The largest known twin prime is (33218925*(2^169690))-1.

http://primes.utm.edu/top20/page.php?id=1
I think (but I'm not sure) that the other twin is (33218925*(2^169690))+1. The website didn't make that very clear.

However, a quick check on a calculator reveals that none of the 20 twin primes have a middle number divisible by 1997.

EDIT:

http://perso.wanadoo.fr/yves.gallot/...rcds.html#twin makes it clear that (33218925*(2^169690))+1 is indeed the other twin.