WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

The Bouniakowsky Conjecture

​
range
100
coefficients of:
5
x
0
4
x
0
3
x
0
2
x
1
1
x
1
0
x
41
In 1857, Bouniakowsky conjectured that if
f(x)
is an irreducible polynomial,
f(x)/gcd(f(0),f(1))
generates an infinite number of primes. Dirichlet proved the conjecture for
ax+b
. Beyond that, neither proofs nor counterexamples are known. Here, a signed logplot is given for a variety of polynomials, with red dots indicating primes.
Wolfram Cloud

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.