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@PeterHeinig Thank you for the tag. I too hate broken links and try to keep things up to date. So this time around, I shall post a self-housed version of the link and in the future update it should I move it. Luckily, even if the typeset version goes the post of Tao with Emerton's wonderful response remains.
Shouldn't Erdös technically have an Erdös number of $2$? He hasn't published with Erdös but he has published with someone that has published with Erdös. This is similar to the 'issue' that prompted Conway to suggest that $-1$ is prime.