New repunit (PRP) primes found, 5794777 and 8177207 decimal digits (PRP records)

[Batalov]

Originally Posted by ATH

You can do a Lucas test with LLR ? (For some reason -q does not work for me in LLR 3.8.23)
cllr64.exe -d -oLucasPRPtest=1 input.txt

input.txt:

ABC (10^$a-1)/9
8177207

or the BPSW version of Lucas test if you use LLR 3.8.24:
cllr.exe -d -oLucasPRPtest=1 -oBPSW=1 -q"(10^8177207-1)/9"

There is a better form, and llr treats it optimally

ABC ($a*$b^$c$d)/$e
1 10 8177207 -1 9

LLR ver >= 3.8.24 will indeed create $temp.npg exactly like that, but even with earlier versions you can use the ABC file above.

[ATH]

Thank you.

I was actually responding to your line:
"We are checking SPRP in 3-4 bases first (the best we can do for this PRP.)"

which I found curious since you can also do Lucas test + Frobenius test with LLR.


Congratulations on this huge PRP!

[paulunderwood]

Originally Posted by ATH

Thank you.

I was actually responding to your line:
"We are checking SPRP in 3-4 bases first (the best we can do for this PRP.)"

which I found curious since you can also do Lucas test + Frobenius test with LLR.


Congratulations on this huge PRP!

I'll gladly run it. Starting now.

[Batalov]

Originally Posted by ATH

which I found curious since you can also do Lucas test + Frobenius test with LLR.
:

But who said that we didn't?

Q: What happens if you simply run a test with llr?
A: it runs PRP, then Lucas and finally Frobenius tests. By default, no special CLI options are needed

Originally Posted by paulunderwood

I'll gladly run it. Starting now.

By all means, sure, - run them. They have already been run, but why not run them once again?

[paulunderwood]

Originally Posted by Batalov

But who said that we didn't?

Q: What happens if you simply run a test with llr?
A: it runs PRP, then Lucas and finally Frobenius tests. By default, no special CLI options are needed

By all means, sure, - run them. They have already been run, but why not run them once again?

Hah. I'll abort my run,

[Batalov]

One thing that I didn't know, is that FBase=a=<some base> is honored by llr when set as Fermat base, that is no surprise.
But! -- what follows (i.e. L+F tests) is decoupled from the choice of a, so Lucas test happens to be all the same in all runs, so one is enough.

Starting probable prime test of (10^8177207-1)/9
Using AVX-512 FFT length 1600K, Pass1=1K, Pass2=1600, clm=1, 24 threads, a = 23
(10^8177207-1)/9 is base 23-Fermat PRP! (8177207 decimal digits)  Time : 25493.017 sec.
Starting Lucas sequence
Using AVX-512 FFT length 1600K, Pass1=1K, Pass2=1600, clm=1, 24 threads, P = 6, Q = 2
_____________...and so on...___________
Using AVX-512 FFT length 1600K, Pass1=1K, Pass2=1600, clm=1, 16 threads, a = 5
10^8177207-1)/9 is base 5-Fermat PRP! (8177207 decimal digits)  Time : 25663.426 sec.
Starting Lucas sequence
Using AVX-512 FFT length 1600K, Pass1=1K, Pass2=1600, clm=1, 16 threads, P = 6, Q = 2
_____________...and so on...___________
Starting probable prime test of (10^8177207-1)/9
Using AVX-512 FFT length 1600K, Pass1=1K, Pass2=1600, clm=1, 16 threads, a = 7
(10^8177207-1)/9 is base 7-Fermat PRP! (8177207 decimal digits)  Time : 25609.258 sec.
Starting Lucas sequence
Using AVX-512 FFT length 1600K, Pass1=1K, Pass2=1600, clm=1, 16 threads, P = 6, Q = 2
_____________...and so on...___________
Starting probable prime test of (10^8177207-1)/9
Using AVX-512 FFT length 1600K, Pass1=1K, Pass2=1600, clm=1, 16 threads, a = 11
(10^8177207-1)/9 is base 11-Fermat PRP! (8177207 decimal digits)  Time : 25643.544 sec.
Starting Lucas sequence
Using AVX-512 FFT length 1600K, Pass1=1K, Pass2=1600, clm=1, 16 threads, P = 6, Q = 2
_____________...and so on...

I'll try to (as Mike likes to say) ...

...options:
FBase=
PBase=
FermatBase=
LucasBaseP=
isLucasBaseQ=
genLucasBaseQ=
generalLucasBase=
genLucasBaseP=
...

sllr  -oLucasBaseP=12 -oLucasPRPtest=1 -oBPSW=1 -d in
Starting Lucas sequence
Using FMA3 FFT length 1600K, Pass1=640, Pass2=2560, clm=1, 24 threads, P = 1, Q = 4  <<< looks like can be controlled

P = 1, Q = 4 is good: kronecker(-15,Rn) = -1
P = 6, Q = 2 is good: kronecker(28,Rn) = -1

[ATH]

Originally Posted by Batalov

But who said that we didn't?

It was clearly a language communication issue:
"We are checking SPRP in 3-4 bases first (the best we can do for this PRP.)"

I understood "(the best we can do for this PRP.)" as "That is all we can do for this PRP, only SPRP tests and nothing else."

[Batalov]

Dear Andreas, yes, it is a language communication issue.
Do you disagree with the phrase: "say anything, - and you will be misinterpreted by at least one"?
Or in other phrasing "A thought, once spoken, is a lie." (Fyodor Tyutchev, translated by Vladimir Nabokov)

At least the thread title, I hope, is unequivocal.

[GP2]

Congratulations. I wonder, in the course of your search are you recording residues and factors for posterity?

[Dr Sardonicus]

Originally Posted by GP2

Congratulations. I wonder, in the course of your search are you recording residues and factors for posterity?

As previously mentioned in this post, the Details section on this page, which Batalov supplied in this post, has that information.

[Batalov]

Discussion of definitions (once again supporting the earlier observation that "A thought, once spoken, is a lie") is moved to a separate thread.