If we do 'pbinom(1,10^10,0.5)', R returns answer zero as we expected;
If we do 'pbinom(1,3.239*10^10,0.5)', R returns answer zero as we expected;
If we do 'pbinom(1,3.241*10^10,0.5)', R returns answer zero as we expected;
If we do 'pbinom(1,3.240*10^10,0.5)', R returns answer 'NaN' as we unexpected!
Very odd, although it is a minor bug as my understanding.
In pbinom(1, 3.24 * 10^10, 0.5) : NaNs produced
FAQ 7.31 is correct.
OTOH, note that our check is R_nonint(n) ['n' is R-level 'size'],
and that is defined in nmath.h as
# define R_nonint(x) (fabs((x) - R_forceint(x)) > 1e-7)
and R_forceint() is typically nearbyint() nowadays,
but I think we should improve the check to become relative, at least for non-small x.