Primes
The first few highly cototient numbers which are primes (sequence A105440 in OEIS) are
- 2, 23, 47, 59, 83, 89, 113, 167, 269, 389, 419, 509, 659, 839.
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Totient function
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- Euler's totient function
- Jordan's totient function
- Nontotient
- Noncototient
- Highly totient number
- Sparsely totient number
- Highly cototient number
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Prime number classes
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| By formula |
- Fermat (22n + 1)
- Mersenne (2p − 1)
- Double Mersenne (22p−1 − 1)
- Wagstaff (2p + 1)/3
- Proth (k·2n + 1)
- Factorial (n! ± 1)
- Primorial (pn# ± 1)
- Euclid (pn# + 1)
- Pythagorean (4n + 1)
- Pierpont (2u·3v + 1)
- Solinas (2a ± 2b ± 1)
- Cullen (n·2n + 1)
- Woodall (n·2n − 1)
- Cuban (x3 − y3)/(x − y)
- Carol (2n − 1)2 − 2
- Kynea (2n + 1)2 − 2
- Leyland (xy + yx)
- Thabit (3·2n − 1)
- Mills (floor(A3n))
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| By integer sequence |
- Fibonacci
- Lucas
- Motzkin
- Bell
- Partitions
- Pell
- Perrin
- Newman–Shanks–Williams
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| By property |
- Lucky
- Wall–Sun–Sun
- Wilson
- Wieferich
- Wieferich pair
- Fortunate
- Ramanujan
- Pillai
- Regular
- Strong
- Stern
- Supersingular (elliptic curve)
- Supersingular (moonshine theory)
- Wolstenholme
- Good
- Super
- Higgs
- Highly cototient
- Illegal
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| Base-dependent |
- Happy
- Dihedral
- Palindromic
- Emirp
- Repunit (10n − 1)/9
- Permutable
- Circular
- Strobogrammatic
- Minimal
- Full reptend
- Unique
- Primeval
- Self
- Smarandache–Wellin
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| Patterns |
- Twin (p, p + 2)
- Triplet (p, p + 2 or p + 4, p + 6)
- Quadruplet (p, p + 2, p + 6, p + 8)
- Tuple
- Cousin (p, p + 4)
- Sexy (p, p + 6)
- Chen
- Sophie Germain (p, 2p + 1)
- Cunningham chain (p, 2p ± 1, …)
- Safe (p, (p − 1)/2)
- Arithmetic progression (p + a·n, n = 0, 1, …)
- Balanced (consecutive p − n, p, p + n)
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| By size |
- Titanic
- Gigantic
- Mega
- Largest known
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| Complex numbers |
- Eisenstein prime
- Gaussian prime
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| Composite numbers |
- Pseudoprime
- Almost prime
- Semiprime
- Interprime
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| Related topics |
- Probable prime
- Industrial-grade prime
- Formula for primes
- Prime gap
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List of prime numbers
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