Distributions of Mersenne divisors
Sidney Kravitz · Mathematics of Computation · 1966
necessarily long proofs of theorems), are usually due to one of two phenomena: First, there is a true redundancy, whereby two phases of the computation (proof) merely cancel each other out. See [6] for the analysis of such a theorem proof. Secondly, the computation (proof) does more than is really needed, or wanted. See [7] for such a theorem proof. In our present case the inefficiency is clearly of the second type. Finally, we note that D. H. Lehmer, in [4], showed how most of the subtractions in (10) could also be eliminated. It is not necessary to compute every ./nyfl+' , but merely those at periodic intervals. It was his method that was used here in computing Table 1. Any interested reader will now have no difficulty in determining precisely how Lehmer manages to obtain this still greater efficiency.