Semiprimes are positive integers of the form n = p*q where p and q are primes that are not necessarily distinct. Semiprimes can occur in arithmetic sequence, and the upper bound changes depending on the distance, d, between semiprimes in the sequence. The goal of this work is to present and prove theorems for different cases of semiprime arithmetic sequences, including d = 2k+1 where k is greater than or equal to 0 and d=2k where k is positive and not a multiple of 3, as well as a general case for finding upper bounds for varying distances. The building of semiprime arithmetic sequences off of prime arithmetic sequences as well as the longest semiprime arithmetic sequences found are also included.
Mike Pinter, Ph.D.
Uselton, Sam C., "A Study of Semiprime Arithmetic Sequences" (2022). Honors Theses. 67.