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Academic Paper from the year 2023 in the subject Mathematics - Analysis, grade: 2.00, , language: English, abstract: In previous work we have shown conclusively that the prime numbers can only exist at particular locations in the range of the counting numbers. A method of investigating the primality of the numbers at these locations is developed here and uses only multiplication tables. A single equation is derived which, in a sense bifurcates into two slightly different forms upon the making of one term explicit. We can even extend the simplest definition of a prime number expressed in [5] by the addition of the phrase ‘ and can only possibly be found in the range of the counting numbers at positions on either side of any number which is divisible by 6 ’.