20180611, 07:21  #12 
Mar 2006
Germany
B24_{16} Posts 

20200702, 03:31  #13 
Nov 2016
4657_{8} Posts 
Some first primes for these (k,b) pairs:
25*30^342051 29*32^17455761 (3PRP, but not prime) 27*34^30861 37*38^1362111 
20200702, 08:34  #14 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
23C4_{16} Posts 

20200702, 09:52  #15 
Nov 2016
37×67 Posts 

20200702, 13:26  #16 
"Oliver"
Sep 2017
Porta Westfalica, DE
367 Posts 

20200702, 15:07  #17 
"Oliver"
Sep 2017
Porta Westfalica, DE
367 Posts 
Hm... Prime95 disagrees.
Code:
{ "status":"C", "k":29, "b":32, "n":1745576, "c":1, "worktype":"PRP3", "res64":"9D673329E37E4DFD", "residuetype":1, "res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fftlength":655360, "errorcode":"00000000", "securitycode":"DC6B3999", "program": { "name":"Prime95", "version":"29.8", "build":6, "port":4 }, "timestamp":"20200702 15:04:16" } 
20200702, 17:07  #18 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
23C4_{16} Posts 

20200702, 17:55  #19 
Sep 2002
Database er0rr
2^{3}×19×23 Posts 

20200703, 08:29  #20 
"Oliver"
Sep 2017
Porta Westfalica, DE
16F_{16} Posts 
On my end, LLR 3.8.23 (for the LucasLehmerRiesel test, since \(k \cdot 32^n  1 = k \cdot 2^{5n}  1\)) and Prime95 29.8b6 for the 3PRP test. Just for the records.

20200703, 17:22  #21 
"Sam"
Nov 2016
2·3·53 Posts 
I also did a test with PFGW to verify weather this number was a 3PRP, or even 3SPRP or not: >pfgw64 q"29*32^17455761" PFGW Version 4.0.0.64BIT.20190528.Win_Dev [GWNUM 29.8] 29*32^17455761 is composite: RES64: [9D673329E37E4DFD] (21103.6482s+0.0182s) > Like everyone else whose wondering, why did you think this number was 3SPRP? (PFGW does 3PRP by default). Both PFGW and LLR are saying this number fails a 3PRP test, so it cannot be a 3SPRP either. 
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