Proof: If no prime less than or equal to $\sqrt{n}$ divides $n$, then $n$ is a prime
7415
why only square root approach to check number is prime
119051
Show that only finitely many positive integers $n$ have the property that for all $m$ for which $1<m<n$ and $\text{gcd}(m,n) = 1$, $m$ is prime.
102650
$\require{enclose}\enclose{horizontalstrike}{\rm Greatest}\!$ Least prime factor of $n$ is less than square root of $n$, proof
111037
Consider numbers of the type $n=2^m+1$. Prove that such an n is prime only if $n=F_K$ for some $ k \in N$, where $F_k$ is a Fermat Prime.
63702
There is a prime between $n$ and $n^2$, without Bertrand
44600
How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?
59036
If $a^{n}-1$ is prime then $a=2$ and $n$ is prime?
158106
Prove that 1 less than the number of equivalence classes divides $p-1$ where $p$ is prime
131385
How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime
29572
Proof that $2^n-1$ does not always generate primes when primes are plugged in for $n$?
103360
Prove $4p-3$ is a square knowing that $n\mid p-1$ and $p\mid n^3-1$, $p$ prime
5841
Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
78342
When is $\phi(n)$ a prime number?
90806
Find all positive integers $n$ such that $n$ is divisible by all the positive integers less than or equal to $\sqrt{n}$
111490
Proof that every number has at least one prime factor
40968
show if $n=4k+3$ is a prime and ${a^2+b^2} \equiv 0 \pmod n$ , then $a \equiv b \equiv 0 \pmod n$
145041
Given that $p$ is a prime and $p\mid a^n$, prove that $p^n\mid a^n$.