Can any number of the form $2p$, for $p>3$ a prime, be written as the sum of two distinct primes?
53231
A slightly stronger version of the Goldbach conjecture?
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.
71110
Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$
157766
Are primes (ignoring $2$) equally likely to be $1~\text{or}~3\pmod 4$?
5142
Infinitely many primes of the form $pn+1$
118629
$p,q$ odd primes, $q\mid a^p-1\Rightarrow q\mid a-1$ or $\,2p\mid q-1$
34617
Number Theory: which primes are a sum of two squares?
140412
If $p$ and $q$ are distinct primes such that $p|c$ and $q|c$, prove that $pq|c$
12365
Show that every prime $p>3$ is either of the form $6n+1$ or of the form $6n+5$
84167
Regarding the sum $\sum_{p \ \text{prime}} \sin p$
132928
Digits of $\pi$ forming primes?
98468
Are there infinitely many primes of the form $n!+1$?
20881
Prove that if $p$ and $q$ are distinct primes such that $pq\mid n^2$ then $pq\mid n$.
2264
Conjecture: the sequence of sums of all consecutive primes contains an infinite number of primes
31267
Sum of all primes under 2 million
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
65764
Partitioning $\{1,2,\ldots,k\}$ into $p$ subsets with equal sums, where $p$ is prime