Template:Prime number classes

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Prime number classes

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v t e Prime number classes
By formula	[[Fermat number\|Fermat ( $2 2 n + 1$ )]] [[Mersenne prime\|Mersenne ( $2 p - 1$ )]] [[Double Mersenne number\|Double Mersenne ( $2 2 p -1 - 1$ )]] [[Wagstaff prime\|Wagstaff $(2 p + 1)/3$ ]] [[Proth prime\|Proth ( $k \cdot2 n + 1$ )]] [[Factorial prime\|Factorial ( $n! \pm 1$ )]] [[Primorial prime\|Primorial ( $p n # \pm 1$ )]] [[Euclid number\|Euclid ( $p n # + 1$ )]] [[Pythagorean prime\|Pythagorean ( $4 n + 1$ )]] [[Pierpont prime\|Pierpont ( $2 m \cdot3 n + 1$ )]] [[Quartan prime\|Quartan ( $x 4 + y 4$ )]] [[Solinas prime\|Solinas ( $2 m \pm 2 n \pm 1$ )]] [[Cullen number\|Cullen ( $n \cdot2 n + 1$ )]] [[Woodall number\|Woodall ( $n \cdot2 n - 1$ )]] [[Cuban prime\|Cuban ( $x 3 - y 3)/(x - y$ )]] [[Leyland number\|Leyland ( $x y + y x$ )]] [[Thabit number\|Thabit ( $3\cdot2 n - 1$ )]] [[Williams number\|Williams ( $(b -1)\cdot b n - 1$ )]] [[Mills' constant\|Mills ( $⌊ A 3 n ⌋$ )]]
By integer sequence	Fibonacci Lucas Pell Newman–Shanks–Williams Perrin Partitions Bell Motzkin
By property	Wieferich (pair) Wall–Sun–Sun Wolstenholme Wilson Lucky Fortunate Ramanujan Pillai Regular Strong Stern Supersingular (elliptic curve) Supersingular (moonshine theory) Good Super Higgs Highly cototient Unique
Base-dependent	Palindromic Emirp [[Repunit\|Repunit $(10 n - 1)/9$ ]] Permutable Circular Truncatable Minimal Delicate Primeval Full reptend Unique Happy Self Smarandache–Wellin Strobogrammatic Dihedral Tetradic
Patterns	[[Twin prime\|Twin ( $p, p + 2$ )]] [[Bi-twin chain\|Bi-twin chain ( $n \pm 1, 2 n \pm 1, 4 n \pm 1, \dots$ )]] [[Prime triplet\|Triplet ( $p, p + 2 or p + 4, p + 6$ )]] [[Prime quadruplet\|Quadruplet ( $p, p + 2, p + 6, p + 8$ )]] k-tuple [[Cousin prime\|Cousin ( $p, p + 4$ )]] [[Sexy prime\|Sexy ( $p, p + 6$ )]] Chen [[Safe and Sophie Germain primes\|Sophie Germain/Safe ( $p, 2 p + 1$ )]] [[Cunningham chain\|Cunningham ( $p, 2 p \pm 1, 4 p \pm 3, 8 p \pm 7, ...$ )]] [[Primes in arithmetic progression\|Arithmetic progression ( $p + a\cdotn, n = 0, 1, 2, 3, ...$ )]] [[Balanced prime\|Balanced ( $consecutive p - n, p, p + n$ )]]
By size	Mega (1,000,000+ digits) Largest known list
Complex numbers	Eisenstein prime Gaussian prime
Composite numbers	Pseudoprime Catalan Elliptic Euler Euler–Jacobi Fermat Frobenius Lucas Somer–Lucas Strong Carmichael number Almost prime Semiprime Interprime Pernicious
Related topics	Probable prime Industrial-grade prime Illegal prime Formula for primes Prime gap
First 60 primes	2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281
List of prime numbers

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