Is there exist some k > 1, such that $10^{2^k} + 1$ is prime?
33177
All numbers of form $10^{k} + 1$ are composite for $k{\gt}2$ proof
98468
Are there infinitely many primes of the form $n!+1$?
38498
Find all primes $p$ such that $(2^{p-1}-1)/p$ is a perfect square
53525
Infiniteness of non-twin primes.
79208
Is the number $-1$ prime?
39698
On uniqueness of sums of prime powers
8710
Bounds for $n$-th prime
63702
There is a prime between $n$ and $n^2$, without Bertrand
69830
How often is $1+\prod_{k=1}^n p_k$ not prime?
100984
Prove that if prime $p$ divide $a_{2k}-2$, then $p$ divide also $a_{2k+1}-1$.
151036
arithmetic progression of primes
68145
If $p$ is an odd prime and $k$ an integer with $0<k<p-1$ then $1^k + 2^k + \ldots + (p-1)^k$ is divisible by $p$
68376
How, if at all, does pure mathematics benefit from $2^{74207281}-1$ being prime?
24988
Prove there exists $m > 2010$ such that $f(m)$ is not prime
10742
Powers of prime factors of a positive integer $n$ in "Mathematica"?
147485
A conjecture about numbers of the form $10^{m}(2^{k}−1)+2^{k-1}−1$, where $m$ is the number of decimal digits of $ 2^{k-1}$.
81250
Infinitude of prime numbers