Is 31 the only number that can be represented by two distinct sums of consecutive powers of primes?
39698
On uniqueness of sums of prime powers
136832
Is 128 the only multi-digit power of 2 such that each of its digits is also a power of 2?
149241
What is the maximum number of consecutive composite numbers possible?
73515
Primes Number Theory
135892
Understanding the proof for showing that there are infinitely many $n\in\mathbb{Z}^+$ such that $n!+1$ is divisible by at least two distinct primes
111037
Consider numbers of the type $n=2^m+1$. Prove that such an n is prime only if $n=F_K$ for some $ k \in N$, where $F_k$ is a Fermat Prime.
152591
For which prime numbers $p$ does the congruence $x^2 + x + 1 \equiv 0 \pmod{p}$ have solutions?
12862
Prove that two distinct numbers of the form $a^{2^{n}} + 1$ and $a^{2^{m}} + 1$ are relatively prime if $a$ is even and have $\gcd=2$ if $a$ is odd
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.
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
56229
On the difference between consecutive primes
27963
How many ways a composite number can be resolved into two factors which are prime to each other?
42932
Prove that $p^j q^i$ cannot be a perfect number for $p, q$ odd, distinct primes.
62792
Can sum of a rational number and its reciprocal be an integer?
25428
Prime numbers of the form $ n^{34} -9$
132928
Digits of $\pi$ forming primes?
132728
Can the sum of the first $p$ factorials ever be a perfect power for $\ p>3\ $?