For questions on prime twins.
5
votes
3answers
206 views
What would be the immediate implications of a formula for prime numbers?
What would be the immediate implications for Math (or sciences as a general) if someone developed a formula capable of generating every prime number progressively and perfectly, also able to prove (or ...
6
votes
0answers
230 views
Partial Solution to the Twin Primes Conjecture — What does it imply? [closed]
But now, as the Mathematician Zhang Yitang from University of New Hampshire in Durham has shown, there is a kind of weak version of the twin prime conjecture. He didn’t prove that a distance of 2 ...
2
votes
1answer
88 views
Idea about Twin-Primes and the generation of natural numbers
Years ago (6 years to be exact) I was fascinate by prime-twins, and still I am, but the years went by and I almost forgot about it until yesterday.
I found my notes again and I don't know if I am on ...
5
votes
1answer
150 views
Modified Euler's Totient function for counting constellations in reduced residue systems
I am working on a modified totient function for counting constellations in reduced residue systems for the same range that Euler's totient function is defined over. This post is separated into three ...
3
votes
1answer
52 views
What happened to the Mertens constant in the strong prime twins conjecture ??
To estimate the amount of primes in an interval $\left(2,x\right)$ one might naively sieve by computing $ x \left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)...\left(1-\dfrac{1}{p_i}\right)$ ...
4
votes
1answer
117 views
Is this the way to estimate the amount of lucky twins?
To estimate the amount of prime twins between $3$ and $x$ we just take $x \prod_{p}(1-2/p)$ where $p$ runs over the primes between $3$ and $\sqrt x$. Lucky numbers are similar to prime numbers. Does ...
2
votes
1answer
72 views
How does sieve that Chen used to prove Chen's theorem work?
In the Number Theory for Computing, Song Y. Yan states that Chen used "complicated arguments based on sieve method", when proving what is now called Chen's theorem.
How does this sieve work? Does it ...
6
votes
3answers
163 views
If the set of primes where $p$, $p+2$ is infinite, would this imply that the set of $p$ and $p+2n$ is also infinite?
If the set of primes $p$ such that $p+2$ is also prime is infinite, would this imply that the set of primes such that $p+2n$ where $n$ is any positive integer for each pair is also infinite?
4
votes
4answers
145 views
Determining the next Twin Prime?
A really simple I question I guess. Is there an algorithm or method such that given an integer N there is a way to determine the next twin prime pair greater than N?
If yes then could you please ...
2
votes
3answers
67 views
Whether twin primes satisfy this one?
It seems that difference of squares of any twin primes $+1$ will always lead to
number which might be
a) A square of a twin prime
b) Itself a twin prime
$C$ = ($A^2$-$B^2$ )+$1$ ------> $(1)$
Where ...
0
votes
2answers
60 views
Primes and Twine primes and their sums.
Need good discussion for
$12|(p + p+2)$, where $p,p+2$ are primes and $> 3$. Why $12$ divides the sum of twin primes?
$a, ar, ar^2, \ldots $ is a Geometric series. I would like to place $a =
...
0
votes
2answers
86 views
Twin primes and modulo
I am so exited to learn math from this site. I posted the question today and I got good replies from members today itself. I will try to answer other number Theory questions in near future. With same ...
4
votes
3answers
140 views
Twin primes satisfy the congruence?
I need a justification for my observation.
In general, we can list twin prime pairs in $(6n-1, 6n+1)$, where $n$ is some positive number. Of course, this is valid except $(3, 5)$. Now, I construct, ...
2
votes
1answer
69 views
some problems related to primes
I would like to learn the following:
a) Prove that the equation $1 + x + x^2 = py$ has integer solutions for infinitely many primes $p$.
b) Twin primes are those difference by 2. Show that 5 is the ...
1
vote
1answer
45 views
What can I say about $x^4 \equiv -4 \mod p$ where $p$ is prime?
What can I say about $x^4 \equiv -4 \mod p$ where $p$ is prime? In general what can I do with powers that are greater than $2$ and where I cannot use reciprocity, legendre/jacobi etc... In general ...
2
votes
1answer
70 views
2 dimensional cellular automaton for prime twins?
Is there a 'simple' 2 dimensional cellular automaton to generate all prime twins ?
With 'simple' I mean not too many states per cell and not so many rules.
Thus a universal turing machine equivalent ...
