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2d
comment When has the Borel-Cantelli heuristic been wrong?
@user, I missed that --- but it seems to me that the result you cite depends on the primality of numbers like $2^{9092392}+40291$, and that those numbers have been shown to be probable primes, but have not been proved to be primes. E.g., en.wikipedia.org/wiki/Megaprime cites this number as a probable prime, but not as a prime.
2d
comment When has the Borel-Cantelli heuristic been wrong?
The work to decide whether 78557 is the smallest such $n$ continues, seventeenorbust.com
Apr
14
comment Characterizing Posets by Functions Into Natural Numbers
Bibliographical details: Novotný, Miroslav, Über gewisse Eigenschaften von Kardinaloperationen, Spisy Přírod. Fak. Univ. Brno 1960 1960 465–484, MR0133241 (24 #A3075).
Apr
14
revised Open problems in Euclidean geometry?
edited tags
Apr
14
revised Which math paper maximizes the ratio (importance)/(length)?
edited tags
Apr
13
revised Fundamental Examples
typos
Apr
13
revised Rediscovery of lost mathematics
edited tags
Apr
13
comment Equivalence of Polignac to finite Goldbach?
I'm not sure which Dickson and/or Hardy-Littlewood conjectures have Goldbach as a special case. I don't even see how Schinel's Hypothesis H implies Goldbach.
Apr
13
comment A question about summation formula involving binomial coefficient
Each of your formulas has both $N$ and $n$ in it. Is that what you mean to write?
Apr
11
comment Has this strong number theoretic conjecture of Euler been proved, and where could I find such a proof?
Search for "Euler's pentagonal number formula".
Apr
11
comment Has this strong number theoretic conjecture of Euler been proved, and where could I find such a proof?
I'm pretty sure Euler proved that formula. See math.stackexchange.com/questions/189157/… for some references.
Apr
10
comment Most interesting mathematics mistake?
@Todd, it certainly isn't easy. To the best of my knowledge, the density of that sequence is still an open question.
Apr
10
comment Axiom of choice for sets of finite sets
May I suggest, Mathieu, that after you have digested the Truss paper, that you return to post a summary here?
Apr
10
comment Notation for $\log \log \cdots \log n$?
As I have mentioned (twice!), people in analytic number theory explain what they mean with their choice of notation.
Apr
10
comment Notation for $\log \log \cdots \log n$?
@Mirko, I think the dynamical system given by the logarithm is not very interesting. I doubt there is a paper in the dynamical systems literature where anyone has used a 4-times iterated logarithm.
Apr
10
comment Notation for $\log \log \cdots \log n$?
@Marc, I think the part of humanity that has a use for logarithms-to-the-base-4 is disjoint from the part of humanity that has a use for $\log\log\log\log x$, so using $\log_4x$ for the latter isn't likely to even come to the attention of anyone who would have expected the former. And, as I mentioned, the convention is to explain the notation immediately upon first using it, so no one will be confused for long.
Apr
10
revised Notation for $\log \log \cdots \log n$?
added 146 characters in body
Apr
10
comment Notation for $\log \log \cdots \log n$?
@Andreas, where, other than in research papers on analytic number theory, is one likely to come across $\log\log\log\log x$?
Apr
10
comment Notation for $\log \log \cdots \log n$?
@Stefan, yes --- so whenever it's used for the iterated logarithm, the author(s) carefully explain just what they mean by it (as in the Ford et al. paper).