Bearing in mind that the first 10 billion zeros are on the critical line it seems likely that is is true.
Ah yes, but the first 10 billion swans looked at ( well maybe not quite that many) were white, ergo all swans are white. .... Fine until someone went to Australia. ( the abbos' all-swans-are-black theory unravelled at the same time of course).
I quite like the story of a group of the scientist, engineer & mathematician in a train to Scotland, when the engineer spots a black sheep in a field, "oh look, sheep are black in Scotland" . The scientist quickly points out that it's a bit of a generalisation, but agrees "there are some black sheep in Scotland". "no, no, no!" says the mathematician, "the most you can say, is that there appears to be at least one field in Scotland, that appears to contain at least one sheep, that appears to be black, ON AT LEAST ONE SIDE"
Say there's a hypothisis that says "all men are shorter than 100 feet" and you duly measure 10 billion men and sure enough, backs the hypothesis. Now then, what if you come across a 99 foot high man ?- which also "confirms" the hypothesis, but would make me doubt it.
My guess is that the Rieman hypothesis is true, but it could of course be unprovable, but that's a whole other story. By the way, there's a million dollar Clay prize if anyone proves it, (or disproves it) - but it must be said Mr Clay isn't exactly giving his money away.
Anyhow, that's enough of that, and I don't really pretend to understand it, nor really get the number theory links
I should just like to add that the previous statement means absolutely nothing to me.