20210422, 04:51  #23 
Mar 2011
Germany
97 Posts 
mprime check confirmed that it is a prime:
[Work thread Apr 22 02:26] (10^57947771)/9 is a probable prime! Wh8: FCA5F7FA,00000000 [Thu Apr 22 02:26:59 2021] {"status":"P", "k":1, "b":10, "n":5794777, "c":1, "knownfactors":["9"], "worktype":"PRP3", "fftlength":1146880, "errorcode":"00000000", "securitycode":"FCA5F7FA", "program":{"name":"Prime95", "version":"30.5", "build":2, "port":8}, "timestamp":"20210422 00:26:59"} 
20210422, 18:15  #24 
Sep 2002
Database er0rr
3×1,451 Posts 

20210422, 18:41  #25 
Jun 2015
Vallejo, CA/.
2^{4}·71 Posts 
Sergei and Ryan: Congratulations to both of you! This is an incredible achievement!
We now have 4 proven repunits and 5 PRP This one took almost 14 years to come to light. I can only hope that in the next 14 years someone proves R49081 to be a prime. 
20210422, 18:45  #26 
Sep 2002
Database er0rr
1101_{16} Posts 

20210422, 18:53  #27 
Jun 2015
Vallejo, CA/.
2^{4}·71 Posts 

20210422, 18:55  #28 
Sep 2002
Database er0rr
4353_{10} Posts 

20210423, 00:47  #29  
Feb 2017
Nowhere
3^{2}×677 Posts 
Quote:
Best of luck, brave Sir! EDIT: ^{†}If I'd bothered checking my own post here which I was incorrectly remembering, I would have seen Partition(1289844341) which is 40000 decimal digits (not 20000) was the largest number proved prime by Primo, and by our intrepid primeprover in the present instance. Last fiddled with by Dr Sardonicus on 20210423 at 01:21 

20210427, 17:17  #31 
Sep 2002
Database er0rr
4353_{10} Posts 
I have had 3 failed Lucas tests (x^24*x+1) at increasing FFT sizes for R5794777. All used the special mod reduction, but no slow/safe iterations at the beginning and end. I am now trying general mod reduction with an increase in FFT size of 6, but this will take weeks.
Serge, have you completed any tests with a Lucas component yet? 
20210427, 23:21  #32 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×4,993 Posts 
... and Frobenuis, too!
Yes. Several trifectas obtained. (a = 3, 7, 11 and 17.) 
20210427, 23:41  #33 
Sep 2002
Database er0rr
3×1,451 Posts 

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