20210512, 09:57  #1 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2,207 Posts 
Discussion of definitions
I think it is important to distinguish (here) between known pseudoprime PRP's and ProbablyPrime PRP's. There is a known Carmichael numbers with much greater digits count.
https://www.mersenneforum.org/showpo...1&postcount=19 Last fiddled with by a1call on 20210512 at 10:27 
20210512, 10:20  #2  
Sep 2002
Database er0rr
F93_{16} Posts 
Quote:
Pseudoprimes are abbreviated to PSP. Last fiddled with by paulunderwood on 20210512 at 10:39 

20210512, 10:40  #3  
"Rashid Naimi"
Oct 2015
Remote to Here/There
4237_{8} Posts 
Quote:
Quote:
Accordingly, a pseudoprime (composite) can be categorized as a PRP with that definition. I still think a distinguishment is in order here. Last fiddled with by a1call on 20210512 at 11:00 

20210512, 13:02  #4  
Feb 2017
Nowhere
2·2,687 Posts 
Quote:
The name of the PariGP function ispseudoprime() has been publicly lamented elsewhere on this Forum precisely because it ignores the above distinction. Last fiddled with by Dr Sardonicus on 20210512 at 13:03 Reason: w 

20210512, 13:27  #5  
Jun 2015
Vallejo, CA/.
1,063 Posts 
Hello Dr Sardonicus. I just learned a new word in English, something that seldom happens. And it is a nice word too.
nu·ga·to·ry /ˈn(y)o͞oɡəˌtôrē/ adjective of no value or importance. "a nugatory and pointless observation" Quote:


20210512, 14:31  #6  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2,207 Posts 
@Dr Sardonicus,
I agree with your assessment that a probable prime should be defined clearly as an integer which passes some probableprimalitytest such as the Fermat test and is not known to be composite aka "ProbablePrime" and if it is known to be composite then it should not be referred to as a ProbablePrime but rather a PseudoPrime. However, The definition of a ProbablePrime (PRP) is vague/imprecise at the moment as indicated by my admittedly superficial internet search: Quote:
Quote:
I even seem to recall that that (or some other Wikipedia article on the subject) indicating (Not the current version) that the term PseudoPrime & ProbablePrime were at some point interchangeable (used by some authors) and since have been distinguished by more recent authors. 

20210512, 19:56  #7  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2,207 Posts 
Quote:
Congrats to both of you gentlemen. You have my outmost respect, please be assured of that. 

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