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2014-06-14, 10:05   #23
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

52×229 Posts

Quote:
 Originally Posted by LaurV This equals (2^2^25-1)(2^2^25+1). Since when F25 is full factored?
Okay, maybe my mistake. I thought that 2ab-1 could be factored by (2a-1) x (1+2a+22a+23a+...+2(b-1)a)

Edit: So, nevermind I guess it is still easy to construct one with 2pq-1?

Last fiddled with by retina on 2014-06-14 at 10:09

2014-06-14, 16:40   #24
BudgieJane

"Jane Sullivan"
Jan 2011
Beckenham, UK

2·32·13 Posts

Quote:
 Originally Posted by Gordon Then there's that pesky thing called a dictionary probable   1. likely to occur or prove true 2. having more evidence for than against, or evidence that inclines the mind to belief but leaves some room for doubt. 3. affording ground for belief. So by definition, it is not completely factored.
Then there's that other pesky thing called a definition: A probable prime is defined as a number that has passed a probable prime test.

2014-06-14, 18:45   #25
Gordon

Nov 2008

7648 Posts

Quote:
 Originally Posted by BudgieJane Then there's that other pesky thing called a definition: A probable prime is defined as a number that has passed a probable prime test.
Yep, probable, see my previous dictionary definition.

This number is 100% NOT competely factored, you can dress it up however you want, but the facts don't lie.

 2014-06-14, 22:00 #26 alpertron     Aug 2002 Buenos Aires, Argentina 52A16 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 173528-digit pseudoprime is composite. What is your proof?
2014-06-14, 22:12   #27
Gordon

Nov 2008

50010 Posts

Quote:
 Originally Posted by alpertron 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 173528-digit pseudoprime is composite. What is your proof?
That's just it you see, I don't need proof of anything, I'm not the one making the unverifiable claim, remember your claim was

"...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...

 2014-06-15, 01:11 #28 MatWur-S530113     Apr 2007 Spessart/Germany 2·34 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 M-numbers knows, that a complete factorization of a M-number with an exponent ~500k will have one or more prp's involved. Simply compare the size of the largest proven prime cofactor of a M-number (I don't know the size, I think somewhere 1000-2000 bits) with the size of this M-number. 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
2014-06-15, 10:32   #29
Gordon

Nov 2008

22×53 Posts

Quote:
 Originally Posted by MatWur-S530113 [snip] that a complete factorization of a M-number with an exponent ~500k will have one or more prp's involved. Simply compare the size of the largest proven prime cofactor of a M-number (I don't know the size, I think somewhere 1000-2000 bits) with the size of this M-number. Do you expectet 500 factors with average size of ~1000 bits and all factors are proven as prime [snip]
Precisely the point, you believe with some degree of confidence that it is prime, it may well be, we'll probably never know in our lifetimes.

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

2014-06-15, 12:11   #30
axn

Jun 2003

13·192 Posts

Quote:
 Originally Posted by Gordon All you do know with 100% certainty is that it is NOT FACTORED COMPLETELY
Consider the two statements:

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?

2014-06-15, 13:49   #31
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

52·229 Posts

Quote:
 Originally Posted by Gordon All you do know with 100% certainty is that it is NOT FACTORED COMPLETELY
Actually we don't know that. It might be completely factored, or it might not. We have a high confidence that it is completely factored. But we can't say for certainty that it is not.

 2014-06-15, 17:06 #32 potonono     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.
2014-06-16, 17:47   #33
R.D. Silverman

Nov 2003

746010 Posts

Quote:
 Originally Posted by retina Actually we don't know that. It might be completely factored, or it might not. We have a high confidence that it is completely factored. But we can't say for certainty that it is not.
You are bandying words and undefined terminology.

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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