Timeline for What is wrong with this counterexample to primality test assuming GRH? [closed]
Current License: CC BY-SA 3.0
32 events
| when toggle format | what | by | license | comment | |
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| Sep 28, 2015 at 7:50 | vote | accept | joro | ||
| Sep 23, 2015 at 14:13 | comment | added | Felipe Voloch | @joro You objected that I both answered and voted to close. Although I disagree that I can't do both, I decided to respect your wishes. Since I stand by my vote to close, I deleted my answer. | |
| Sep 23, 2015 at 13:41 | comment | added | joro | @ToddTrimble Thanks, just to make sure my last edit of the question makes sense. | |
| Sep 23, 2015 at 13:27 | comment | added | Todd Trimble | Yes, he answered, and then deleted the answer a short time ago. | |
| Sep 23, 2015 at 13:24 | comment | added | joro | @ToddTrimble I believe Voloch answered this question and then deleted the answer, would someone 10K+ confirm this? | |
| Sep 23, 2015 at 13:10 | comment | added | Todd Trimble | I've had to delete two comments from this thread that were flagged as rude/offensive. May I please ask commenters to refrain from getting too personal. | |
| Sep 23, 2015 at 13:04 | review | Reopen votes | |||
| Sep 23, 2015 at 13:34 | |||||
| Sep 23, 2015 at 12:46 | history | edited | joro | CC BY-SA 3.0 |
on meta [Is it frowned upon to answer a question and vote to close?]
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| Sep 23, 2015 at 10:50 | history | closed |
Felipe Voloch Lucia Boris Bukh Jeremy Rouse Emil Jeřábek |
Not suitable for this site | |
| Sep 22, 2015 at 13:27 | comment | added | joro | @Lucia Do you mean I should not read very literally? Like switching inequalities? | |
| Sep 22, 2015 at 10:58 | comment | added | GH from MO | @quid: You are right. I meant "by votes to close" instead of "by downvotes". | |
| Sep 22, 2015 at 10:08 | comment | added | user9072 | @GHfromMO One cannot close a question by down-votes. Closing and up/downvoting are completely unrelated. | |
| Sep 21, 2015 at 21:36 | comment | added | GH from MO | Please do not close this question by downvotes, because my answer contains useful information (I hope). | |
| Sep 21, 2015 at 19:17 | comment | added | Lucia | This question is based on reading very literally a carelessly worded sentence from a paper. There is already a good answer pointing out what was intended. The particular questions raised here do not strike me as showing much "research effort." Therefore I am voting to close this. | |
| Sep 21, 2015 at 18:30 | review | Close votes | |||
| Sep 23, 2015 at 10:55 | |||||
| Sep 21, 2015 at 18:20 | comment | added | GH from MO | @joro: If you read Granville's paragraph carefully, you will see that the part in parentheses is irrelevant for testing the square-freeness of $n$. That is, the statement in the first line is correct (without GRH), and its full proof is given in the paragraph. | |
| Sep 21, 2015 at 16:11 | answer | added | GH from MO | timeline score: 14 | |
| Sep 21, 2015 at 15:44 | comment | added | joro | @GHfromMO Don't mind it closed at all, vote as you wish. What is a reference for a correct statement of the claim? | |
| Sep 21, 2015 at 15:32 | comment | added | GH from MO | @joro: As Felipe said, Granville made a silly mistake. He is an expert on Carmichael numbers, but he is also human (errare humanum est). This question should be closed. | |
| Sep 21, 2015 at 13:48 | comment | added | joro | @quid Might be wrong, but the bold title 2j. Lenstra’s polynomial time test as to whether an integer that is conjecturally prime suggests to me so. | |
| Sep 21, 2015 at 13:36 | comment | added | user9072 | I do not quite understand; as far as I can see; the parenthetical remark is not part of the description or verification of Lenstra's algorithm. | |
| Sep 21, 2015 at 11:12 | comment | added | joro | @quid Thanks. I think the question matches the paper. Granville might give "interpretation" of Lenstra algorithm. | |
| Sep 21, 2015 at 10:52 | comment | added | user9072 | To me he does not appear to quote Lenstra, the way I read it is just a side-remark (that might be imprecise). | |
| Sep 21, 2015 at 10:38 | history | edited | joro | CC BY-SA 3.0 |
minor additions
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| Sep 21, 2015 at 10:35 | comment | added | joro | @FelipeVoloch No problem spamming Granville, but what to ask him (except reference)? He quotes Lenstra, not Bach. | |
| Sep 21, 2015 at 9:38 | comment | added | Felipe Voloch | Bach's theorem says that (under GRH) if $G$ is a proper subgroup of $(\mathbb{Z}/n)^*$, there exists $a \notin G, 1 < a \le 2(\log n)^2$. If $n$ is not Carmichael $a^{n-1} \equiv 1 \pmod n$ is a proper subgroup. If you don't like that, you can use $a^{(n-1)/2}(a|n) \equiv 1 \pmod n$ (Solovay-Stassen) or complain to Granville for making a silly mistake. | |
| Sep 21, 2015 at 9:33 | comment | added | joro | Granville have hypothesis $n > 32$, not sure if this applies for the rest. | |
| Sep 21, 2015 at 9:29 | comment | added | joro | @FelipeVoloch If you don't want n to be Carmichael number then this shouldn't be called primality test IMHO. | |
| Sep 21, 2015 at 9:27 | comment | added | joro | @FelipeVoloch According to the conjecture about prime triplets, there are infinitely many triplets of this kind, so n can be arbitrary large. Thanks for the link. | |
| Sep 21, 2015 at 9:24 | comment | added | Felipe Voloch | Maybe you don't want $n$ to be a Carmichael number either. | |
| Sep 21, 2015 at 9:17 | comment | added | Felipe Voloch | I don't know what the issue is but here is the source of these types of bounds. Maybe there is some hypothesis, like n has to be sufficiently large. ams.org/journals/mcom/1990-55-191/S0025-5718-1990-1023756-8 | |
| Sep 21, 2015 at 9:01 | history | asked | joro | CC BY-SA 3.0 |