How can I prove or disprove that the formula $2^{2{^{2^{2^2\dots}}}}+1$ gives a prime number?
45700
How can I know if $2^{2^{2^{2^{2}}}}+1=?$ is prime?
127205
Explain proof of irreducibility of $x^{p-1} + 2x^{p-2}+ \dots +(p-1)x + p$
65511
Proving the following false: $f(x)=2x+1$ produces a prime number if and only if x is prime
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.
30134
For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
76282
Prime number expressible as $2^2+3^3+5^5+7^7+11^{11}+\cdots$
138409
Proof of infinitely many primes, clarification
62169
Product of all prime numbers on the interval [m+1, 2m] is $\le \left(\begin{matrix} 2m \\m\end{matrix}\right)$
75206
If $a$, $a+2$ and $a+4$ are prime numbers then, how can one prove that there is only one solution for $a$?
1837
Showing that $1^k+2^k + \dots + n^k$ is divisible by $n(n+1)\over 2$
110695
Divisor of $2^{2^n} + 1$ modulus $2^{n+1}$
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
58182
How to prove that $\mathbb{Q}[\sqrt{p_1}, \sqrt{p_2}, \ldots,\sqrt{p_n} ] = \mathbb{Q}[\sqrt{p_1}+ \sqrt{p_2}+\cdots + \sqrt{p_n}]$, for $p_i$ prime?
50781
$(n+1)$th prime $p_{n+1}$ less than or equal to $p_1p_2\dots p_n+1$
126945
checking if a number is a prime
48587
Why is $1$ not a prime number?
41614
Formula for prime counting function