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

[MrRepunit]

mprime check confirmed that it is a prime:
[Work thread Apr 22 02:26] (10^5794777-1)/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, "known-factors":["9"], "worktype":"PRP-3", "fft-length":1146880, "error-code":"00000000", "security-code":"FCA5F7FA", "program":{"name":"Prime95", "version":"30.5", "build":2, "port":8}, "timestamp":"2021-04-22 00:26:59"}

[paulunderwood]

Originally Posted by paulunderwood

I am currently testing it for Lucas over x^2-4*x+1

It failed. I am rerunning with 3 FFT sizes bigger. ETA 3 days.

[rudy235]

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.

[paulunderwood]

Originally Posted by rudy235

I can only hope that in the next 14 years someone proves R49081 to be a prime.

I am 10.5 months into certification -- I now guess it will be done by Christmas

[rudy235]

Originally Posted by paulunderwood

I am 10.5 months into certification -- I now guess it will be done by Christmas

That is so cool! How are you going about it?

[paulunderwood]

Originally Posted by rudy235

That is so cool! How are you going about it?

Primo on a 3990X 24/7.

[Dr Sardonicus]

Originally Posted by paulunderwood

I am 10.5 months into certification -- I now guess it will be done by Christmas

I was wondering whether anyone was trying to prove it prime. I decided getting enough factors of N-1 was probably hopeless, but that Primo had an outside chance, but it might take a long time. IIRC, if successful it would more than double^† the number of decimal digits for the largest number proved prime by Primo.

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 prime-prover in the present instance.

[paulunderwood]

R5794777 is "officially" the top PRP.

[paulunderwood]

I have had 3 failed Lucas tests (x^2-4*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?

[Batalov]

... and Frobenuis, too!

Yes. Several trifectas obtained. (a = 3, 7, 11 and 17.)

[paulunderwood]

Originally Posted by Batalov

... and Frobenuis, too!

Yes. Several trifectas obtained. (a = 3, 7, 11 and 17.)

Thanks. I give up on running generic mod reduction. It would be better to spend a few hours writing slow intro and outro into my code.