On Prime Determinants

When a number $k$ has the property that all prime numbers greater than $k$ are of the form $kn\pm 1$ where $n$ is an integer greater than 0, we say that $k$ is a prime determinant. In this paper, I will prove that 1, 2, 3, 4, 6 are prime determinants, and give reasons why no other numbers are.

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