Where N is this case represents 1 collision per second. This means, on a per collision basis, the probability that the proton proton chain is initiated is very small (10^-17)

The total lifetime of the proton fuel is then given by the actual collision rate R_col * (10^-17)

or

4 x 10⁷ * (10^-17) = 4 x 10¹⁶ s ~ 10¹⁰ yrs