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Neither 1 nor 100 are prime numbers. To be prime, a number must have exactly two factors; itself and 1. Neither 1 nor 100 fall into this category of numbers.

The number 1 is neither prime nor composite because it has only one factor; itself. If 1 were to be regarded as being prime, then the Fundamental Theorem of Arithmetic would not hold. That is; every whole number greater than one can be expressed uniquely (except for their order) as the product of prime numbers. But if 1 were prime then the uniqueness aspect would fail because n = 1*n = 1*1*n = 1*1*1*n and so on. 1 is therefore a special class of number that is neither prime or composite, we simply refer to it as a unit.

The number 100 is a composite number because it has many factors besides itself and one; 1, 2, 4, 5, 10, 20, 25, 50 and 100 are all factors of 100.

Any algorithm that regards either the unit 1 or the composite 100 as being a Prime number is clearly not a valid algorithm.

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