Most wanted
I post here some results in need to make the Database 'databaseable' :)
There're many remarks like (90 primes to 50k)' in there (see data for 10^9 at the end) and i filled them up from time to time on my own. Also there're many high weighted k's without any prime displayed for now So everyone is invited to resolve such remarks. 
Knocked out one of these annoying little buggers (k=4259877765), which is listed as "91 primes 050K". I searched it for n=050K with LLR; I then reverified the primes with PFGW since LLR apparently had to do a PRP test for some of the lower ones. Many of them, apparently, were then subsequently proven by LLR, but since they're all very small anyway I figured I'd buzz them through PFGW to play things safe.
So, without further ado, here are the 91 primes for n=050K: 4, 6, 10, 15, 16, 24, 25, 32, 34, 37, 38, 47, 53, 54, 56, 64, 74, 85, 86, 90, 102, 105, 106, 110, 117, 119, 130, 137, 166, 168, 175, 185, 196, 205, 212, 310, 322, 363, 369, 389, 423, 482, 503, 506, 561, 593, 659, 715, 893, 1029, 1042, 1149, 1157, 1278, 1350, 1626, 1692, 1829, 1867, 1895, 2041, 2782, 2845, 2926, 3705, 3785, 3946, 4512, 4969, 5360, 5490, 6203, 6228, 6646, 7992, 8222, 8505, 13332, 14469, 14978, 16527, 16972, 20916, 21000, 21168, 24577, 28763, 28847, 29956, 48093, 49429 
llr wont work if the k is larger than 2^n

[quote=henryzz;151210]llr wont work if the k is larger than 2^n[/quote]
Yeah, I noticed some error messages to that effect. Example output:[code] max@max:/tmp$ ./llr d q4259877765*2^41 4259877765 > 2^4, so we can only do a PRP test for 4259877765*2^41. Starting probable prime test of 4259877765*2^41 Using generic reduction FFT length 32 4259877765*2^41 is a probable prime. Time : 0.769 ms.[/code]But what was more confusing is what I got for some of the later results:[code]max@max:/tmp$ ./llr d q4259877765*2^1191 Starting probable prime test of 4259877765*2^1191 Using generic reduction FFT length 32 4259877765*2^1191 is a probable prime. Time : 0.352 ms. Please credit George Woltman's PRP for this result! Starting Lucas Lehmer Riesel prime test of 4259877765*2^1191 Using General Mode (Rational Base) : Mersenne fftlen = 32, Used fftlen = 32 V1 = 5 ; Computing U0...done. 4259877765*2^1191 is prime! Time : 0.314 ms.[/code]Yes, this is for just *one* number. It apparently did a PRP test for this number, and then after find it probably prime, did an LLR test on it as a proof! Does anyone know why it does this? 
[QUOTE=mdettweiler;151263]Yes, this is for just *one* number. It apparently did a PRP test for this number, and then after find it probably prime, did an LLR test on it as a proof! Does anyone know why it does this?[/QUOTE]
:rtfm: [QUOTE=LLR Readme.txt] Version 3.6 : The program is now directly linked with the George Woltman's gwnums library archive, and the source does no more contain included gwnums C code files. It has been rather much tested on no SSE2 machines, so the "Beta" has been removed. The k*b^n±1 numbers, were the base b is a power of two, are now converted into base two numbers before beeing processed, instead of doing a PRP test on them. [COLOR="Red"]An iteration in the "Computing U0" loop is two times more timeconsuming than a computing power one, so it is better to make a previous PRP test before a LLR one, as soon as the k multiplier's bit length reaches 10% of the bit length of the number to test. That is that is done in this version. On the other hand, the Proth test is slightly faster than the PRP one, so, it is done directly.[/COLOR] To avoid any confusion, the output line for composite numbers now shows of which algorithm the residue is the result : RES64: "xxxxxxxxxxxxxxxx" (PRP test) LLR RES64: "xxxxxxxxxxxxxxxx" (LLR test) Proth RES64: "xxxxxxxxxxxxxxxx" (Proth test) [/QUOTE] 
[quote=axn;151264]:rtfm:[/quote]
Ah, I see. I *did* read through the readme file, but I must have missed the part about doing a "previous PRP test before an LLR one". Thanks. :smile: 
I always use PFGW for n<=1000. LLR used to have a bug where it would sometimes report primes as composites or visaversa on small n (even for k's that were not very large) and even for n>50 at times. There is an RPS thread about it. Presumably it has been fixed but it seems as though people keep finding another situation that wasn't considered and so it has been "fixed" several times.
Regardless of the size of k, I don't trust LLR for n<=1000 and so always use PFGW for it. PFGW seems to be able to handle about any size of k accurately. That is the safest way to go for very small primes. Gary 
the WINGUIVersion of LLR V3.7.1c (20081221) from J.Penne can be found here: [url]http://jpenne.free.fr/[/url]
i've tested all primes from the Database for n=1 to 300k and no errors were found! i did this before and sent Jean some small issues about that and he updated his LLRVersion so all seems to be fine with small n or kvalues now! 
Filling the GAPS for
[B]Riesel list (k·2n1 prime) for 10^7 < [I]k[/I] < 10^8[/B] [URL]http://www.rieselprime.de/Data/10e07.htm[/URL] [code] K Highest N value 16545165 10k 29058315 10K 47912205 10K 19474455 50k 20934375 50K 24107655 50K 27114615 50K 28397655 50K 35900025 50K 44702775 50K 51010245 50K 78290355 50K 80555475 50K 96623835 50K[/code]Found 14k with primes reported but not listed. Will report the results when done. Thanks cipher 
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[B]COMPLETED[/B]
[code]16545165 10k 29058315 10K 47912205 10K [/code]Tested upto n<10k Attach with all the primes for all three K [ATTACH]3682[/ATTACH] I will post the results for remaining 11k's in 3 days. [B]Correction[/B] 16545165 listed 62 primes for n <10k i only found 61 29058315 listed 60 primes for n <10k i only found 59 47912205 listed 61 primes for n <10k i only found 60 Thanks Cipher kar_bon: primes for these 3 k's inserted 
One more K knocked out 50K, approx LLR time 4 hours, so the remaining 10 K will take approx 4044 hours of LLR i will submit them in 2 days. Primes found 89 just as it was reported originally.
[code] 3, 5, 9, 10, 11*, 14, 17*, 18, 27, 32, 35, 37, 51, 64, 68*, 89, 91, 100, 102, 113, 119, 145, 185, 200, 225, 230, 248, 286, 408, 492, 553, 554, 606, 613, 663, 673, 707, 718, 745, 781, 798, 844, 950, 963, 999, 1033, 1042, 1229, 1308, 1333, 1419, 1522, 1884, 2010, 2098, 2284, 2354, 3008, 3194, 3258, 3533, 3998, 4120, 4212, 4534, 4824, 5255, 6791, 7140, 7171, 7345, 8830, 9620, 10270, 11453, 12785, 13088, 15685, 16770, 17828, 20523, 20750, 23855, 33887, 40062, 41613, 41793, 44450, 49581[/code]Thanks cipher kar_bon: primelist changed, twins (*) marked, inserted in 10^7page 
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Filling the GAPS for
[B]Riesel list (k·2n1 prime) for 10^7 < [I]k[/I] < 10^8 [Completed] Remaining 10k LLR'd upto n=50k [/B][CODE]19474455*2^n1 [completed] 20934375*2^n1 [completed] 24107655*2^n1 [completed] 27114615*2^n1 [completed] 28397655*2^n1 [completed] 35900025*2^n1 [completed] 44702775*2^n1 [completed] 51010245*2^n1 [completed] 78290355*2^n1 [completed] 80555475*2^n1 [completed] 96623835*2^n1 [completed][/CODE] Here is the File with all the primes for the above range. [ATTACH]3691[/ATTACH] Thanks, cipher P.S: Kar_bon please look in the range [B]Riesel list (k·2n1 prime) for 10^7 < [I]k[/I] < 10^8 and let me know if i might have missed any k's[/B] kar_bon: all primes inserted with marked twins/SophieGermain. all comments "(xx primes to 50k)" for the range 10^7 < [i]k[/i] < 10^8 filled. remarkable: k=35900025 got 3 SophieGermain pairs >1000! many thanks! 
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Filling the GAPS for
[B]Riesel list (k·2n1 prime) for 10^8 < [I]k[/I] < 10^9 [Completed] 22k LLR'd upto n=50k [/B][code] 175977945*2^n1 [completed] 178140105*2^n1 [completed] 199140045*2^n1 [completed] 228461805*2^n1 [completed] 228986175*2^n1 [completed] 240924255*2^n1 [completed] 244133175*2^n1 [completed] 249671565*2^n1 [completed] 272605245*2^n1 [completed] 272936235*2^n1 [completed] 281804985*2^n1 [completed] 384158775*2^n1 [completed] 418791945*2^n1 [completed] 445419975*2^n1 [completed] 555567045*2^n1 [completed] 682980375*2^n1 [completed] 687218805*2^n1 [completed] 719053335*2^n1 [completed] 776668035*2^n1 [completed] 828512685*2^n1 [completed] 857996205*2^n1 [completed] 949473525*2^n1 [completed] [/code]Here is the File with all the primes for the above range. [ATTACH]3733[/ATTACH] Thanks, cipher P.S: Kar_bon please look in the range [B]Riesel list (k·2n1 prime) for 10^8 < [I]k[/I] < 10^9 and let me know if i might have missed any k's[/B] 
1 Attachment(s)
Filling the GAPS for
[B]Riesel list (k·2n1 prime) for 10^9 < [I]k[/I] < 10^10 [Completed] 7k LLR'd upto n=50k [/B][code] 8594430075*2^n1 [Completed] 8614926705*2^n1 [Completed] 8629569795*2^n1 [Completed] 8670014925*2^n1 [Completed] 8713308285*2^n1 [Completed] 8858158725*2^n1 [Completed] 9158021565*2^n1 [Completed] [/code]Here is the File with all the primes for the above range. [ATTACH]3737[/ATTACH] Thanks, cipher P.S: Kar_bon please look in the range [B]Riesel list (k·2n1 prime) for 10^9 < [I]k[/I] < 10^10 and let me know if i might have missed any k's[/B] 
1 Attachment(s)
Here is the zip file which have an html and text file of the gaps from 10^8 to 10^10, filled by D.Zaveri (cipher). I checked twins.
Note to kar_bon: k=384158775 and 8713308285 has a different number of primes than expected. I've not yet double checked the results. 
I've inserted all primes and twins from cipher in the summary pages.
Thanks also Merfighters for the htmlpage. 
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