[QUOTE=R.D. Silverman;375973]You are bandying words and undefined terminology.
[/QUOTE] what's being pointed out is that without knowing if the PRP is prime or not, we can not know with 100% certainty that it is not completely factored Gordon made that claim. As did you by saying [QUOTE]Since the number in question has not been represented as the product of primes, then it most definitely has NOT been completely factored.[/QUOTE] I would replace primes with known primes otherwise you're claiming you know that a 173000 + digit number isn't prime. edit: I just realized you could use modular arithmetic to limit what it is and if the factorization fits the required number of each remainder. maybe that'll lead me to your logic. 
[QUOTE=R.D. Silverman;375973]the number in question has not been represented as the product of primes[/QUOTE]
Can you prove this statement? I thought a number was prime or not prime independent of our ability to prove that. The number has been represented as a product. It's possible that it is a product of primes, so it's possible the number has been completely factored. 
[QUOTE=wblipp;375983]Can you prove this statement?
[/QUOTE] What drugs are you on? The number has been represented as the product of SOME primes and a single large PROBABLE PRIME. It is *conjectured* that it is the product of primes. Perhaps you need to learn what a conjecture is?? 
[QUOTE=R.D. Silverman;375984]Perhaps you need to learn what a conjecture is??[/QUOTE]
Perhaps you need to get out more.... 
[QUOTE=potonono;375900]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.[/QUOTE]
Well said! (Possibly, I think, maybe.) :smile: 
[QUOTE=science_man_88;375974]I just realized you could use modular arithmetic to limit what it is and if the factorization fits the required number of each remainder. maybe that'll lead me to your logic.[/QUOTE]
Each reindeer, did you say? 
[QUOTE=chalsall;375986]Perhaps you need to get out more....[/QUOTE]
Can we cease with the contentless needling of forum members? 
[QUOTE=Prime95;375996]Can we cease with the contentless needling of forum members?[/QUOTE]Probably not.

[QUOTE=R.D. Silverman;375984]What drugs are you on?[/QUOTE]
Allopurinol. Baby aspirin. I'm supposed to be taking Simvastatin, but my gout won't tolerate it. I don't think any of these affect my mathematical reasoning. Let's see if we can figure out what you are trying to say, and where our disagreement. We all agree that: [QUOTE=R.D. Silverman;375984]The number has been represented as the product of SOME primes and a single large PROBABLE PRIME.[/Quote] We all agree that [QUOTE]It is *conjectured* that it is the product of primes.[/QUOTE] We have all accepted your definition [QUOTE]A number is completely factored when it is represented as the product of primes.[/QUOTE] Where we appear to separate is your statement that: [QUOTE]the number in question has not been represented as the product of primes[/QUOTE] I don't see how you can possibly know that. The given representation is either a product of primes, or it isn't, entirely independent of our ability to prove that. Hence it is a complete factorization or it is not, independent of our ability to prove it. Your definition of "completely factored" does NOT require the proof of the primes. Nobody here can PROVE the given factorization is complete  and I don't think anybody has claimed that recently in the thread. But it is also true the nobody here can PROVE the given factorization is incomplete  yet you have asserted that this true. If you disagree, please try to explain why. 
Perhaps Bob MEANT to give this definition:
A number is completely factored when it is proven to be represented as the product of primes. Everything he said would have made sense if "is proven" had been included in his definition of "fully factored." 
[QUOTE=wblipp;376003]I don't see how you can possibly know that. The given representation is either a product of primes, or it isn't, entirely independent of our ability to prove that. Hence it is a complete factorization or it is not, independent of our ability to prove it. Your definition of "completely factored" does NOT require the proof of the primes. Nobody here can PROVE the given factorization is complete  and I don't think anybody has claimed that recently in the thread.
But it is also true the nobody here can PROVE the given factorization is incomplete  yet you have asserted that this true. If you disagree, please try to explain why.[/QUOTE] We don't have to prove that it is incomplete. Anyone claiming that it is complete must do so. You are really having trouble with this. The SET of primes is a strict SUBSET of the set of probable primes. A prime is a probable prime. The converse is not true in general. You can not assert that a number is the product of primes when all we know is that it is the product of some primes and an integer that may or may not be prime. Asserting that the number is a product of primes is a CONJECTURE. We have good evidence that the conjecture is correct, but we do not know it to be true. 
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