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2008-06-24, 07:00   #89
gd_barnes

May 2007
Kansas; USA

240018 Posts

Quote:
 Originally Posted by Siemelink 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 Sierp Base 3: 2980832*3^38101+1 is prime. so only one k < 3M !
Quote:
 Originally Posted by Siemelink 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 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

 2008-06-24, 17:37 #90 michaf     Jan 2005 1110111112 Posts 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...)
 2008-06-27, 06:35 #91 gd_barnes     May 2007 Kansas; USA 280116 Posts 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
2008-06-27, 06:46   #92
gd_barnes

May 2007
Kansas; USA

72×11×19 Posts

Quote:
 Originally Posted by michaf 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

 2008-06-27, 06:52 #93 gd_barnes     May 2007 Kansas; USA 72×11×19 Posts 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
2008-06-27, 07:22   #94
michaf

Jan 2005

479 Posts

Quote:
 Originally Posted by gd_barnes 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

2008-06-27, 07:29   #95
gd_barnes

May 2007
Kansas; USA

72×11×19 Posts

Quote:
 Originally Posted by michaf 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

 2008-06-30, 19:10 #96 michaf     Jan 2005 479 Posts 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
2008-06-30, 19:15   #97
michaf

Jan 2005

1DF16 Posts

Quote:
 Originally Posted by gd_barnes 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

2008-06-30, 20:38   #98
gd_barnes

May 2007
Kansas; USA

72×11×19 Posts

Quote:
 Originally Posted by michaf 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

2008-06-30, 20:47   #99
gd_barnes

May 2007
Kansas; USA

72·11·19 Posts

Quote:
 Originally Posted by michaf 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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