On Wed, Feb 19, 2020 at 9:07 PM Simon Rubinstein-Salzedo < complexzeta@gmail.com> wrote:
We aren't doing things like that in Varun's class. But Varun, you have my material from the analytic number theory class from last spring. This problem is similar to some that are discussed in chapters 8 and especially 9 of that book.
Simon
Thanks, Simon! Varun, from Chapter 9 can you get (Awesome) Julian's result? He says "It's a number theory question. The answer is roughly 1.78*log(D)/log(N), for D small compared to N (using Mertens' theorem). This is a poor approximation for your case, though, which has D close to √N; in that case, 1 – ((log log√N) – log log D) should be a decent approximation (again using Mertens' theorem)." This fits my experience! [1.78 ~ e^𝜸.] —Bill
On Wed, 19 Feb 2020 at 19:25, Bill Gosper <billgosper@gmail.com> wrote:
On Wed, Feb 19, 2020 at 2:25 PM Varun Rajkumar <pi.fermet@gmail.com> wrote:
Bill, my eulercircle class is doing combinatorics. But your email was not asking that question.
Varun, you may be right. My question was " What is the probability that N is prime if it's coprime to D! ?"
What subject is this if not Combinatorics? Number Theory? Combinatoric Number Theory?? —Bill On Thu, Feb 13, 2020 at 9:30 PM Rudy Rucker <rudy@rudyrucker.com> wrote:
From the peanut gallery.
When I can't sleep I factor all the numbers less than a hundred, usually working down from 99. And going off on tangents. And if I went to sleep in the 70s the day before I restart there. If I feel extra ambitious I jump up into numbers less than 200, but blessed sleep soon comes. In the same vein, I had a bout of computing larger and larger Fibonacci series numbers this fall.
Factoring 5 and 6 digit numbers in my head? Not yet... On 2/13/2020 7:43 PM, Bill Gosper wrote:
Here's a question I often ask myself but am too lazy to attack. (And I'm working on a 3D print.) I like to factor 5 or 6 digit numbers in my head. There's a bag of tricks for finding small factors, but eventually you wind up slogging through division by consecutive primes. When I've reached, say, ¾ √N, I often get bored|tired and then cheat by trying PrimeQ, and then when it says True, I'm glad I cheated. It seems to me that this happens improbably often. What is the probability that N is prime if it's coprime to D! ? —Bill
-- Rudy Rucker | rudy@rudyrucker.com |
On Thu, 13 Feb 2020 at 22:48, Bill Gosper <billgosper@gmail.com> wrote: