Carol / Kynea search (Near-power primes)

[rogue]

(2^520363-1)^2-2 is prime! It has been almost 9 years since the last Carol prime has been found.

[wombatman]

Well done!

[Batalov]

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...

[rogue]

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.

[Jean Penné]

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

[rogue]

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.

[rogue]

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.

[Batalov]

C-K primes attracted interest from David B.:

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.

[rogue]

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.

[Batalov]

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)

[lalera]

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!