We define the primal and dual linear programming problems involving interval numbers as the way of traditional linear programming problems. We discuss the solution concepts of primal and dual linear programming problems involving interval numbers without converting them to classical linear programming problems. By introducing new arithmetic operations between interval numbers, we prove the weak...

It is shown that all positive integers can be divided into numbers that can lead to a pair of twin primes by a simple algebraic operation and numbers that cannot. The paper devises a formula for finding the numbers in each category, and shows that the numbers in the second category can be arranged in infinite groups and super-groups with an inner symmetry, a precise interval length and a well-d...