http://mathworld.wolfram.com/PocklingtonsCriterion.html(adsbygoogle = window.adsbygoogle || []).push({});

I'm confused by the statement of this theorem. Either there's a mistake in the explanation, or I'm missing something pretty big.

Let me take an example and go through step by step. Let p=3 and k=4. p is an odd prime and 1 <= 4 <= 8. 3 does not divide 4.

The statement on MathWorld seems to say that 1 and 2 are equivilent:

1. 25 = 2 * 4 * 3 + 1 is prime.

2. There exists an a such that GCD(a^4+1, 25)=1.

5*5=25 is not prime. Checking briefly:

GCD(1,25)=1

GCD(2,25)=1

GCD(17,25)=1

GCD(82,25)=1

GCD(257,25)=1

GCD(626,25)=1

What am I misunderstanding?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Pocklington's Criterion?

Loading...

Similar Threads - Pocklington's Criterion | Date |
---|---|

Criterion for (non)decomposability of a representation? | Jul 25, 2013 |

Rings: Eisenstein criterion | May 26, 2012 |

Sylvester's Criterion for Infinite-dimensional Matrices | Apr 26, 2012 |

Primality Criterion for F_n(132) | Feb 22, 2012 |

**Physics Forums - The Fusion of Science and Community**