# Tagged Questions

Prime numbers are natural numbers greater than 1 not divisible by any smaller number other than 1. This tag is intended for questions about, related to, or involving prime numbers.

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### Finding 8 co-primes $\le 2^n$

We can find 8 co-prime integers $\le 2^n$ for sufficiently large $n$. I'm looking for asymptotic bounds for the minimum distance away from $2^n$ we have to go before finding 8 co-primes. In other ...
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### Explain Carmichael's Function To A Novice

I understand that the Carmichael Function (I'm going to call C()) is essentially the smallest positive integer m, where $a^m$ is congruent $1 \pmod n$ for all $a$ co-prime to $n$ and less than $n$. 6 ...
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### Why are the first 5 Fermat numbers prime?

The $n$th Fermat number $F_n$ is defined as $F_n = 2^{2^n}+1$. The first five Fermat numbers, $F_0,F_1,F_2,F_3,F_4$, are all prime. Why is this? It seems like a fairly surprising coincidence that ...
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### prove if n - natural number divide number $34x^2-42xy+13y^2$ then n is sum of two square number

prove if n - natural number divide number $34x^2-42xy+13y^2$ where x,y are relatively prime then n is sum of two square number. I don't know what is going on in this exercise. I will be grateful ...
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### Prove that $3^{(q-1)/2} \equiv -1 \pmod q$ then q is prime number.

$q=2^m+1, m\ge 2$. Prove that if $$3^{(q-1)/2} \equiv -1 \pmod q$$ then q is prime number. I want to use if $q-1 | \phi(q)$, then q is prime number. But I don't know how to transform above equation. ...
I made a function that determines how "prime-y" a number is; if $f(x) = 1$ then $x \in primes$. The function is $$f(x) = \frac{\pi(x) - \#\{p \in primes | p<x, p \space| \space x\}}{\pi(x)}$$ ...