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I've got a Python script that grinds out Amicable Pairs by trying out each integer: $i, i+1, i+2,\ldots$ . I've now found all APs with $1 \leq n \leq 65,000,000$. At this point I'm finding that it takes $24$ minutes per each additional million. To get into much larger $n$ I'll need to find a way to filter out substantial numbers of $n$ in advance. Have any been discovered?

My list of the first 202 APs: http://tutoree7.pastebin.com/dpEc0RbZ

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    Amicable pairs are studied in the literature as period two aliquot sequences, so using that keyword might point you to some relevant literature.2010-11-20
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    I actually recently just did a very similar thing with Gaussian integers in Sage, and even for smallish ones (norms around 20,000) it was taking a very long time, so I was wondering if I could rule things out in that case.2010-11-20

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