how does sage factor a Mersenne number?
E.g. 2^67-1. Does it simply have/use a lookup-table for Mersennes?
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By default, Sage delegates integer factorization to PARI, so you should have a look to their documentation and source code to know the details of the algorithm they use. It seems not to look at any table, since if you look to close numbers (e.g. 2^67-5), you will notice similar timings.
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