Proof of Lesser/Fortunate Conjecture (c) JGW 2009

[bea...@gmail.com]

Turns out to be easiest to prove these two simultaneously:

p +/- y! = q

any_factor(p) > y <=> any_factor(q) > y [by modular arithmetic]

so, so long as p < y^2 OR q < y^2

p prime <=> q prime [by symmetry]

[bea...@gmail.com]

Actually, as I wrote to Joshua2 (on mersenneforum) - I'm no longer
100% certain this is a full proof (though I _think_ what I have here,
so far _is_ correct) - specifically, is there any reason to assume
that one of p, q WILL be < y^2 ? I don't know - it might still be
allright? If anyone can reassure me as to its completeness and/or
provide any missing step I'd be grateful...
thanks,
J