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 2016-04-15, 01:02 #23 rogue     "Mark" Apr 2003 Between here and the 11001000111112 Posts (2^520363-1)^2-2 is prime! It has been almost 9 years since the last Carol prime has been found.
 2016-04-15, 01:03 #24 wombatman I moo ablest echo power!     May 2013 23×223 Posts Well done!
2016-04-15, 02:17   #25
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

957110 Posts

Quote:
 Originally Posted by rogue (2^520363-1)^2-2 is prime! It has been almost 9 years since the last Carol prime has been found.
Great job! Just a little short of Top5k, pity...

I am curious to compare ABC $a^$b-$a^$c$d form (with "2 1040726 520364 -1") as input to LLR to PFGW (where the number can be input in many different ways). Should be more or less the same in terms of time, I expect. "Using generic reduction FMA3 FFT length 100K", etc... 2016-04-15, 04:03 #26 rogue "Mark" Apr 2003 Between here and the 59×109 Posts Quote:  Originally Posted by Batalov Great job! Just a little short of Top5k, pity... I am curious to compare ABC$a^$b-$a^$c$d form (with "2 1040726 520364 -1") as input to LLR to PFGW (where the number can be input in many different ways). Should be more or less the same in terms of time, I expect. "Using generic reduction FMA3 FFT length 100K", etc...
It's using PFGW because of the format. I could probably modify the client to create an LLR friendly format.

2016-04-16, 16:32   #27
Jean Penné

May 2004
FRANCE

22×5×29 Posts

Quote:
 Originally Posted by rogue It's using PFGW because of the format. I could probably modify the client to create an LLR friendly format.
The format accepted by LLR for Carol/Kynea is ABC (2^$a$b)^2-2
so, it works only for base two, sorry...
I can generalize to ABC (%lu^$a$b)^2-2, it will be done in next release.

Regards,
Jean

2016-04-16, 17:19   #28
rogue

"Mark"
Apr 2003
Between here and the

59·109 Posts

Quote:
 Originally Posted by Jean Penné The format accepted by LLR for Carol/Kynea is ABC (2^$a$b)^2-2 so, it works only for base two, sorry... I can generalize to ABC (%lu^$a$b)^2-2, it will be done in next release. Regards, Jean
Thanks. A simple change to the client should be all that I need to do. First I will compare the timings with pfgw.

Last fiddled with by rogue on 2016-04-16 at 17:25

2016-04-16, 19:47   #29
rogue

"Mark"
Apr 2003
Between here and the

59×109 Posts

Quote:
 Originally Posted by rogue Thanks. A simple change to the client should be all that I need to do. First I will compare the timings with pfgw.
pfgw is about 15% faster on my iMac than the latest llr for these numbers.

2016-06-15, 15:04   #30
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

100101011000112 Posts

C-K primes attracted interest from David B.:
Quote:
 Originally Posted by David Broadhurst ...how about finding some Big-Ears and Noddy primes: http://harvey563.tripod.com/Carol_Kynea.txt using a cubic sieve:-? Best! David
Maybe the time has come, indeed.

2016-06-15, 15:20   #31
rogue

"Mark"
Apr 2003
Between here and the

144378 Posts

Quote:
 Originally Posted by Batalov C-K primes attracted interest from David B.: Maybe the time has come, indeed.
Someone else is welcome to write such a sieve.

2016-06-15, 16:54   #32
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

17·563 Posts
cksieve 3.1.7 -- A sieve for Near-Cube (b^n+-1)^3-2 numbers

I will adapt cksieve, then, to sieve for these under a separate option.
_____________________

EDIT (Jun/16): It seems to work. (I've recreated the known Near-Cube primes for b=2, and started sieving above the known range and reserve b=2 to n=10^6.)
For the Near-Cubes, I called this a cksieve v.3.x program; I have not merged the two sources. The branched source is attached.
I used Adleman-Manders-Miller cubic root implementation. There is 1 root for some p and {3 or none} for others.
Validated factors by GP (and the program's internals). The source snapshot is attached.
EDIT: version 3.1.7 is obsolete.

UPDATE: ver 3.1.8 (Jun/17): Searching on the "correct" side of the cube for (b^n-1)^3+2 now.
(The new ABC header is a bit ugly but it does the job. We need (b^n+1)^3-2 and (b^n-1)^3+2)
Attached Files
 cksieve_3.1.8.zip (50.6 KB, 156 views)

Last fiddled with by Batalov on 2016-06-18 at 05:51

 2016-06-17, 17:16 #33 lalera     Jul 2003 10011000112 Posts hi, here are the results for near-cube numbers done with cksieve v3.1.7 and openpfgw b=6, n=1 to 10000 (6^2+1)^3-2 (6^3+1)^3-2 (6^44+1)^3-2 (6^48+1)^3-2 (6^57+1)^3-2 (6^188+1)^3-2 (6^738+1)^3-2 works fine!

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