Questions tagged [twin-primes]

For questions on prime twins.

A twin prime is a prime number that differs from another prime number by two, for example the twin prime pair $(41, 43)$. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair.

It is currently unknown whether or not there are infinitely many pairs of twin primes. However, it is known (Brun's theorem) that the sum of the inverses of the twin primes is finite (it is about $1.902$).

289 questions

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Why doesn't this twin prime counting function work?

Quite some time ago, I made a function $f(x)$ which I thought would give me the minimum amount of prime twins equal to or lower than $x$. I have tested this function for large values of $x$ and it seems to work perfectly fine. But I think the…

twin-primes

asked Sep 11 '15 at 13:39

Mastrem

8,331

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Number of "primal" sequences of consecutive numbers of the form $p_1, 2p_2, 3p_3,\dots$ for primes $p_1, p_2,\dots$

I am interested in the number of "primal" sequences of consecutive numbers of the form $p_1, 2 p_2, 3 p_3,\ldots, k p_k$ for primes $p_1, p_2,\ldots, p_k$. For instance, there are $56,157$ sequences of the form $p_1, 2 p_2 = p_1 + 1$ for $p_1 <…

twin-primes

asked Aug 12 '20 at 13:36

fairflow

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1 answer

Twin prime gaps

I realize that because it is only conjectured that there are infinitely many twin primes, we can't say, "There will always be a twin prime between _____ and _____." Like we can for primes. Still, do we even have any conjectures regarding twin primes…

twin-primes

asked Apr 10 '16 at 07:16

Elem-Teach-w-Bach-n-Math-Ed

1,205

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Twin indices of the form $K = 6 (a n)^b$

Let $K \ge 6$ (usually called twin index) be the number between a pair of twin primes, and let $k = K / 6$. It is easy to see that all $k = n^2$ (where $n$ is a generic integer) are divisible by 5 (ex.: 25, 100,1225, 3600, 4900, 5625,…

twin-primes

asked May 09 '18 at 21:12

adinc

-2

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1 answer

Why the twin prime conjecture isn't proved already by Euclid's theorem?

I was wondering how Euclid showed that there are infinitely many primes by generating a prime number from finitely many primes, and if it could be used to answer if there are infinitely many pairs of primes whose difference is 2. I show my approach…

twin-primes

asked Oct 05 '20 at 19:28