Grimm, C. A. A conjecture on consecutive composite numbers. (English) Zbl 0197.32001 Am. Math. Mon. 76, 1126-1128 (1969). Page: −4 −3 −2 −1 ±0 +1 +2 +3 +4 Show Scanned Page Cited in 1 ReviewCited in 4 Documents Keywords:number theory × Cite Format Result Cite Review PDF Full Text: DOI Online Encyclopedia of Integer Sequences: Grimm numbers (1): a(n) = largest k so that for each m in {n+1, n+2, ..., n+k} there corresponds a different prime factor p_m. Grimm numbers (2): a(n) = largest k so that for each composite m in {n+1, n+2, ..., n+k} there corresponds a different divisor d_m with 1 < d_m < m. Consider the consecutive composite numbers between prime(n) and prime(n+1). Letting k=prime(n+1)-prime(n)-1, a(n) is the number of these numbers that have all primes factors less than k.