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 + x^{2} |

3 | 1 + x + x^{3}, 1 + x^{2} + x^{3} |

4 | 1 + x+ x^{4}, 1 +x^{3} + x^{4} |

5 | 1 + x^{2} + x^{5}, 1 + x + x^{2} + x^{3} + x^{5}, 1 + x^{3} + x^{5}, 1 + x + x^{3} + x^{4} + x^{5}, 1 + x^{2} + x^{3} + x^{4} + x^{5}, 1 + x + x^{2} + x^{4} + x^{5}, |

More information and explanations can be found at http://mathworld.wolfram.com/PrimitivePolynomial.html