# Questions tagged [twin-primes]

For questions on prime twins.

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### Potential progress concerning the twin prime conjecture

The twin prime conjecture posits that there are an infinite number of twin primes, or equivalently that there is no largest twin prime pair. I conjecture more specifically that for any twin prime pair ...
1 vote
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### primes of the form 2+pq

Is it always possible to demonstrate the existence of at least one prime number of the form 2 + pq, where p is an arbitrarily large prime number and q is a prime number greater than p? Other word, if ...
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### Is some twin prime average the sum of two twin prime averages, two ways?

Accoring to this question and a linked duplicate, it's been verified empirically up to some number that all twin prime averages greater than six, are the sum of two smaller twin prime averages. I was ...
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### Describing the probability that n is of the form $K^2+1$ , and it is a prime number.

I was reading a book called "Math Talks for Undergraduates" by Serge Lang. I was introduced to the Prime Number Theorem that states that $pi(x)$ (representing the number of primes $<=$ x) ...
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### $H(n)=\lfloor\dfrac{b}{n}\rfloor- \lfloor \dfrac{a}{n} \rfloor=$ (roughly) # odd pairs $o, o+2 \in [a,b]$ such that $n \mid o$ or $n \mid o+2$

I came up with the following formula and deleted that question so that I don't have two questions on the same formula. Conjecture. Let $a, b, n \in 2\Bbb{N} + 1$ be odd natural numbers. Then the ...
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### Why are some numbers "paired" in their prime distribution

Sorry I'm not sure exactly how to word the question. I was exploring off-by-one primes for each number, as I found it curious enormous primes were searched to be one off a power of $2$, and all primes ...
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### Generating new prime number by adding $40$ to larger number of twin primes

A long time ago one of my classmates claimed he discovered a formula for prime numbers and he became so famous among students and our teacher. If we have two digits twin prime numbers (primes which ...
1 vote
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### A slight generalization of the Sieve of Sundaram that might shed light on the $6n \pm 1$ phenomenon of sequence A002822.

There's the $n$ such that $6n \pm 1$ is a twin prime pair sequence: https://oeis.org/A002822 It contains all twin prime averages (divided by $6$) other than $4$. Notice this sequence: Positive ...
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### In an infinite consecutive set of only all the prime numbers, should we expect consecutive twin prime numbers to exist infinitely?

I am aware that in an infinite consecutive set of all positive integers, in theory there should be infinite twin prime numbers, but let's imagine an infinite set of only all the prime numbers. Here ...
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Due to https://oeis.org/A024702 we have that $p^2 - 1 ≡ 0$ (mod 24). For twin primes, we then must also have that in this case $(p+2)^2 - 1 ≡ 0$ (mod 24), which is the same as saying that \$p^2 + 4p + ...