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Jan
22
comment Is there a known mathematical equation to find the nth prime?
@Liviu: Suppose you have a fast test for (1) whether a number is prime or not and (2) a fast test to find the number of primes less than or equal to a given number. If I claim that a number $p$ is the $n$th prime, all you have to do is check that $p$ is prime using (1) and check that $\pi(p)=n$ by (2). (1) is relatively easy, but (2) is hard. See mathworld.wolfram.com/PrimeCountingFunction.html for an overview on the latter. There are two classes of fast approaches to (2), analytic and combinatorial, and they are roughly tied at record sizes (at smaller sizes combinatorial is better).
Jan
21
answered How, if at all, does pure mathematics benefit from $2^{74207281}-1$ being prime?
Jan
21
comment Is there a known mathematical equation to find the nth prime?
@Liviu: Use a $\pi(x)$ algorithm to get a good guess and sieve from there. If for some reason your guess is very far off, take a second guess and sieve from that point. If you are currently at the 20th prime you shouldn't start sieving yet. :p
Jan
19
asked Bounds on the heights of the minimal polynomials of the algebraic coefficients of linear recurrence relations
Jan
19
revised Prime and Repunits
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Jan
19
answered Prime and Repunits
Jan
19
comment an upper bound for number of primes in the interval $[n^2+n,n^2+2n]$
@ttt: I don't think so; it should be more than $\pi(0.499n)$ infinitely often. With $x=10^9$ I find 24127792 which is much closer to $\pi(10^9/2)=26355867$ than to $\pi(10^9/10)=5761455.$
Jan
19
awarded  Good Answer
Jan
18
answered an upper bound for number of primes in the interval $[n^2+n,n^2+2n]$
Jan
18
comment Is there a known mathematical equation to find the nth prime?
@Liviu: Suppose you want the millionth prime and you find an $x$ with 998,000 primes less than it. You just need to "count up" 2000 primes. The expected length needed is then about $2000\log x$, but you should probably add, say, 10% or so in case the primes don't cooperate.
Jan
14
answered Twin prime conjecture hypothesis
Jan
14
comment The $n$th prime number is $85489307341$. How to find $n$?
@Piquito: $\operatorname{Li}(x)$ is much sharper than $x/\log x.$
Jan
14
comment The $n$th prime number is $85489307341$. How to find $n$?
@TitoPiezasIII: Probably not. It seems that the next term is oscillatory. In any case the oscillatory component is at least $\Theta_\pm(\sqrt x)/\log^kx$ where $k$ is some constant I forgot (maybe 2).
Jan
14
comment Optimal Strategy for this schoolyard game - (Charge, block, shoot)
FWIW, I asked about this at Economics to see if anyone was familiar with this type of game: economics.stackexchange.com/q/10220/4834
Jan
12
revised Applications of Perfect Numbers
Skylake bug
Jan
7
reviewed Leave Open Does category-theory have an interesting perspective on the phrase 'under the induced operations'?
Jan
7
reviewed Close convergence of a decreasing sequence
Jan
7
reviewed Approve What is the general equation of lines going through 'a' particular point?
Jan
5
comment How the amount that is wagered influences the way bankroll goes?
@SarpSTA: Good luck with your new question.
Jan
5
comment How the amount that is wagered influences the way bankroll goes?
@SarpSTA: I see. I think that's different enough to be a new question -- I'm not sure you can use the same setup when you want a different number of rounds depending on the outcome. I can't immediately see the answer although I'm sure someone can help you.