I didn't want to go so much in details and confuse the man. :D
Oliver said few times that the [URL="http://www.mersenneforum.org/showpost.php?p=251781&postcount=575"]exponent is limited to 32 bits[/URL], does it matter? For higher, use Factor5 or so. I was one of the guys asking long ago about factoring OBD exponents, and got reply from Uncwilly about Factor5, the discussion is somewhere around.

edit @Dubslow: size of k does not limit the size of the expo. When expo gets higher, k gets smaller. The factor candidate has to fit the barret/whatever/kernel when squared mod factor. The expo is just a string of bits which says how many times you do the square-shift trick.

[QUOTE=LaurV;306169]
edit @Dubslow: size of k does not limit the size of the expo. When expo gets higher, k gets smaller. The factor candidate has to fit the barret/whatever/kernel when squared mod factor. The expo is just a string of bits which says how many times you do the square-shift trick.[/QUOTE]

:doh!:

Yeah, I screwed up. Too lazy to care though.