There is a list of base 2 pseudoprimes up to 2

^{64}.

http://www.janfeitsma.nl/math/psp2/index
When you guys were doing the search up to 2

^{64} it would have been faster to do the Lucas test only if the number was a known 2-PSP.

Unfortunately the list only goes up to 2

^{64}. Is there a fast way to generate the list of 2-PSP. When checking for gaps we need to do one Lucas test for every 1400 numbers. To check from 2

^{64} to 2

^{64} + 2.33 * 10

^{16} (Gap=1552) would require 1.66*10

^{13} Lucas tests. Can the list of 2-PSP be computed faster than this? We wouldn't even need to rerun what has already been done. We could just check for large gaps around the 2-PSPs.