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The article focuses on the discussion concerning the developments in the theory of coverings, delivered by mathematician Carl Pomerance at the Joint Mathematics Meeting that was held on January 6-9, 2008 in San Diego, California. Pomerance states that theory of coverings refers to a collection of number sequences that which when integrated forms into a single integer. He provides a discussion on the arithmetic progression developed by Pace Nielsen which focuses on starting step size at 36 which results in a total of 1040 different arithmetic progressions. Pomerance asserts that coverings play significant role in the field of number theory which includes generating sequences that avoids prime numbers.