Request from Phil

[michaf]

Originally Posted by fatphil

I presume that's not just _size_ 2^100000, but of _form_ k*2^100000+/-1.
That's basically LLR/PRP/PFGW's sweet spot - absolutely no point in running Phrot for those forms on an x86 machine. That and GW's SSE2 convoluions work, and YEAFFT's don't, so I have to stick with 8 plain old FPU registers.

This is the 'base 5' project, after all, so it matters not.

Oh right :) think I shopped in the wrong store... trying again with base 5

[michaf]

A second try gives:

F:\Math\phrot.0.45.cygp3>phrot -q "75076*5^103583-1"
Actually testing 1876900*1953125^11509-1 (11510/24576 limbs)
75076*5^103583-1 [] is PRP. (t=364.20s)

LLR give 664 seconds!

(So even a build for the P3 is waaay faster on an athlon64 :) )

48820*72^48820-1 [] is PRP. (t=1070.17s)
83660*72^83660-1 [] is PRP. (t=4642.49s)

So it works fine on 150,000+ digits an my Athlon 2400+. I did run other programms in the background.

Great piece of software, Phil

[fatphil]

Thanks everyone for helping test!

Can people attach, URL, or mail me (yahoo.co.uk - thefatphil) some *small* composite results. So I can do tests by the hundred or thousand.

Partial good news is that I seem to reproduce 32-bits of what I think the LLR residue will be (I've written a Pari/GP script to just perform the calculation). It's not totally clear what LLR does in terms of the signedness of the residues yet. FFTs are done with balanced limbs - my result is signed; I don't know if LLR's is.
I have no idea why it craps out at 32 bits though. That would be enough to put almost complete confidence in the results, if they were to always agree.

[fatphil]

Originally Posted by thommy

48820*72^48820-1 [] is PRP. (t=1070.17s)
83660*72^83660-1 [] is PRP. (t=4642.49s)

So it works fine on 150,000+ digits an my Athlon 2400+. I did run other programms in the background.

Great piece of software, Phil

After R/S5, I was going straight over to the GC/W searchers to offer them access to this code too - I'd not forgotten about them!

[michaf]

Phil,

I've emailed you a result-file with 3232 composites of form k*5^100-1
I hope this is what you meant :>

Cheers, Micha

[fatphil]

Attached - Version 0.46, with a new -b switch to select the witness. b=3 will replicate a RES64 as from PFGW or LLR.
Be warned, this still doesn't do roundoff error checking, and may not be safe for very big numbers. I don't know how big 'very big' is.

Note to admin - can you enable '.tgz' as a recognised extension please? I much prefer that to '.tar.gz'.

[fatphil]

Originally Posted by axn1

LLR tests only k*2^n±1 numbers, so, we will do a PRP test of 164852*5^100524-1
164852*5^100524-1 is not prime.  RES64: A850C2F3D5ABB57E  Time: 1082.993 sec.

$ ./phrot.cygp3 -b=3 -q 164852*5^100524-1
Actually testing 20606500*1953125^11169-1 (11171/24576 limbs)
164852*5^100524-1 [-721640,-696027,-954307,-805292] is composite LLR64=A850C2F3D5ABB57E. (t=1529.02s)

Imagine dancing bananas here if that presses your buttons.

Phil

[axn]

Originally Posted by fatphil

Imagine dancing bananas here if that presses your buttons.

Had to be done!

There doesn't appear to be any loss in speed by using b=3. Will there be any change in the FFT break points because of base 3?

Time to run all the small composites thru the program.

[fatphil]

Originally Posted by axn1

Had to be done!

There doesn't appear to be any loss in speed by using b=3. Will there be any change in the FFT break points because of base 3?

Time to run all the small composites thru the program.

Heheh - my adblock filter at home removes all those icons, so I have no idea what you've just inserted into the thread!

For S/R5's candidates (and GC/W), the witness shouldn't make any difference to FFT sizes, which will occur at the predictable places where the exponent increases beyond the FFT size. Presently, I stick 9 fives into the FFT limb, but as the size increases, I'll need to reduce that to 8. I don't think the program can work out when that is required presently. There's an undocumented switch -a<num> for increased paranoia which will almost certainly kick it down to 8.

[masser]

Does anyone know if the residues from PRP match the residues of LLR?


Via phrot with b = 3:

254*5^474558-1 [-316717,355923,344018,772502] is composite LLR64=34691A2F4DA6F620. (t=9989.12s)

Via PRP:

254*5^474558-1 is not prime. RES64: EF65F8011E5542EE. OLD64: FBE69A2253DBFA1A

Could someone test this number with LLR?