k=22544089918041953*E(130) generates 216 known primes

[Lennart]

Primality testing 22544089918041953*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*2^517692-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction AVX FFT length 50K, Pass1=640, Pass2=80 on A 517824-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 99.97%
22544089918041953*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*2^517692-1 is prime! (1788.9399s+0.0009s)

Lennart

[Batalov]

I ksieve'd for a day (to 1T only, n=1-1.2M) in the recordable range* and added this prime to the collection:
22544089918041953*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*2^1025897-1

I'll post the rest of the sieve, later. Will possibly sieve and run some more.

[Kosmaj]

Hi Batalov,

Congrats on a nice prime!
Can you also include RPS in your new prover's code?

Thanks!

[Batalov]

Sure thing. I emailed C.C. (and added a comment to the prime, too).

I put the asterisk in my morning message, but forgot to post the footnote. It is this:
_______________________
*Note that the Top-5000 cutoff plane will pass exactly 1,000,000 bits today or tomorrow. For the record, right now it is still at 999,400 bits' size, but the 1,290,000-bits abominable primes keep on pouring in. Mark my words Next state of the Top5000 database will be that all primes from position ~1,500 to 5,000 will be ~1,290,000 bits.

[pinhodecarlos]

Originally Posted by Thomas11

Here is for convenience the input file in NewPGen format needed for LLR. Please help yourself to cut out your ranges.

It would be nice if some of you could post some comparative timings for LLR and PFGW (PRP test).

BTW.: I'm already running a new sieve for the candidates up to n=1M (I've completely underestimated your interest and machinery in this sub-project). The new sieve file will be ready for testing around Monday next week.

Please update first post attachment.
http://www.mersenneforum.org/showpos...4&postcount=36

[ATH]

LLR vs PFGW timings on 1480472640274704456611717878515654164205*2^716611-1:




Laptop i7 2720QM 2.20 Ghz:

LLR 3.8.9:
Lucas Lehmer Riesel prime test: 1115 sec (deterministic)
Strong Fermat PRP: 1422 sec
Lucas PRP: 2837 sec
Frobenius PRP: 1300 sec

PFGW 3.7.7:
Strong Fermat PRP: 1215 sec
[N-1, Brillhart-Lehmer-Selfridge] 1973 sec (still came out PRP even if it should be deterministic)




Q9450(Yorksfield) 2.66 Ghz:

LLR 3.8.9:
Lucas Lehmer Riesel prime test: 2193 sec
Strong Fermat PRP: 2179 sec
Lucas PRP: 4746 sec
Frobenius PRP: 2179 sec

PFGW 3.7.7:
Strong Fermat PRP: 2229 sec
[N-1, Brillhart-Lehmer-Selfridge] 3350 sec (came out as PRP)

[Batalov]

Taking 1000-1030, for the record.

[ATH]

Originally Posted by Jean Penné

For k > 2^53, the use of generic modular reduction is required, so the calculus becomes 3 times slower, but it is due do the gwnum library usage, and PFGW has the same limitation!

Regards,
Jean

The slowdown seems to happen at a very specific k-value near 7.5*10¹⁴ or ~2^49.4:

750599937895082*2^498496-1, iteration : 10000 / 498497 [2.00%]. Time thusfar : 2.700 sec.
750599937895083*2^498496-1, iteration : 10000 / 498496 [2.00%]. Time thusfar : 9.986 sec.

750599937895081*2^716611-1, iteration : 10000 / 716611 [1.39%]. Time thusfar : 4.459 sec.
750599937895083*2^716611-1, iteration : 10000 / 716611 [1.39%]. Time thusfar : 15.067 sec.

750599937895086*2^1025897-1, iteration : 10000 / 1025898 [0.97%]. Time thusfar: 5.908 sec.
750599937895087*2^1025897-1, iteration : 10000 / 1025897 [0.97%]. Time thusfar: 21.928 sec.

[Kosmaj]

I added the LLR input file (in the n=730-800k range only) to the zip file in the top post.

BTW, if you find a reportable prime using LLR please give credit to ksieve instead of srsieve/Psieve.

[lsoule]

Taking 732-740

[Batalov]

Originally Posted by Batalov

Taking 1000-1030, for the record.

Done. Attached.

(There's probably ~5-8% avoidable tests there; the input list was only sieved to 1T. With more sieving, there would be only ~1933 tests per each range of 10k; in the attached file, there are ~2090 per 10k.)