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

[Batalov]

The last two known repunits were found back in 2007. Welcome, the year 2021.

With Ryan Propper, we decided to give a boost to the project which changed a few homes over the years. (We don't know the latest live site. skoberne site is defunct. Perhaps, Kurt's subpage.)

So, we might go up to p<10,000,000 and so far found one. We are using MT llr and gr-mfaktc to 64 bits for presieve.
It is submitted to PRPtop, to Mathworld and to UTM (in category of thesaurus of primes). Wikipedia and OEIS 004023 will be updated when sourced with other pages.

It is R_5794777, and perhaps unsurprisingly it has 5794777 decimal digits (all "1"s).

It also happens to be the largest currently known PRP.

[paulunderwood]

Originally Posted by Batalov

R_5794777

That is one hell of a PRP. Congrats on such a large find.

[Jeff Gilchrist]

Nice, congrats.

[Dr Sardonicus]

Wow, heck of a find! Not a whole lot of more-than-million-decimal-digit PRPs known.

Hmm. OEIS lists R_p exponents as 2, 19, 23, 317, 1031, 49081, 86453, 109297, 270343, ...

and gives 2007 for last two. It seems that 1031 is the largest exponent for which primality is actually proved

So, have all primes 270343 < p < 5794777 been ruled out as exponents for decimal repunit primes? That too would be a heck of an achievement.

[Batalov]

Kurt's site ascertains that region below 4300447 is finished.
We have not double-checked that region. We will check all eligible candidates in range 4,300,447 < p < 10,000,000 (or maybe less, -- whatever resources will allow).

[axn]

Originally Posted by Batalov

We are using MT llr and gr-mfaktc to 64 bits for presieve.

How does LLR performance compare with P95/mprime on this type? Do you have any data?

[T.Rex]

Originally Posted by Batalov

.
It is R_5794777, and perhaps unsurprisingly it has 5794777 decimal digits (all "1"s).

Wowww So Big. Congratulations!

[Batalov]

Originally Posted by axn

How does LLR performance compare with P95/mprime on this type? Do you have any data?

It is almost the same, but operationally speaking, running single jobs is cleaner with LLR2. (Prime95 stays running forever after worktodo.txt is spent/empty, and needs to be killed, or source tampered with and recompiled - but that would only converge its evolution into a clone of LLR). Ryan prefers LLR. Currently using sllr from Jean's site. (Also trying the one with 30.6 gwnum as the engine, off-line, as a test.)

LLR does the Prime95 computational trick since a few releases back - i.e. PRP-tests the (k*b^n+c)/e form using (k*b^n+c) transform, nor a general transform. With monic (k=1), c=-1, it is of course ridiculously fast compared to general form, -- theoretically as fast as testing Mersennes of the same size.

[JeppeSN]

Good one!

Maybe it will be clear when the PRP Top entry becomes visible, but what types of PRP tests has this one "passed", as of now?

/JeppeSN

[axn]

Originally Posted by Batalov

It is almost the same, but operationally speaking, running single jobs is cleaner with LLR2. (Prime95 stays running forever after worktodo.txt is spent/empty, and needs to be killed, or source tampered with and recompiled - but that would only converge its evolution into a clone of LLR). Ryan prefers LLR. Currently trying the one with 30.6 gwnum as the engine.

LLR does the Prime95 computational trick since a few releases back - i.e. PRP-tests the (k*b^n+c)/e form using (k*b^n+c) transform, nor a general transform. With monic (k=1), c=-1, it is of course ridiculously fast compared to general form, -- theoretically as fast as testing Mersennes of the same size.

Cool.

BTW, mprime does have the ability to exit when out of work (conveniently called ExitWhenOutOfWork). Not sure if that was done for other platforms as well.

[Dr Sardonicus]

Originally Posted by Batalov

Kurt's site ascertains that region below 4300447 is finished.
We have not double-checked that region. We will check all eligible candidates in range 4,300,447 < p < 10,000,000 (or maybe less, -- whatever resources will allow).

If you click on an interval in the Details section on the page you link to, you get all the results - factors or PRP test residues.

It appears that there's a typo on the line with the big announcement:

10ˆ600000 . . . . . . R5794777 = PRP . . . . . . S. Batalov - Ryan Propper (Apr 2021)

I believe the exponent should be 6000000 rather than 600000.