Charles

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Name Charles
Member for 3 years
Seen 21 hours ago
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May
12
awarded  Yearling
Apr
18
comment Is rigour just a ritual that most mathematicians wish to get rid of if they could?
This should be re-opened as CW.
Apr
18
revised Non-ZFC set theory and nonuniqueness of the hyperreals: problem solved?
minor edits: fix spelling etc.
Apr
16
comment Product over the primes
@joro: I do not know of any reasonable lower bound. A crude one can be obtained with the prime zeta function.
Apr
13
revised Random “pseudoprime” number generator ??
LaTeX
Apr
12
revised Is the smallest primitive root modulo p a primitive root modulo p^2?
correct link
Apr
11
answered At what point would an elementary generalization of Bertrand’s Postulate be interesting?
Mar
20
comment Sums of Squares
oeis.org/A069003
Mar
17
comment Does erosion mix faster than a riffle shuffle?
@Anthony Quas: But $K\approx2\sqrt n$ so the lower bound is just two shuffles. Right?
Mar
5
comment are there infinitely many triples of consecutive square-free integers?
Dickson's conjecture does apply, you just have to use (say) 12n+1, 6n+1, and 4n+1. But that's a pretty big sledgehammer to apply to a little problem like this!
Mar
5
comment Polynomial-time algorithm to compare numbers in Conway chained arrow notation
Robert Munafo writes that he knows Hypercalc cannot compute an ordering (or even a partial ordering) for chained-arrow notation, but he would love to learn of an algorithm that does.
Feb
22
comment AKS Algorithm Pseudoprimes
No solutions to (2) up to $10^9$.
Feb
12
comment AKS Algorithm Pseudoprimes
@Dominick Reinhold: Not much help for a = 1, though.
Feb
10
comment For consecutive primes $a\lt b\lt c$, prove that $a+b\ge c$.
(Of course 2.001 can be replaced by 2 unconditionally.)
Feb
1
comment Saying things rapidly about integer factorisations
Finding the value of "such-and-such" seems very hard.
Feb
1
comment Why do primes dislike dividing the sum of all the preceding primes?
oeis.org/A007506
Jan
27
comment Concise model of modern fiat money and its non-conservation
Its assets are not quite separate from the US government, since it turns over its profits to the Treasury (in weekly payments based on last year's profit).
Jan
21
comment Constructing prime numbers
@Denis: I think so.
Jan
8
awarded  Popular Question
Jan
7
awarded  Nice Question
Dec
19
comment Any published references for this $O(n)$ time, $O(n^\epsilon)$ space identity for the count of primes?
Perhaps you intended to write $O(n^\epsilon)$ space? This of course cannot be done in $O(\epsilon)=O(1)$ space. But I don't even see how that can be done. What is memoized and what is recomputed?
Dec
12
revised Maximum size of powers with a given difference
minor fixes
Dec
11
revised Maximum size of powers with a given difference
abs
Dec
11
comment Maximum size of powers with a given difference
So the weaker version gives $a^x\ll n^{2+\varepsilon}$. But this applies only to the common case of exponents 2 and 3; is this the worst case?
Dec
11
comment Maximum size of powers with a given difference
Hmm. I don't know the exponents a priori, so the first result is $a^x\ll n^{6+\varepsilon}$ in my case (if I'm not mistaken). The second doesn't seem to apply at all since my $x$ is not fixed.
Dec
11
asked Maximum size of powers with a given difference
Dec
11
revised Are there ever three perfect powers between consecutive squares?
links
Dec
7
comment Ratio of consecutive divisors and average
annals.math.princeton.edu/2008/168-2/p01