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Is there a polynomial that takes infinitely many prime values?

Is there a polynomial that takes infinitely many prime values?

I merely add that what is conjectured is that if an irreducible polynomial f(x)∈Z[x] satisfies 1=gcd{f(1),f(2),f(3),f(4),…} then f(n) is prime for infinitely many n. This is known as Bunyakovsky’s conjecture. It has not been proven for any polynomial of degree greater than 1.

What are some methods for determining if a polynomial is prime?

If the only factors a polynomial are 1 and itself, then that polynomial is prime. To learn all about prime polynomials, check out this tutorial!

Is there a function to generate prime numbers?

Legendre showed that there is no rational algebraic function which always gives primes. In 1752, Goldbach showed that no polynomial with integer coefficients can give a prime for all integer values (Nagell 1951, p.

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What is a prime Trinomial?

A prime trinomial is a trinomial that cannot be factored over the rational numbers. That is, if a trinomial is prime, then it cannot be written as the product of two binomials with rational coefficients and constants.

Is x2 9 a prime polynomial?

The polynomial x2−9 x 2 – 9 is not prime because the discriminant is a perfect square number.

What makes a polynomial irreducible?

A polynomial is said to be irreducible if it cannot be factored into nontrivial polynomials over the same field.

Can prime numbers be predicted?

Although whether a number is prime or not is pre-determined, mathematicians don’t have a way to predict which numbers are prime, and so tend to treat them as if they occur randomly.

Which is the largest prime number?

Currently, the largest known prime number is 282,589,933−1. This prime, along with the previous seven largest primes to be discovered, are known as Mersenne primes, named after the French mathematician Marin Mersenne (1588–1648).

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Are all prime numbers odd?

First, except for the number 2, all prime numbers are odd, since an even number is divisible by 2, which makes it composite. So, the distance between any two prime numbers in a row (called successive prime numbers) is at least 2.

Is 15×2 10x 9x 7 a prime polynomial?

The polynomial 15×2+10x−9x+7 15 x 2 + 10 x – 9 x + 7 is prime because the discriminant is not a perfect square number.