Coupling Special Pair of Rectangles with Woodall and Euclid Primes

This study aims to systematically identify pairs of rectangles wherein the sum of their respective areas corresponds precisely to either a Woodall prime or a Euclid prime. For each such prime encountered, the investigation further delineates the total number of contributing rectangle pairs, with a clear distinction drawn between primitive configurations—those with co-prime side lengths—and non-primitive ones, which may share common factors. Key Words: Pair of rectangles, Woodall prime, Euclid Prime, Primitive, Non-primitive, Area.