I have recently read in a dataset with p<10e343 that has been set to zero. So here is what the R documentation says
.Machine # the smallest non-zero normalized floating-point number, a power of the radix, i.e., double.base ^ double.min.exp. $double.xmin 2.225074e-308 # the largest normalized floating-point number. Typically, it is equal to (1 - double.neg.eps) * double.base # ^ double.max.exp, but on some machines it is only the second or third largest such number, being too small # by 1 or 2 units in the last digit of the significand $double.xmax 1.797693e+308