Further tabulation of the Erdös-Selfridge function

Abstract

For a positive integer k k , the Erdös-Selfridge function is the least integer g ( k ) > k + 1 g(k) > k+1 such that all prime factors of ( g ( k ) k ) \binom {g(k)}{k} exceed k k . This paper describes a rapid method of tabulating g ( k ) g(k) using VLSI based sieving hardware. We investigate the number of admissible residues for each modulus in the underlying sieving problem and relate this number to the size of g ( k ) g(k) . A table of values of g ( k ) g(k) for 135 ≤ k ≤ 200 135 \leq k \leq 200 is provided.