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Old 2018-06-11, 07:21   #12
kar_bon
 
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Quote:
Originally Posted by sweety439 View Post
[...], 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)
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Old 2020-07-02, 03:31   #13
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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
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Old 2020-07-02, 08:34   #14
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Quote:
Originally Posted by sweety439 View Post
...
29*32^1745576-1 (3-PRP, but not prime)
Really, not prime? What is it? a composite? Or impossible to prove?
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Old 2020-07-02, 09:52   #15
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Quote:
Originally Posted by Batalov View Post
Really, not prime? What is it? a composite? Or impossible to prove?
This is a strong PRP base 3.
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Old 2020-07-02, 13:26   #16
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Quote:
Originally Posted by Batalov View Post
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)
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Old 2020-07-02, 15:07   #17
kruoli
 
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Quote:
Originally Posted by sweety439 View Post
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,
  "res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
  "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"
}
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Old 2020-07-02, 17:07   #18
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Quote:
Originally Posted by sweety439 View Post
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.
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Old 2020-07-02, 17:55   #19
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Quote:
Originally Posted by sweety439 View Post
29*32^1745576-1 (3-PRP, but not prime)
How was this ~2,600,000 digit number tested?
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Old 2020-07-03, 08:29   #20
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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.
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Old 2020-07-03, 17:22   #21
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Quote:
Originally Posted by sweety439 View Post
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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