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visits member for 2 years, 9 months
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Jul
24
comment Limit of Sum $\sum \frac{p(k+1) - p(k)}{p(k)^2}$ ? (corrected)
Yes, thanks, I don't trust my results that far but the differences were getting small quickly.
Jul
20
comment Euclid's proof of the infinitude of primes to prove this question
@MichaelHardy: This is a really nice paper and worth several readings. Thanks for the reference and the surprising answer.
Jul
19
comment Euclid's proof of the infinitude of primes to prove this question
@MichaelHardy: Your comment surprised me. I understand that $S$ is then extended to a larger finite set of primes. If it is error to call it a proof by contradiction it is a common error. Would you mind elaborating briefly?
Jul
9
comment Are NSA Mathematicians second-rate?
This doesn't seem to be about math.
Jul
8
comment Asymptotic density of powers of primes
Well--not so sure. $\pi(11) = 5.$ But we have $2,2^2,2^3,3,3^2,5,7,11$ or cardinality of 8...?
Jul
8
comment Asymptotic density of powers of primes
That's how I understand it although I am not familiar with $\Pi(x)$ in that form. It is the cardinality of the set of powers of primes less than or equal to x. At least that's how it looks to me.
Jul
8
comment Asymptotic density of powers of primes
Under the Wiki entry for Prime Number Theorem, Chebyshev's $\psi(x) = \sum_{p^k \leq x} \log p$ is asymptotic to x. Comparing this to your $\Pi(x)$ would seem to confirm Antonio Vargas' answer and I think give a proof. You should write $\psi(x)$ as a product.
May
26
comment Statements with rare counter-examples
This rings a bell...duplicate?
May
13
comment A product for 1/e?
Do you think for $|F_i|< 1|$ we could also just say $\log(1 + (-F_i)) \approx -F_i,~$ ...etc.? And so $\sum (-F_i) \approx -1$ and exactly in the limit as n gets large?
May
12
comment A product for 1/e?
@Ian: Fair enough. I only have time to remove it at the moment. I think my computer was using a $\Gamma$ function or something to interpolate and I will have to go back and check.
May
11
comment Grade School Math: Bad math, or new meanings?
@DavidMitra: A digit represents one of ten numbers. But if I stipulate that it the digit 1 also represents (say) 1000 by virtue of its place in a number that might be a contract if you understand and accept it. The problem with the question as I see it is that this is not at all clear.
May
11
comment Grade School Math: Bad math, or new meanings?
Right, I see both sides but it's not a good test question. Additionally, if the answer is (1), what does "1 times greater than..." mean?
May
1
comment sum of primes: approximate closed form?
If you had an approximate expression for the percentage of primes from 1 to n and multiplied it by n that would give you an approximate expression for the number of primes from 1 to n...
Apr
24
comment Pseudo Proofs that are intuitively reasonable
@robjohn: It is talking about the same function, yes, and I think my argument is overstated.
Apr
24
comment Pseudo Proofs that are intuitively reasonable
@robjohn: I think my answer is essentially a duplicate of yours. If you agree I will take mine down in the interest of good site husbandry. I didn't see this at the time.
Apr
22
comment Pseudo Proofs that are intuitively reasonable
@robjohn: The idea was paraphrased from an unnamed source in the text I cited. I will look at your answer (time permitting) and edit mine if that seems indicated. The answer was not given with reference to yours and I don't doubt your assertion is correct. Thanks.
Apr
18
comment Estimating the integrated Tchebychev function and calculating its error
@AndrewKelley: thanks, will look at this.
Mar
14
comment How much percentage are the Pythagorean triples among numbers?
Discussion of this point at p. 38 of Lehmer's paper.
Mar
5
comment Bookkeeping question in claim about arithmetic functions in a proof
@MayankPandey: I haven't looked at this in 2 years but T(x) is defined in the first formula: a sum of $\psi$ functions. It occurs in Nagura's 1952 paper.
Jan
13
comment Origin of Littlewood's idea about sign changes of $Li(x) - \pi(x)$
Ingham, The Distr. of Prime Numbers, p. 92, note, cites Phragmen's result as a "less precise result pointing in the same direction" as that of Schmidt, who proved a Littlewood-type result but assumed the Riemann Hypothesis. Maybe this sharpens my question about your last paragraph (or not).