# what is the Best known Upper bound on Twin Primes?

Let’s learn what is the Best known Upper bound on Twin Primes. The most accurate or helpful solution is served by Mathoverflow.

There are ten answers to this question.

Best solution

What is the best known upper bound for the number of twin primes?

A quantitative form of the twin prime conjecture asserts that the the number of twin primes less than $n$ is asymptotically equal to $2\, C\, n/ \ln^2(n)$ where $C$ is the so-called twin prime constant. A variety of sieve methods (originating with Brun) can be used show that the number of twin primes less than $n$ is at most $A\, n/ \ln^2 (n)$ for some constant $A>2C$. My question is: What is the smallest known value of $A$? I'd also be interested in learning what the best known constants are...

J Wu, Chen's double sieve, Goldbach's conjecture, and the twin prime problem, Acta Arith 114 (2004)...

Mark Lewko at Mathoverflow

Other solutions

Giant numbers (Ex: how many primes are smaller than the largest known?)

Many sites say that the largest known prime is "2^57,885,161 − 1, a number with 17,425,170 digits." Given this and well known research about the density of primes, I think it's at least possible to estimate the number of primes between 1 and...

I have two links for you: The Prime Number theorem and also what I think you are getting at with all...

Has someone proven a lower bound on the number of primes less than or equal to x that are congruent to 1(mod3)?

I know the approximation that has been proven of this from Dirichlet's theorem, but I am interested in a lower bound provided that x is greater than a certain value. For example, has someone proved something like the number of primes less than or equal...

This may be of some help, http://www.math.ubc.ca/~gerg/slides/chen… The densities of primes in...

Are there proven results for a lower and upper bound of the modular prime counting function?

For example, is there a proven lower and upper bound for the number of primes less than x that are congruent to 1(mod3)? In general, for numbers a and b, is there a proven lower and upper bound for the number of primes less than x that are congruent...

1) http://en.wikipedia.org/wiki/Dirichlet%2… The theorem states exactly that.

How does the Cantor set relate to primes and the zeta function?

It's trivial to dismiss any relationship between these things existing in different domains and having no researched connection, but there is some joy to thinking of it and a bit of mathematics is required in that pursuit. To aid that end, I'll describe...

It doesn't. Not in any reasonable way.

Anonymous at Quora

Do we know for sure that there aren't any prime numbers smaller than the current biggest known prime?

Do we even know if it is probable or not? Here's another one... Based on the gaps between all the known primes to date (taking into account possibilities of undiscovered primes that're smaller than other known primes) what is the next biggest prime to...

There probably are undiscovered primes smaller than the largest known one. Computers searching for large...

How do we keep finding primes?

So apparently the mathematical community has somehow determined that 2^43112609 - 1 is prime, and that number is the largest known prime number. How did mathematicians come up with that? Are they actually checking every single number to find primes?...

The largest known primes are found on ordinary PC's with free software. Small primes can be computed...

Who is this well-known dramatist from around the 1900s (thoughts on cinema replacing theater)?

I'm reading an article by Georg Lukács in 1913 called "Thoughts on an Aesthetics of Cinema". This article mentions "a well-known dramatist" who "occasionally fantasized that the cinema could replace theater" at the...

I find it ironic that his name is almost the same as the guy who directed star wars.

According to the Wikipedia: 2003663613 Â· 2195000 Â± 1. The numbers have ...

You can download a list of the 5000 largest known primes, but since there are infinite primes they can...

Anonymous at ChaCha

Related Q & A: