# Primitive Polynomials

Primitive polynomials for Galois field generation up to GF(2^1200), GF(3^660), GF(5^430), and GF(7^358)

(2644 elements)

## Examples

### Basic Examples

Retrieve the resource:

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Retrieve the default content:

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### Visual Examples

Show the data for GF(267). The number 267-1 has a factorization 193707721×761838257287 (Cole, 1903) that gives a normalization close to 1:

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Generate the first 600 powers of x using a polynomial modulus of 1+x+x2+x5+x67:

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Show the approximate count via multiplication of the count normalization by (pn-1)/n and compare that to the actual polynomial count:

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Show the count normalizations for the first four primes:

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Show the degrees where trinomial primitive polynomials exist for the first four primes:

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Wolfram Research, "Primitive Polynomials" from the Wolfram Data Repository. (2017) https://doi.org/10.24097/wolfram.48521.data