On 09/06/14 at 08:38pm, Steven D'Aprano wrote:
> But even that's not how the specialists do it. If you want to check whether
> (say) 2**3000+1 is prime, you don't want to use trial division at all...

When I was interested in these things, specialists would use the [number
field sieve](https://en.wikipedia.org/wiki/General_number_field_sieve).

I coded a Mathematica implementation fifteen years ago or so. It was a
lot of work :)

Manolo
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