# Nilotpal Sinha

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 Name Nilotpal Sinha Member for 1 year Seen 1 hour ago Website Location Age
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 2d answered Are sums of the inverses of prime siblings finite? 2d comment Are sums of the inverses of prime siblings finite?If I understand your question correctly, you are asking the following. The sum of the reciprocal of primes is divergent but the sum of the reciprocal of twin primes is convergent (as shown by Brun). Your question is there any gap $d$ greater than 2 (2 is for twin primes) between primes for which the sum of the reciprocal primes differing by $d$ is convergent. Is this understanding correct? May20 comment Philosophy behind Yitang Zhang’s work on the Twin Primes Conjecture@Gerhard Paseman: I would rather NOT ask you about system design but I would definitely ask this question in this forum because if it is more than perfectly fitted here :) May18 comment Sequences equidistributed modulo 1But this is nothing but the extension of the Equidistributuion Theorem (first result) to polynomials, which was done my Weyl himself. So not just $n^2$, but any polynomial $s_n=f(n)$ is trivial. May18 revised Sequences equidistributed modulo 1added 408 characters in body May18 comment Sequences equidistributed modulo 1@Noam: While your example is correct, it is highly trivial because if we take $a$ to be normal in base $b$, then by the very definition of normality, we can construct similar example in that base $b$. Please note that in my examples of Weyl, Vonogradov had Hlawka, there is no such assumption on the normality constant which makes them non trivial. My question is can we have such a non trivial example such that $s_i/s_n$ does approach equidistribution modulo 1. May18 revised Sequences equidistributed modulo 1deleted 2 characters in body; added 6 characters in body May18 asked Sequences equidistributed modulo 1 May7 revised Square and reversed integeradded 374 characters in body; added 89 characters in body May7 answered Square and reversed integer May3 comment Why is it hard to prove that the Euler Mascheroni constant is irrational?"There are a lot more connections known between π and e and other numbers than between γ and other numbers." This may not entirely true. The numbers $e^{\gamma}$ pops up every now and then in the theory of primes. For example Merten's Theorems, Cramer-Granville's conjecture etc to name a few. But I do agree that the connection between $\gamma$ and other numbers that has nothing to do with primes directly or indirectly is far less common. May3 awarded ● Yearling Apr28 revised A divergent series related to the number of divisors of of p-1edited body Apr26 answered Integer dynamics hitting infinitely many primes Apr25 answered A divergent series related to the number of divisors of of p-1 Mar13 comment Multivariate functions whose value is independent of the order of the arguments@Survit: That practical application for which I need such a function has discrete arguments (positive integers) but we want to keep it flexible enough to accommodate all positive real values if required in future. Mar13 comment Multivariate functions whose value is independent of the order of the arguments@Qiaochu: That is because the current application for which I need such a function has discrete arguments (positive integers) but we want to keep it flexible enough to accommodate all positive real values if required in future. Mar13 asked Multivariate functions whose value is independent of the order of the arguments Feb28 awarded ● Enthusiast Feb27 accepted How can an integer be factorized as n*m so that n^m has the highest value. Feb27 answered How can an integer be factorized as n*m so that n^m has the highest value. Feb21 awarded ● Popular Question Feb20 revised Probability that randomly chosen integers from a restricted set of natural numbers are coprimeedited tags Feb19 comment Most inconsistent ranking@Kevin: Thanks for the insight and the lower bound. In my problem, I have a ranking system which gave me the rank matrix. In the best case when the ranking system is completely consistent, the variance of each row will be zero and hence the total sum will be zero. In my case I have a finite total sum of variance say $S$ and I want to compare it against the worst or the maximum possible total sum $S_{kn}$ in order to quantify how consistent the rank matrix is. I am updating this comment in the question. Feb19 revised Most inconsistent rankingadded 521 characters in body; added 14 characters in body; deleted 3 characters in body Feb19 comment Most inconsistent ranking@Kevin: Yes this is the right understanding Feb19 revised Most inconsistent rankingadded 92 characters in body; added 6 characters in body; edited tags Feb19 revised Most inconsistent rankingadded 51 characters in body Feb19 comment Most inconsistent ranking@ Gerry, I have now defined the sum of variance of the rows in condition number 2. Feb19 revised Most inconsistent rankingDefine $S(k,n)$ after Gerry's comment; added 1 characters in body Feb19 asked Most inconsistent ranking Feb17 awarded ● Notable Question Feb14 awarded ● Good Question Feb13 comment 2^(p-1)-1 = 0 mod p^2No conditions are known yet. Feb13 revised Mathematical techniques to reduce the amount of storage memoryedited title Feb13 awarded ● Mortarboard Feb12 awarded ● Popular Question Feb12 awarded ● Nice Answer Feb12 awarded ● Nice Question Feb12 awarded ● Self-Learner Feb12 answered Mathematicians whose works were criticized by contemporaries but became widely accepted later Feb12 comment Mathematicians whose works were criticized by contemporaries but became widely accepted later@Yemon. No I had no such intention to distinguish between the two. All as wanted to know the lesser known mathematicians or stories that need to be heard. How do I make it community Wiki? Feb12 asked Mathematicians whose works were criticized by contemporaries but became widely accepted later Feb11 awarded ● Cleanup Feb11 revised On a sum involving prime numbersadded 82 characters in body Feb11 awarded ● Civic Duty Feb5 awarded ● Disciplined Feb5 asked Mathematical techniques to reduce the amount of storage memory Feb4 accepted Sum involving binomial coefficients Feb4 comment Sum involving binomial coefficients@Pietro Yes there is such an integral which is in fact a contour integral. $$s(n,r) = \frac{n!}{2\pi r!}\int_{|z|=1} z^{-n-1} \log^r (z+1)dz$$ @Danne, Yes I am sure.