Therefore, with this prior, the chance of a trillion births is well over 20%, rather than the 5% chance given by the standard DA. If formula_13 is reduced further by assuming a flatter prior "N" distribution, then the limits on" N" given by "n" become weaker. An formula_13 of one reproduces Gott's calculation with a birth reference class, and formula_13 around 0.5 could approximate his temporal confidence interval calculation (if the population were expanding exponentially). As formula_22 (gets smaller) "n" becomes less and less informative about "N". In the limit this distribution approaches an (unbounded) uniform distribution, where all values of "N" are equally likely. This is Page et al.'s "Assumption 3", which they find few reasons to reject, "a priori". (Although all distributions with formula_23 are improper priors, this applies to Gott's vague-prior distribution also, and they can all be converted to produce proper integrals by postulating a finite upper population limit.) Since the probability of reaching a population of size 2"N" is usually thought of as the chance of reaching "N" multiplied by the survival probability from "N" to 2"N" it seems that Pr("N") must be a monotonically decreasing function of "N", but this doesn't necessarily require an inverse proportionality.