Show that if the smallest prime factor $p$ of the positive integer $n$ exceeds $n^{\frac{1}{3}}$ then $\frac{n}{p}$ must be a prime or 1.
54547
Prove this number must be a prime number or 1.
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
140294
prove that $n >2$ and $n$ is a prime then $n$ is odd
70308
Prove that if $p$ and $p+2$ are both prime integers greater than $3$, then $6$ is a factor of $p+1$.
5206
Highest power of a prime $p$ dividing $N!$
92483
Without using prime factorization, find a prime factor of $\frac{(3^{41} -1)}{2}$
132728
Can the sum of the first $p$ factorials ever be a perfect power for $\ p>3\ $?
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
84603
Prove that if $p$ is a prime such that $p^2+2$ is a prime then $p=3$.
10861
Let$\ p_n$ be the$\ n$-th prime. Can you give me a proof for$\ \prod_{i=1}^\infty \frac{p_i-1}{p_i}=P\approx \frac{1}{11.0453}$?
105623
Prime factorization knowing n and Euler's function
6700
An Olympiad problem in prime numbers :can we proof that "n" is prime in this case "
71110
Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$
131385
How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime
68688
n-th prime number is less than $4^n$
31312
If a prime divides a product then it must divide a factor of the product [Euclid's Lemma]
102650
$\require{enclose}\enclose{horizontalstrike}{\rm Greatest}\!$ Least prime factor of $n$ is less than square root of $n$, proof