query: A question in Number Theory - prove there exist m>2010 s.t f(m) is not prime
positive_passages.docid: 24988
positive_passages.text: Prove there exists $m > 2010$ such that $f(m)$ is not prime
negative_passages.docid: 73515
negative_passages.text: Primes Number Theory
negative_passages.docid: 24444
negative_passages.text: Prove that $371\cdots 1$ is not prime
negative_passages.docid: 123544
negative_passages.text: Show that $n = 3^{100} + 2$ is not a prime number.
negative_passages.docid: 31990
negative_passages.text: Is $\{\frac{m}{10^n}\mid m,n\in\mathbb Z,\ n\geq 0\}$ dense in $\mathbb R$?
negative_passages.docid: 56229
negative_passages.text: On the difference between consecutive primes
negative_passages.docid: 45341
negative_passages.text: $(m, m+2)$ is twin prime, iff $4((m-1)! + 1) \equiv -m \pmod {m(m+2)}$
negative_passages.docid: 76032
negative_passages.text: Prove that if m is a square integer then m is neither congruent to 2 modulo 5 nor congruent to 3 modulo 5
negative_passages.docid: 42932
negative_passages.text: Prove that $p^j q^i$ cannot be a perfect number for $p, q$ odd, distinct primes.
negative_passages.docid: 75685
negative_passages.text: Prove that there is prime number and natural so $n\times q$ digits are $1$.
negative_passages.docid: 77070
negative_passages.text: Prove Euler's Theorem when the integers are not relatively prime
negative_passages.docid: 89066
negative_passages.text: Find all integers less than $m$ that are relatively prime to it
negative_passages.docid: 66238
negative_passages.text: Proving $\mathbb{Z}[\sqrt {10}]$ is not a UFD
negative_passages.docid: 2147
negative_passages.text: Different ways to prove there are infinitely many primes?
negative_passages.docid: 126494
negative_passages.text: Prove that there doesn't exist any integer $x \ge 3$ such that $x^2-1$ is prime.
negative_passages.docid: 80658
negative_passages.text: Prove that the number $19\cdot8^n+17$ is not prime, $n\in\mathbb{Z}^+$
negative_passages.docid: 37947
negative_passages.text: Prove that if a number $n > 1$ is not prime, then it has a prime factor $\le \sqrt{n}$.