Sigh,
I now realize this was a test for the OP to show how well his method works. Well, ok um you can use the rest of this as a comparison I guess.
Quote:
Originally Posted by bbb120
please tell me the least twin primes which great than 10^1000

10^1000 + 9705091 is the smaller of the pair.
I'm sure it's online somewhere. It took about 2 minutes for my Macbook to find it. They are ES BPSW, and then I let Pari/GP prove them, a little over 1 minute each.
The software I used have chosen 80000 * log
_{2}(high) as the depth, purely because empirically that seemed to work well at a variety of sizes. Each candidate that passes this sieve is subjected to MR base 2 for both low and high, then ES Lucas for both low and high. It took 2.5 seconds for a width of 1e5, 13s for 1e6, 124s for 1e7 where it found one (I just ran it multiple times with a bigger window, redoing the previous part).