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?

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# Pocklington's Criterion?

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