Tagged Questions

19
votes
3answers
2k views

Yitang Zhang: Prime Gaps

Has anybody read Yitang Zhang's paper on prime gaps? Wired reports "$70$ million" at most, but I was wondering if the number was actually more specific. EDIT$^1$: Are there any experts here who can ...
5
votes
3answers
224 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 ...
7
votes
0answers
339 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 ...
3
votes
1answer
54 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
79 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
165 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
146 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
68 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
63 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
88 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
141 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
46 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 ...