query: Can a polynomial return only prime numbers?
positive_passages.docid: 156940
positive_passages.text: There does not exist a polynomial $p(x)$ with integer coefficients which gives a prime number $\forall x\in \mathbb{Z}$
negative_passages.docid: 147047
negative_passages.text: Does there exist a polynomial $p(x) \in \mathbb C[x]$ such that $p(x) \notin \mathbb R[x]$ and $p(x)p(-x)=p(x^2)$?
negative_passages.docid: 137218
negative_passages.text: Does there exist a polynomial $f(x)$ with real coefficients such that $f(x)^2$ has fewer nonzero coefficients than $f(x)$?
negative_passages.docid: 53012
negative_passages.text: Irreducibility of a polynomial if it has no root (Capelli)
negative_passages.docid: 105679
negative_passages.text: Can $\pi$ or $e$ be a root of a polynomial with algebraic coefficients?
negative_passages.docid: 63493
negative_passages.text: Why 4 is not a primitive root modulo p for any prime p?
negative_passages.docid: 115758
negative_passages.text: Remainder of division when $p$ is not prime
negative_passages.docid: 73612
negative_passages.text: Is there a Non-prime Number that is Divisible only by Numbers Greater than its Square Root?
negative_passages.docid: 135768
negative_passages.text: Find $P(n+1)$ for a polynomial P
negative_passages.docid: 65511
negative_passages.text: Proving the following false: $f(x)=2x+1$ produces a prime number if and only if x is prime
negative_passages.docid: 87101
negative_passages.text: Irreducible but not prime in $K[X,Y]/(X^2-Y^3)$
negative_passages.docid: 34864
negative_passages.text: Can I select a large random prime using this procedure?
negative_passages.docid: 80907
negative_passages.text: Primes dividing a polynomial
negative_passages.docid: 75733
negative_passages.text: Divisibility of prime numbers
negative_passages.docid: 133975
negative_passages.text: Localising a polynomial ring and non-maximal prime ideal
negative_passages.docid: 45954
negative_passages.text: How to get a list of monomials of a polynomial without coefficients?
negative_passages.docid: 134068
negative_passages.text: When polynomials f(x) and f'(x) are relatively prime, f(x) has no repeated roots. Why?