LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

FURTHER TABULATION OF THE ERDÖS-SELFRIDGE FUNCTION

Abstract. For a positive integer k, the Erdös-Selfridge function is the least integer g(k)> k + 1 such that all prime factors of �g(k) � exceed k. This k paper describes a rapid method of tabulating 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). A table of values of g(k) for 135 ≤ k ≤ 200 is provided. 1

Further Tabulation of the Erdös-Selfridge Function ∗

For a positive integer k, the Erdös-Selfridge function is the least integer g(k)> k + 1 such that all prime factors of � � g(k) exceed k. This k paper describes a rapid method of tabulating 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). A table of values of g(k) for 135 ≤ k ≤ 200 is provided.