20210420, 21:28  #1 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9823_{10} Posts 
New repunit (PRP) primes found, 5794777 and 8177207 decimal digits (PRP records)
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 grmfaktc 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. 
20210420, 22:07  #2 
Sep 2002
Database er0rr
2^{5}·3·43 Posts 

20210420, 23:01  #3 
Jun 2003
Ottawa, Canada
3·17·23 Posts 
Nice, congrats.

20210421, 00:41  #4 
Feb 2017
Nowhere
3×5^{2}×7×11 Posts 
Wow, heck of a find! Not a whole lot of morethanmilliondecimaldigit 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. 
20210421, 01:12  #5 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
11×19×47 Posts 
Kurt's site ascertains that region below 4300447 is finished.
We have not doublechecked that region. We will check all eligible candidates in range 4,300,447 < p < 10,000,000 (or maybe less,  whatever resources will allow). 
20210421, 02:26  #6 
Jun 2003
23×233 Posts 

20210421, 03:00  #7 
Feb 2004
France
3^{2}·103 Posts 

20210421, 05:35  #8  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10011001011111_{2} Posts 
Quote:
LLR does the Prime95 computational trick since a few releases back  i.e. PRPtests 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. 

20210421, 07:16  #9 
"Jeppe"
Jan 2016
Denmark
10110000_{2} Posts 
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 
20210421, 08:08  #10  
Jun 2003
1010011101111_{2} Posts 
Quote:
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. 

20210421, 14:48  #11  
Feb 2017
Nowhere
1011010001111_{2} Posts 
Quote:
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. 

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