query: Why is it that the product of first N prime numbers + 1 another prime?
positive_passages.docid: 144050
positive_passages.text: Is there an infinite number of primes constructed as in Euclid's proof?
negative_passages.docid: 102064
negative_passages.text: Prime number between $n$ and $n!+1$
negative_passages.docid: 104753
negative_passages.text: $\sum_{k=1}^nH_k = (n+1)H_n-n$. Why?
negative_passages.docid: 50596
negative_passages.text: $p_1p_2...p_n +1$ is not square for $p_k = k$'th prime
negative_passages.docid: 79208
negative_passages.text: Is the number $-1$ prime?
negative_passages.docid: 78342
negative_passages.text: When is $\phi(n)$ a prime number?
negative_passages.docid: 22441
negative_passages.text: Does the sum of reciprocals of primes converge?
negative_passages.docid: 39915
negative_passages.text: Let $n$ be an integer such that if $d | n$ then $d + 1 | n + 1.$ Show that $n$ is a prime number
negative_passages.docid: 78259
negative_passages.text: Prime factorization
negative_passages.docid: 12751
negative_passages.text: What does var prime = num != 1; mean?
negative_passages.docid: 95111
negative_passages.text: 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.
negative_passages.docid: 111037
negative_passages.text: 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.
negative_passages.docid: 53967
negative_passages.text: distribution of prime numbers
negative_passages.docid: 10861
negative_passages.text: Let$\ p_n$ be the$\ n$-th prime. Can you give me a proof for$\ \prod_{i=1}^\infty \frac{p_i-1}{p_i}=P\approx \frac{1}{11.0453}$?
negative_passages.docid: 75378
negative_passages.text: how to prove this extended prime number theorem?
negative_passages.docid: 140006
negative_passages.text: Are there infinitely many primes and non primes of the form $10^n+1$?
negative_passages.docid: 48587
negative_passages.text: Why is $1$ not a prime number?