A primitive polynomial is a polynomial that generates all elements of an extension field from a base field. Primitive polynomials are also irreducible polynomials. The following table lists the primitive polynomials (mod 2) of orders 1 through 5.
n | primitive polynomials |
1 | 1 + x |
2 | 1 + x + x2 |
3 | 1 + x + x3, 1 + x2 + x3 |
4 | 1 + x+ x4, 1 +x3 + x4 |
5 | 1 + x2 + x5, 1 + x + x2 + x3 + x5, 1 + x3 + x5, 1 + x + x3 + x4 + x5, 1 + x2 + x3 + x4 + x5, 1 + x + x2 + x4 + x5, |
More information and explanations can be found at http://mathworld.wolfram.com/PrimitivePolynomial.html