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Are all prime numbers composite?

Published in Prime Numbers 1 min read

No, prime numbers are not composite.

A number is either prime, composite, or neither (like 1). Prime and composite numbers are defined based on their factors:

  • Prime Number: A number greater than 1 that has exactly two distinct positive factors: 1 and itself. Examples include 2, 3, 5, 7, 11, and so on.

  • Composite Number: A number greater than 1 that has more than two distinct positive factors. Examples include 4 (1, 2, 4), 6 (1, 2, 3, 6), 8 (1, 2, 4, 8), and so on.

Therefore, prime numbers, by definition, cannot be composite, and composite numbers cannot be prime. They are mutually exclusive categories for integers greater than 1.

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