Balanced primes
Bell primes
Carol primes
Chen primes
Circular primes
Cousin primes
Cuban primes
Cullen primes
Dihedral primes
Eisenstein primes without imaginary part
Emirps
Euclid primes
Euler irregular primes
Euler (p, p − 3) irregular primes
Factorial primes
Fermat primes
Generalized Fermat primes
Fibonacci primes
Fortunate primes
Gaussian primes
Good primes
Happy primes
Harmonic primes
Higgs primes for squares
Highly cototient primes
Home primes
Irregular primes
(p, p − 3) irregular primes
(p, p − 5) irregular primes
(p, p − 9) irregular primes
Isolated primes
Kynea primes
Leyland primes
Long primes
Lucas primes
Lucky primes
Mersenne primes
Mersenne divisors
Mersenne prime exponents
Double Mersenne primes
Generalized repunit primes
Other generalizations and variations
Mills primes
Minimal primes
Newman–Shanks–Williams primes
Non-generous primes
Palindromic primes
Palindromic wing primes
Partition primes
Pell primes
Permutable primes
Perrin primes
Pierpont primes
Pillai primes
Primes of the form n4 + 1
Primeval primes
Primorial primes
Proth primes
Pythagorean primes
Prime quadruplets
Quartan primes
Ramanujan primes
Regular primes
Repunit primes
Residue classes of primes
Safe primes
Self primes in base 10
Sexy primes
Smarandache–Wellin primes
Solinas primes
Sophie Germain primes
Stern primes
Strobogrammatic primes
Super-primes
Supersingular primes
Thabit primes
Prime triplets
Truncatable prime
Left-truncatable
Right-truncatable
Two-sided
Twin primes
Unique primes
Wagstaff primes
Wall–Sun–Sun primes
Weakly prime numbers
Wieferich primes
Wilson primes
Wolstenholme primes
Woodall primes