20190317, 18:08  #1 
"Luke Richards"
Jan 2018
Birmingham, UK
120_{16} Posts 
PRP test largely on input number
Hi,
It's been ages since I devoted some attention to prime numbers. After a year or so since I came to accept that the cause was hopeless, I'm now wondering again about factoring 3^{504206}+1, having discovered last March that 3^{504206}+2 is a PRP. Thanks to some people on here, I found some factors of 3^{504206}+1. Some smallish ones are known to be composite, but there is this one here: http://factordb.com/index.php?id=1100000001124718606 Which is of unknown status. If it is composite, fine. If its a PRP, I could then dedicate some time to trying to prove its primality, thus prove the primality of my original PRP. Any suggestions on suitable software for PRPtesting the large factor linked above? LLR won't allow such a complicated input. 
20190317, 18:46  #2 
"Rashid Naimi"
Oct 2015
Remote to Here/There
3·641 Posts 
Congratulations!
according to PFGW: Code:
.....3315861 is 3PRP! (1388.4907s+0.6161s) 
20190317, 18:56  #3  
Sep 2003
29·89 Posts 
Quote:
Note, you have to choose a PRP base other than 3, since that will give you a false positive here. You could choose 2 or 5, for instance: Code:
./pfgw64 b5 help Enter expression followed by carriage return: (3^504206+1)*(3^226+1)*(3^194+1)*(3^46+1)/(3^21922+1)/(3^5198+1)/(3^4462+1)/628417430425585476026210 PFGW Version 3.8.3.64BIT.20161203.x86_Dev [GWNUM 28.6] (3^504206+1)*(3^....0425585476026210 is composite: RES64: [07271415C222E58C] (780.3876s+0.0099s) 

20190317, 19:02  #4  
"Luke Richards"
Jan 2018
Birmingham, UK
2^{5}×3^{2} Posts 
Quote:
Well, quite. I am aware of this. But in a series of highly improbable possibilities, if this had been PRP I'd have subtracted 1 from it and attempted to factor that number, in the hope that I would then get some large PRP factor, and so on. Not likely, but worth spending an hour or two looking into. Thanks to both of you for running it in PFGW. Are you running OpenPFGW? 

20190317, 19:11  #5 
Sep 2003
29×89 Posts 
I am running pfgw64 from pfgw_linux_3.8.3_20170121.zip
I don't recall where I downloaded it, but based on this forum thread, it probably did come from the OpenPFGW archive at sourceforge 
20190317, 19:24  #6 
"Rashid Naimi"
Oct 2015
Remote to Here/There
11110000011_{2} Posts 
I stand corrected. In base 5:
Code:
....36795483315861 is composite: RES64: [07271415C222E58C] (1229.6702s+0.6114s) https://sourceforge.net/projects/openpfgw/ Last fiddled with by a1call on 20190317 at 19:24 
20190317, 22:32  #7  
"Luke Richards"
Jan 2018
Birmingham, UK
120_{16} Posts 
Quote:
When I try the same input, I get: Code:
Illegal instruction (core dumped) Any idea what I'm doing wrong? 

20190317, 22:42  #8  
"William"
May 2003
New Haven
924_{16} Posts 
Quote:


20190318, 02:45  #9  
Jun 2003
11144_{8} Posts 
Quote:
3^504205+1 does have a few algebraic factors, but not nearly as many as the other one. 

20190318, 03:50  #10 
Sep 2003
2581_{10} Posts 

20190318, 06:14  #11 
"Luke Richards"
Jan 2018
Birmingham, UK
2^{5}·3^{2} Posts 

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