- Any natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
- Any natural number (including 1) that is divisible only by itself and 1.

- additive prime number
- annihilating prime number
- Bell number prime number
- Carol prime number
- Catalan prime number
- centered decagonal prime number
- centered heptagonal prime number
- centered square prime number
- centered triangular prime number
- Chen prime number
- circular prime number
- cousin prime number
- Cuban prime number
- Cullen prime number
- Delannoy number prime number
- deletable prime number
- dihedral prime number
- double factorial prime number
- double Mersenne prime number
- Eisenstein prime number without imaginary part
- emirp
- Euclid prime number
- Euclid-Mullin Sequence prime number
- Euler irregular prime number
- even prime number
- factorial prime number
- Fermat prime number
- Fibonacci prime number
- fortunate prime number
- Gaussian prime number
- generalized Fermat prime number base 10
- Genocchi number prime number
- Gilda's prime number
- good prime number
- happy prime number
- harmonic prime number
- Higgs prime number for squares
- highly cototient number prime number
- irregular prime number
- isolated prime number
- Kynea prime number
- left-truncatable prime number
- Leyland prime number
- long prime number
- Lucas prime number
- lucky prime number
- Markov prime number
- Mersenne prime number
- Mills prime number
- minimal prime number
- Motzkin prime number
- Newman–Shanks–Williams prime number
- non-generous prime number
- odd prime number
- Padovan prime number
- palindromic prime number
- palindromic wing prime number
- partition prime number
- Pell prime number
- permutable prime number
- Perrin prime number
- Pierpont prime number
- Pillai prime number
- prime number of Binary Quadratic Form
- primeval prime number
- primorial prime number
- Proth prime number
- Pythagorean prime number
- Quartan prime number
- Ramanujan prime number
- regular prime number
- repunit prime number
- right-truncatable prime number
- safe prime number
- Schröder prime number
- Schröder-Hipparchus number prime number
- self prime number
- sexy prime number
- Smarandache-Wellin prime number
- Smarandache–Wellin prime number
- Solinas prime number
- Sophie Germain prime number
- star prime number
- Stern prime number
- super-prime number
- supersingular prime number
- swinging prime number
- Thabit number prime number
- twin prime number
- two-sided prime number
- Ulam number prime number
- unique prime number
- Wagstaff prime number
- Wall–Sun–Sun prime number
- Weakly prime numbers
- Wedderburn-Etherington number prime number
- Wieferich prime number
- Wilson prime number
- Wolstenholme prime number
- Woodall prime number

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