prime numbers. show that $p_{n+1} \le {p_1 \cdot \ldots \cdot p_n +1}$
44857
Why the $(n+1)$th prime number cannot exceed the smallest prime divisor of $p_1\dotsc p_n + 1$
134963
Proving a non-prime (composite) number $> 1$ has a divisor $d \leq\sqrt q$
51382
Proving that either $2^n-1 $ or $ 2^n+1$ is not prime
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
27784
Proving that $\left(\mathbb Q[\sqrt p_1,\dots,\sqrt p_n]:\mathbb Q\right)=2^n$ for distinct primes $p_i$.
48691
Product of all prime numbers upto some prime $p$
1837
Showing that $1^k+2^k + \dots + n^k$ is divisible by $n(n+1)\over 2$
106767
$|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
54286
Let $p$ a prime number, then prove that : $\sum \limits_{k=0}^{p} \binom {p}{k} \binom{p+k}{k} \equiv 2^p +1 \pmod{p^2}$
154475
Prove that if $2^n - 1$ is prime, then $n$ is prime for $n$ being a natural number
12365
Show that every prime $p>3$ is either of the form $6n+1$ or of the form $6n+5$
131488
Show that $p^3+4$ is prime
66877
Showing groups of order $p^{k}(p+1)$ are not simple, p prime
8710
Bounds for $n$-th prime
107924
Prove (or derive) the de Polignac formula for the prime decomposition of $n!$
59479
For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$