Definition:Prime Number/Definition 4

Definition

A prime number $p$ is an integer greater than $1$ that has no positive integer divisors other than $1$ and $p$.

That is:

$\Bbb P = \set {p \in \N: \forall x \in \N, x \ne 1, x \ne p: x \nmid p}$

Also see

• Equivalence of Definitions of Prime Number

• Results about prime numbers can be found here.

Sources

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• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.2$: More about Numbers: Irrationals, Perfect Numbers and Mersenne Primes: Footnote $1$
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.16$: The Sequence of Primes
• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.1$: Mathematical Induction: Exercise $5$
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• For a video presentation of the contents of this page, visit the Khan Academy.