20140614, 10:05  #23  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
5^{2}×229 Posts 
Quote:
Edit: So, nevermind I guess it is still easy to construct one with 2^{pq}1? Last fiddled with by retina on 20140614 at 10:09 

20140614, 16:40  #24  
"Jane Sullivan"
Jan 2011
Beckenham, UK
2·3^{2}·13 Posts 
Quote:


20140614, 18:45  #25  
Nov 2008
764_{8} Posts 
Quote:
This number is 100% NOT competely factored, you can dress it up however you want, but the facts don't lie. 

20140614, 22:00  #26 
Aug 2002
Buenos Aires, Argentina
52A_{16} Posts 
Well, if you want me to be completely pedantic, if you know that the Mersenne number shown is not 100% completely factored, that means that the 173528digit pseudoprime is composite. What is your proof?

20140614, 22:12  #27  
Nov 2008
500_{10} Posts 
Quote:
"...completely factorized" So for that to be true there can be no PRP rubbish spouted, show all the factors else you are making a false and misleading claim. Amazing how many people on here struggle with simple English and seem to believe that Probable == Definitively It doesn't... 

20140615, 01:11  #28 
Apr 2007
Spessart/Germany
2·3^{4} Posts 
Congratz Dario, nice found. Your prp is now listet as #6 of Henri Lifchitz's page of Mersenne cofactors:
http://www.primenumbers.net/prptop/s...&action=Search @Gordon: maybe an expression like '(prp)completet' is more accurate, but everyone who is interestet in factoring such large Mnumbers knows, that a complete factorization of a Mnumber with an exponent ~500k will have one or more prp's involved. Simply compare the size of the largest proven prime cofactor of a Mnumber (I don't know the size, I think somewhere 10002000 bits) with the size of this Mnumber. Do you expectet 500 factors with average size of ~1000 bits and all factors are proven as prime (with primo or so)? And the complete thread is talking about "looking for prp's". See f.e.: http://www.mersenne.ca/prp.php?show=...ponent=1000000 Dario's prp is already included mfg Matthias 
20140615, 10:32  #29  
Nov 2008
2^{2}×5^{3} Posts 
Quote:
All you do know with 100% certainty is that it is NOT FACTORED COMPLETELY I am reminded of this famous quote “The less people know, the more stubbornly they know it.” Osho 

20140615, 12:11  #30  
Jun 2003
13·19^{2} Posts 
Quote:
A: We do NOT know with 100% certainty that it is factored completely. B: We do know with 100% certainty that it is NOT factored completely. Do you believe these two to be identical? 

20140615, 13:49  #31 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
5^{2}·229 Posts 

20140615, 17:06  #32 
Jun 2005
USA, IL
193 Posts 
I possibly more or less but not definitely rejected the idea that there is in no way any amount of uncertainty that I undeniably do or do not know that it is completely factored.

20140616, 17:47  #33  
Nov 2003
7460_{10} Posts 
Quote:
Start by defining "completely factored". My definition would be: A number is completely factored when it is represented as the product of primes. Since the number in question has not been represented as the product of primes, then it most definitely has NOT been completely factored. 

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