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2018-06-11, 07:21   #12
kar_bon

Mar 2006
Germany

B2416 Posts

Quote:
 Originally Posted by sweety439 [...], for b=293, I found no prime, it is likely tested to at least n=5000.
"almost"..."likely".... very mathematically!

18*293^4019+1 is prime! (9916 decimal digits)

 2020-07-02, 03:31 #13 sweety439     Nov 2016 46578 Posts Some first primes for these (k,b) pairs: 25*30^34205-1 29*32^1745576-1 (3-PRP, but not prime) 27*34^3086-1 37*38^136211-1
2020-07-02, 08:34   #14
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

23C416 Posts

Quote:
 Originally Posted by sweety439 ... 29*32^1745576-1 (3-PRP, but not prime)
Really, not prime? What is it? a composite? Or impossible to prove?

2020-07-02, 09:52   #15
sweety439

Nov 2016

37×67 Posts

Quote:
 Originally Posted by Batalov Really, not prime? What is it? a composite? Or impossible to prove?
This is a strong PRP base 3.

2020-07-02, 13:26   #16
kruoli

"Oliver"
Sep 2017
Porta Westfalica, DE

367 Posts

Quote:
 Originally Posted by Batalov Really, not prime? What is it? a composite? Or impossible to prove?
29*2^8727880-1 is not prime. LLR Res64: 0B55843E108EED8C Time : 9786.482 sec.

(32^1745576 = 2^8727880)

2020-07-02, 15:07   #17
kruoli

"Oliver"
Sep 2017
Porta Westfalica, DE

367 Posts

Quote:
 Originally Posted by sweety439 This is a strong PRP base 3.
Hm... Prime95 disagrees.

Code:
{
"status":"C",
"k":29,
"b":32,
"n":1745576,
"c":-1,
"worktype":"PRP-3",
"res64":"9D673329E37E4DFD",
"residue-type":1,
"fft-length":655360,
"error-code":"00000000",
"security-code":"DC6B3999",
"program":
{
"name":"Prime95",
"version":"29.8",
"build":6,
"port":4
},
"timestamp":"2020-07-02 15:04:16"
}

2020-07-02, 17:07   #18
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

23C416 Posts

Quote:
 Originally Posted by sweety439 This is a strong PRP base 3.
Or there is an alternative explanation - you have some unstable computer(s).
And now all of your results are suspect.

2020-07-02, 17:55   #19
paulunderwood

Sep 2002
Database er0rr

23×19×23 Posts

Quote:
 Originally Posted by sweety439 29*32^1745576-1 (3-PRP, but not prime)

 2020-07-03, 08:29 #20 kruoli     "Oliver" Sep 2017 Porta Westfalica, DE 16F16 Posts On my end, LLR 3.8.23 (for the Lucas-Lehmer-Riesel test, since $$k \cdot 32^n - 1 = k \cdot 2^{5n} - 1$$) and Prime95 29.8b6 for the 3-PRP test. Just for the records.
2020-07-03, 17:22   #21
carpetpool

"Sam"
Nov 2016

2·3·53 Posts

Quote:
 Originally Posted by sweety439 This is a strong PRP base 3.

I also did a test with PFGW to verify weather this number was a 3-PRP, or even 3-SPRP or not:

>pfgw64 -q"29*32^1745576-1"
PFGW Version 4.0.0.64BIT.20190528.Win_Dev [GWNUM 29.8]

29*32^1745576-1 is composite: RES64: [9D673329E37E4DFD] (21103.6482s+0.0182s)
>

Like everyone else whose wondering, why did you think this number was 3-SPRP? (PFGW does 3-PRP by default). Both PFGW and LLR are saying this number fails a 3-PRP test, so it cannot be a 3-SPRP either.

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