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Academic Paper from the year 2023 in the subject Mathematics - Number Theory, grade: 2.00, , language: English, abstract: A procedure is developed for determining the primality of a number, N, but does not examine the number, rather a function of that number. The function has several properties, by means of which many of the non-primes may be identified and discarded without further investigation. Using the concept of cage numbers (defined in the text) a matrix of all of the counting numbers is produced, where, with the exception of the prime numbers 2 and 3, all of the prime numbers are embedded in one column of the matrix. Strings of consecutive numbers are extracted from the matrix, and it is seen that the only places within the whole of the range of the counting numbers where prime numbers can exist is at the positions of the second and penultimate numbers within a string By means of the function of N, all of the odd numbers may be generated and examined for primality.
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