A natural number $n$ is prime if and only if, for all primes $p \le \sqrt n$, $p$ does not divide $n$.
73612
Is there a Non-prime Number that is Divisible only by Numbers Greater than its Square Root?
34680
Percentage of primes among the natural numbers
65511
Proving the following false: $f(x)=2x+1$ produces a prime number if and only if x is prime
154475
Prove that if $2^n - 1$ is prime, then $n$ is prime for $n$ being a natural number
152172
Does there exist a positive irrational number $\alpha $, such that for any positive integer $n$ the number $\lfloor n\alpha \rfloor$ is not a prime?
101882
Does this polynomial evaluate to prime number whenever $x$ is a natural number?
102889
If $2^n - 1$ is prime from some integer $n$, prove that n must also be prime.
30134
For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
47471
The square of n+1-th prime is less than the product of the first n primes.
39915
Let $n$ be an integer such that if $d | n$ then $d + 1 | n + 1.$ Show that $n$ is a prime number
119486
Upper and Lower bounds on the nth prime number
126945
checking if a number is a prime
77806
Proving if $a$ is not a multiple of prime $p$, then an integer $b$ exists such that $p^b - 1$ is a multiple of $a$
95111
Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.
44600
How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?
63702
There is a prime between $n$ and $n^2$, without Bertrand
131385
How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime