Let $f(x) = x^2 + x + 41$. Show that $f(n)$ is prime for $0 \le n \le 39$, but $f(40)$ is composite.
63999
Is the notorious $n^2 + n + 41$ prime generator the last of its type?
80242
Prove that $n^{2003}+n+1$ is composite for every $n\in \mathbb{N} \backslash\{1\}$
58114
For which primes p is $p^2 + 2$ also prime?
131488
Show that $p^3+4$ is prime
81221
The prime number theorem over a finite field - Lang's *Algebra*, Chapter V, Exercise 23(b)
68221
Question regardles primes and the fundamental theorem of arithmetic
120147
For what prime numbers $p$ is $x^2+x+1$ irreducible in $\mathbb{F}_p[X]$
92737
primes whose difference is a multiple of $n$
92483
Without using prime factorization, find a prime factor of $\frac{(3^{41} -1)}{2}$
146304
prove $(n)$ prime ideal of $\mathbb{Z}$ iff $n$ is prime or zero
2593
Proof for Mersenne primes?
40968
show if $n=4k+3$ is a prime and ${a^2+b^2} \equiv 0 \pmod n$ , then $a \equiv b \equiv 0 \pmod n$
24988
Prove there exists $m > 2010$ such that $f(m)$ is not prime
130846
Prove or disprove: If $a \in \mathbb{Z}$, $a > 0$, and $p$ is a prime such that $p^4 \mid a^3$, then $p^2 \mid a$.
84603
Prove that if $p$ is a prime such that $p^2+2$ is a prime then $p=3$.
70308
Prove that if $p$ and $p+2$ are both prime integers greater than $3$, then $6$ is a factor of $p+1$.
119657
If $ f _p(x)=1+x+x^2+ \cdots +x^{p-1} $ where $p$ is prime number, $e$ is any positive integer.