# Charles

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## Registered User

 Name Charles Member for 3 years Seen 21 hours ago Website Location UTC -5:00 Age
 May12 awarded ● Yearling Apr18 comment Is rigour just a ritual that most mathematicians wish to get rid of if they could? This should be re-opened as CW. Apr18 revised Non-ZFC set theory and nonuniqueness of the hyperreals: problem solved?minor edits: fix spelling etc. Apr16 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. Apr13 revised Random “pseudoprime” number generator ??LaTeX Apr12 revised Is the smallest primitive root modulo p a primitive root modulo p^2?correct link Apr11 answered At what point would an elementary generalization of Bertrand’s Postulate be interesting? Mar20 comment Sums of Squaresoeis.org/A069003 Mar17 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? Mar5 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! Mar5 comment Polynomial-time algorithm to compare numbers in Conway chained arrow notationRobert 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. Feb22 comment AKS Algorithm PseudoprimesNo solutions to (2) up to $10^9$. Feb12 comment AKS Algorithm Pseudoprimes@Dominick Reinhold: Not much help for a = 1, though. Feb10 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.) Feb1 comment Saying things rapidly about integer factorisationsFinding the value of "such-and-such" seems very hard. Feb1 comment Why do primes dislike dividing the sum of all the preceding primes?oeis.org/A007506 Jan27 comment Concise model of modern fiat money and its non-conservationIts 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). Jan21 comment Constructing prime numbers@Denis: I think so. Jan8 awarded ● Popular Question Jan7 awarded ● Nice Question Dec19 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? Dec12 revised Maximum size of powers with a given differenceminor fixes Dec11 revised Maximum size of powers with a given differenceabs Dec11 comment Maximum size of powers with a given differenceSo 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? Dec11 comment Maximum size of powers with a given differenceHmm. 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. Dec11 asked Maximum size of powers with a given difference Dec11 revised Are there ever three perfect powers between consecutive squares?links Dec7 comment Ratio of consecutive divisors and average annals.math.princeton.edu/2008/168-2/p01