- **Data**
(*https://www.mersenneforum.org/forumdisplay.php?f=21*)

- - **Mersenne number factored (disbelievers are biting elbows)**
(*https://www.mersenneforum.org/showthread.php?t=19407*)

[QUOTE=wblipp;376029]Yes, I'm really having trouble with this. My problem is that I am not at all concerned with anyone claiming that it is complete. My problem is that I am concerned with someone claiming that it is incomplete.
[/QUOTE] What you are concerned with is irrelevant. We do not know that the factorization is complete. This is a fact. The probable prime may not be prime. Do you understand that "not complete" means "incomplete"?? Why is this so hard for you? [QUOTE] And I think that you have claimed that the factorization is incomplete. I'll lay out my logic is excruciating detail. [/QUOTE] It isn't logic. It is simple bandying of words. [QUOTE] I think you have made the much stonger assertion that the factorization in known to be incomplete. [/QUOTE] What "much stronger assertion"?? Your claim is idiotic. We do not have a complete factorization into primes until we have a set of integers whose product equals the original number and each integer in our set is prime. We do not have that!!!!! Therefore we do not have a complete factorization. Therefore it is incomplete BY THE DEFINITION OF INCOMPLETE. [QUOTE] Because of #3, your assertion in #4 is equivalent to asserting the known factorization is NOT a factorization into primes. [/QUOTE] This is a correct assertion. We have a factorization into SOME primes, plus a number that may or may not be prime. PRIME does NOT equal PROBABLE PRIME. We do not have a factorization into primes, since we do not know if the ultimate factor is prime. |

[QUOTE=R.D. Silverman;376047]What you are concerned with is irrelevant. We do not know that
the factorization is complete. This is a fact. The probable prime may not be prime. Do you understand that "not complete" means "incomplete"?? Why is this so hard for you?[/QUOTE] The confusion seems straightforward: the claims "the factorization is known to be incomplete" and "the factorization is not known to be complete" have been confounded. The latter is correct, while the former is incorrect. |

[QUOTE=CRGreathouse;376049]The confusion seems straightforward: the claims "the factorization is known to be incomplete" and "the factorization is not known to be complete" have been confounded. The latter is correct, while the former is incorrect.[/QUOTE]
Does "incomplete factorization" mean: "known to have more prime factors than is currently known" (i.e. the factorization is known to be incomplete) [your first phrase] or "may have more prime factors than is currently known". I argue the latter. A factorization is complete when we know all of its prime factors. It a number might have additional unknown prime factors than what is already known, then it must be considered incomplete. |

[QUOTE=R.D. Silverman;376047]We have a factorization into SOME primes, plus a number that may or may not be prime.[/QUOTE]
Isn't this the same as [INDENT][B]We have a factorization that may or may not be a factorization into primes [/B][/INDENT] Isn't that the same as[INDENT][B]We have a factorization that may or not be a complete factorization[/B][/INDENT] Isn't that the same as[INDENT][B]The number may or may not be completely factored[/B][/INDENT] And doesn't that make the following assertion [B]unproven[/B]?[INDENT][B]The number is not completely factored[/B][/INDENT] |

[QUOTE=wblipp;376056][INDENT][B]The number is not completely factored[/B][/INDENT][/QUOTE]
Parsing this sentence is like parsing "[URL="http://en.wikipedia.org/wiki/Syntactic_ambiguity"]Eduardum occidere nolite timere bonum est[/URL]." (А Рussian textbook example sentence is "[URL="http://ru.wikipedia.org/wiki/Казнить_нельзя_помиловать"]Казнить нельзя помиловать[/URL].") One person will see [I]potatoe[/I]: {The number} is {not completely} {factored} and another will see [I]potahto[/I]: {The number} is not {completely factored} |

[QUOTE=R.D. Silverman;376055]I argue the latter. A factorization is complete when we know all of its prime factors. It a number might have additional unknown prime factors than what is already known, then it must be considered incomplete.[/QUOTE]
That's not what your definition of "completely factored" says. This changes your definition in the manner I suggested you might have in mind very early in this exchange. All I've been doing is showing that, BY YOUR DEFINITION, you CANNOT prove the number is not completely factored. Apparently you have been working off your intuition instead your definition. |

[QUOTE=R.D. Silverman;376055]A factorization is complete when we know all of its prime factors. It a number might have additional unknown prime factors
than what is already known, then it must be considered incomplete.[/QUOTE] Perhaps you mean to say "A factorization is complete when we know that we know all of its prime factors." For the case under consideration, it is likely that that the factors we know are all the prime factors. The extra level of "know" is necessary if we want to move from "it is not known to be completely factored" to "it is not completely factored." |

[QUOTE=wblipp;376060]Perhaps you mean to say "A factorization is complete when we know that we know all of its prime factors."
For the case under consideration, it is likely that that the factors we know are all the prime factors. The extra level of "know" is necessary if we want to move from "it is not known to be completely factored" to "it is not completely factored."[/QUOTE] You are losing sight of the fact that the [U]original claim[/U] was this number is [I]COMPLETELY FACTORED[/I], which we now all seem to accept we don't know, [B][U]therefore the original claim is FALSE[/U][/B]. Why? The opposite of true is always false, it is binary, it's one or the other. Until proven true it's false. It's not that difficult. |

[QUOTE=R.D. Silverman;376055]Does "incomplete factorization" mean[/QUOTE]
Indeed, this is the ambiguity to which I referred. |

[QUOTE=Gordon;376062]You are losing sight of the fact that the [U]original claim[/U] was this number is [I]COMPLETELY FACTORED[/I], which we now all seem to accept we don't know, [B][U]therefore the original claim is FALSE[/U][/B].
Why? The opposite of true is always false, it is binary, it's one or the other. Until proven true it's false. It's not that difficult.[/QUOTE] because you made a claim that you knew 100% that it was not completely factored. which in theory means you know it to be composite, because you know all the PRP's factors is off the table if it is indeed composite, Because, this means you know the full factorization of the number originally talked about. Your turn to prove it can not be a prime. |

[QUOTE=Gordon;376062]Until proven true it's false. It's not that difficult.[/QUOTE]
Until a statement is proven false it might still be true. Or its state may be unknown. |

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