Weds. before I can review it as the Riesel base 25 verification is taking many hours and more k's can be eliminated on it then what Siemlink has already found due to the base 5 project.

I hope that no new bases are started for the next several months now!


Gary
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