Number Representations & States

"how numbers are stored and used in computers"

Types of primes

Balanced primes

A prime number that is the arithmetic mean of the nearest prime above and below it

Bell primes

Prime numbers that are also Bell numbers, which count the number of ways to partition a set

Catalan primes

Prime numbers that are also Catalan numbers, which appear in various counting problems

Chen primes

Prime numbers p where p + 2 is either prime or a product of two primes

Circular primes

Prime numbers that remain prime after any cyclic rotation of their digits

Cluster primes

Groups of consecutive prime numbers that are unusually close together

Cousin primes

Pairs of prime numbers that differ by 4

Cuban primes

Prime numbers that can be expressed as the difference of two consecutive cube numbers

Cullen primes

Prime numbers of the form n × 2^n + 1, where n is a positive integer

Delicate primes

Prime numbers that become composite when any single digit is altered

Dihedral primes

Prime numbers that remain prime when read forwards, backwards, upside down, or in a mirror

Eisenstein primes

Prime numbers in the Eisenstein integers, a complex number system

Emirp primes

Prime numbers that yield a different prime number when their digits are reversed

Euclid primes

Prime numbers formed by multiplying the first n primes and adding 1

Euler irregular primes

Prime numbers that divide the numerators of certain Bernoulli numbers

Factorial primes

Prime numbers that are one more or one less than a factorial

Fermat primes

Prime numbers of the form 2^(2^n) + 1, where n is a non-negative integer

Fibonacci primes

Prime numbers that are also Fibonacci numbers

Fermat primes

Prime numbers of the form 2^(2^n) + 1, where n is a non-negative integer

Fortunate primes

The smallest prime number that needs to be added to avoid gaps in the primorial sequence

Gaussian primes

Prime numbers in the Gaussian integers, which are complex numbers with integer coordinates

Good primes

Prime numbers p where the number of solutions to certain congruences follows a specific pattern

Happy primes

Prime numbers that eventually reach 1 when repeatedly replacing the number by the sum of squares of its digits

Harmonic primes

Prime numbers p where the harmonic numbers H(p-1) have certain divisibility properties

Higgs primes

Prime numbers related to certain particle physics calculations

Highly cototient primes

Prime numbers that appear frequently as values of the cototient function

Home primes

Numbers that eventually reach a prime through iterative digit multiplication

Irregular primes

Prime numbers that divide the class number of certain cyclotomic fields

Isolated primes

Prime numbers with no other primes nearby within a certain distance

Leyland primes

Prime numbers of the form x^y + y^x where x and y are integers greater than 1

Long primes

Prime numbers where the decimal expansion of their reciprocal has a particularly long period

Lucas primes

Prime numbers that appear in the Lucas sequences

Lucky primes

Prime numbers that are also lucky numbers in the sieve of Josephus

Mersenne primes

Prime numbers of the form 2^n - 1, where n is a positive integer

Mills primes

Prime numbers generated by Mills' constant through floor function iteration

Minimal primes

Prime numbers that cannot be made smaller by changing any single digit

Newman-Shanks-Williams primes

Prime numbers that appear in the Newman-Shanks-Williams number sequence

Non-generous primes

Prime numbers that do not give away too many residues in their multiplicative group

Palindromic primes

Prime numbers that read the same forwards and backwards

Partition primes

Prime numbers related to the partition function in number theory

Pell primes

Prime numbers that appear in the Pell number sequence

Permutable primes

Prime numbers that remain prime under any permutation of their digits

Perrin primes

Prime numbers that appear in the Perrin sequence

Pierpont primes

Prime numbers of the form 2^u × 3^v + 1, where u and v are non-negative integers

Pillai primes

Prime numbers p where p - 1 divides the factorial of p-1

Primes of quadratic square plus one

Prime numbers that can be expressed as n^2 + 1 for some integer n

Primeval primes

Prime numbers that appear early in certain sequences related to prime counting

Primorial primes

Prime numbers that are one more or one less than the product of the first n primes

Proth primes

Prime numbers of the form k × 2^n + 1, where k is odd and less than 2^n

Pythagorean primes

Prime numbers that can be expressed as the sum of two square numbers

Quadratic primes

Prime numbers generated by quadratic polynomials

Quartan primes

Prime numbers related to certain quartic number fields

Ramanujan primes

The nth Ramanujan prime is the smallest number such that there are at least n primes in any interval of given length

Regular primes

Prime numbers that do not divide the class number of certain cyclotomic fields

Repunit primes

Prime numbers consisting only of ones in their decimal representation

Residue classes of primes

Prime numbers that belong to specific arithmetic progressions

Safe primes

Prime numbers p where (p-1)/2 is also prime

Self primes

Prime numbers with special properties related to their digit sum

Sexy primes

Pairs of prime numbers that differ by 6

Smarandache-Wellin primes

Prime numbers formed by concatenating the first n prime numbers

Solinas primes

Prime numbers of special form used in cryptography

Sophie Germain primes

Prime numbers p where 2p + 1 is also prime

Stern primes

Prime numbers that appear in the Stern sequence

Super primes

The nth super prime is the nth prime number in the sequence of prime numbers

Supersingular primes

Prime numbers related to certain elliptic curves

Thabit primes

Prime numbers of the form 3 × 2^n - 1, where n is a positive integer

Prime triplets

Three consecutive prime numbers that are as close as possible to each other

Truncatable primes

Prime numbers that remain prime when digits are successively removed from left to right or right to left

Twin primes

Pairs of prime numbers that differ by 2

Unique primes

Prime numbers with unique properties not shared by other categories

Wagstaff primes

Prime numbers of the form (2^p + 1)/3, where p is an odd prime

Wall-Sun-Sun primes

Prime numbers that satisfy certain congruences related to Fibonacci numbers

Wieferich primes

Prime numbers p where 2^(p-1) - 1 is divisible by p^2

Wilson primes

Prime numbers p where the Wilson quotient (p-1)! + 1 is divisible by p^2

Wolstenholme primes

Prime numbers p where certain binomial coefficients satisfy special congruences modulo p^3

Woodall primes

Prime numbers of the form n × 2^n - 1, where n is a positive integer

Wright primes

Prime numbers with special properties related to certain arithmetic functions