daniel
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 Apr 17 comment What percentage of prime number factorials plus 1 are themselves prime? It's not an arithmetic sequence and I'm pretty sure it's an open question whether there are infinitely many primes of this form. Apr 17 comment What percentage of prime number factorials plus 1 are themselves prime? Suppose that, for sufficiently large $p,$ $p!+1$ is never a prime? Apr 11 comment Can we replace the upper limit condition of the Sieve of Eratosthenes $\sqrt{n}$ with the value $\sqrt{p}$ where $p$ is the last sieved prime $\lt n$? Right. I was confused by the suggestion of a counter-example. Given $p(\pi(\sqrt{n}))$ if there were a composite of primes g.t. $p$ it would exceed $n.$ So it is just the sieve. Apr 11 comment Can we replace the upper limit condition of the Sieve of Eratosthenes $\sqrt{n}$ with the value $\sqrt{p}$ where $p$ is the last sieved prime $\lt n$? I am confused. The point of the sieve is that you need not look for composites of primes g.t. $\sqrt{n}$ because they will exceed $n$ If you stipulate that the greatest prime not exceeding $\sqrt{n}$ is p, that is as far as you need go. The advantage of the classical sieve is that you don't have to find that penultimate prime. Is this the idea? Mar 24 comment Consecutive prime numbers multiplication pattern Maybe just an indirect reflection of the distance between consecutive primes. Mar 18 comment Inequality for primes Use the prime number theorem and convenient error bounds. Mar 18 comment Sum of first n primes math.stackexchange.com/questions/1693478/… Mar 17 comment $(x+1)^2 + (y+1)^2 + xy(x+y+3)=2$ $(-2+1)^2+(0+1)^2+(-2)0(-2+0+3)=2$? Mar 17 comment $(x+1)^2 + (y+1)^2 + xy(x+y+3)=2$ Well, x = -2, y=0 is a solution. Mar 17 comment It is possible a Skewes number between twin primes? Can you discard such extreme question? There is no reason in principle why Li(x) cannot cross $\pi(x)$ between two twin primes. Li(x) has a positive slope. $\pi(x)$ is flat between primes. I don't follow your argument but if you are trying to use $n/\log n$ to make an argument about $\pi(n)$ between twin primes I do not think the error of the prime number theorem supports this. Mar 14 comment Analytic continuation for $\zeta(s)$ using finite sums? @PeterHumphries: Yes, this is the phrase. Thank you. Mar 13 comment We know the asymptotic density of primes. What about the asymptotic density of numbers with n prime factors? The generalized prime number theorem is set out in this question. math.stackexchange.com/questions/168307/…. Mar 13 comment Analytic continuation for $\zeta(s)$ using finite sums? Elegant answer, much appreciated (+1). Mar 13 comment Analytic continuation for $\zeta(s)$ using finite sums? Very interesting (+1) and will be studying this for a few days at least. Thanks. Mar 9 comment Looking for help on writing a mathematical argument clearly and concisely I am wondering if you can have equality in (3). If not then your conclusion is correct as given and I don't see a mistake. Feb 24 comment Finding a number of twin primes less than a certain number Zhang's theorem is also worth mentioning but I think (4) is far enough afield. Feb 24 comment Twin-prime sieve Won't edit this again but maybe the sieve works fine and it n just cannot be proven to increase as as $p_k$ increases w/o bound. Would still be interested in an answer that discusses the difficulties involved. Feb 20 comment Is $a\pi(x) \ge \pi(ax)$ where $a$ is a positive integer Will try to fix this up soon. These are really modest bounds. Feb 20 comment How does sieve that Chen used to prove Chen's theorem work? Haberstam and Richert's Sieve Methods (Dover) contains a relatively accessible version of Chen's theorem in the last chapter (it appeared as they were going to press). If you can get through the first 60 pages of preparatory material you will be in a good position to understand Chen's argument. Feb 11 comment Why are very large prime numbers important in cryptography? If you have a question the site functions best if you post it as a question rather than an answer.