Most wanted

[kar_bon]

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.

[mdettweiler]

Knocked out one of these annoying little buggers (k=4259877765), which is listed as "91 primes 0-50K". I searched it for n=0-50K with LLR; I then re-verified 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=0-50K:

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

[henryzz]

llr wont work if the k is larger than 2^n

[mdettweiler]

Originally Posted by henryzz

llr wont work if the k is larger than 2^n

Yeah, I noticed some error messages to that effect. Example output:

max@max:/tmp$ ./llr -d -q4259877765*2^4-1
4259877765 > 2^4, so we can only do a PRP test for 4259877765*2^4-1.
Starting probable prime test of 4259877765*2^4-1
Using generic reduction FFT length 32
4259877765*2^4-1 is a probable prime.  Time : 0.769 ms.

But what was more confusing is what I got for some of the later results:

max@max:/tmp$ ./llr -d -q4259877765*2^119-1
Starting probable prime test of 4259877765*2^119-1
Using generic reduction FFT length 32
4259877765*2^119-1 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*2^119-1
Using General Mode (Rational Base) : Mersenne fftlen = 32, Used fftlen = 32
V1 = 5 ; Computing U0...done.
4259877765*2^119-1 is prime!  Time : 0.314 ms.

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?

[axn]

Originally Posted by mdettweiler

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?

Originally Posted by 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.

-An iteration in the "Computing U0" loop is two times more time-consuming
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.

-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)

[mdettweiler]

Originally Posted by axn

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.

[gd_barnes]

I always use PFGW for n<=1000. LLR used to have a bug where it would sometimes report primes as composites or visa-versa 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

[kar_bon]

the WIN-GUI-Version of LLR V3.7.1c (2008-12-21) from J.Penne can be found here: http://jpenne.free.fr/

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 LLR-Version so all seems to be fine with small n- or k-values now!

[cipher]

Filling the GAPS for
Riesel list (k·2n-1 prime) for 10^7 < k < 10^8

http://www.rieselprime.de/Data/10e07.htm

      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

Found 14k with primes reported but not listed. Will report the results when done.

Thanks cipher

[cipher]

COMPLETED

16545165 10k
29058315 10K
47912205 10K

Tested upto n<10k
Attach with all the primes for all three K gapprime.txt

I will post the results for remaining 11k's in 3 days.

Correction
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

[cipher]

One more K knocked out 50K, approx LLR time 4 hours, so the remaining 10 K will take approx 40-44 hours of LLR i will submit them in 2 days. Primes found 89 just as it was reported originally.

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

Thanks cipher

kar_bon:
primelist changed, twins (*) marked, inserted in 10^7-page