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- Abc conjecture
- Abelian group
- Abundant number
- Agoh-Giuga conjecture
- All ones function
- Arithmetic derivative
- Arithmetic function
- Artin's conjecture on primitive roots
- Artin's conjecture on primitive roots for two
- Asymptotic density
- Beal conjecture
- Beal conjecture fails over Gaussian integers
- Bertrand's postulate
- Bitwin chain
- Brahmagupta-Fibonacci two-square identity
- Brocard's problem
- Brun's theorem
- Bunyakovsky conjecture
- Calkin-Wilf tree
- Carmichael number
- Carmichael number is not semiprime
- Carmichael number is square-free
- Catalan's Diophantine problem
- Catalan's conjecture
- Chebyshev function
- Chen's theorem
- Chen's theorem on Goldbach's conjecture
- Chen's theorem on primes and semiprimes with fixed separation
- Chen prime
- Chowla's conjecture on the first Dirichlet prime
- Cohn's irreducibility criterion
- Completely multiplicative function
- Composite Fermat number
- Composite Fermat number implies Poulet number
- Congruence condition for minus one to be a quadratic residue
- Congruence condition for two to be a quadratic residue
- Congruence condition on prime divisor of cyclotomic polynomial evaluated at an integer
- Coprime partition maximization problem
- Cousin primes
- Covering set
- Cramér's prime gap conjecture
- Cullen number
- Cunningham chain
- Cunningham chain of the first kind
- Cunningham chain of the second kind
- Dedekind psi-function
- Dedekind series
- Dedekind zeta-function
- Deficient number
- Dickman-de Bruijn function
- Dickson's conjecture
- Dirichlet's theorem for modulus eight
- Dirichlet's theorem for modulus four
- Dirichlet's theorem on primes in arithmetic progressions
- Dirichlet L-function
- Dirichlet L-function for the Legendre symbol
- Dirichlet character
- Dirichlet eta-function
- Dirichlet product
- Dirichlet series
- Dirichlet series of Dirichlet product equals product of Dirichlet series
- Divisibility-preserving function
- Divisor count function
- Divisor count summatory function
- Divisor power sum function
- Divisor sum function
- Elliott-Halberstam conjecture
- Erdős conjecture on arithmetic progressions
- Euclid number
- Euclid prime
- Euler's criterion
- Euler's false attempted generalization of Fermat's last theorem
- Euler's four-square identity
- Euler-Jacobi pseudoprime
- Euler product formula for Dirichlet series of completely multiplicative function
- Euler product formula for Dirichlet series of multiplicative function
- Euler pseudoprime
- Euler totient function
- Every integer is a quadratic residue for infinitely many primes
- Every integer that is not a perfect square is a quadratic nonresidue for infinitely many primes
- Every prime is the smallest quadratic nonresidue for infinitely many primes
- Every prime p is a p-adic nonresidue for some prime
- Exponent bound for prime gap of 0.535
- F3
- Factorial
- Factorial prime
- Feit-Thompson conjecture
- Fermat's last theorem
- Fermat's little theorem
- Fermat-Catalan conjecture
- Fermat equation
- Fermat number
- Fermat primality test
- Fermat prime
- Fermat prime greater than three implies three is primitive root
- Fermat prime implies every quadratic nonresidue is a primitive root
- Fermat pseudoprime
- First Chebyshev function
- Formula for number of pairs of adjacent quadratic residues modulo a prime
- Formula for probability of relatively prime integer being a Fermat liar
- Formula relating Dirichlet product and summatory function
- Full reptend prime
- Funky definitions of prime number
- Generalization of Riemann hypothesis for number fields
- Generalized Cullen number
- Generalized Fermat number
- Generalized Riemann hypothesis
- Giuga number
- Goldbach's conjecture
- Goldston-Pintz-Yildirim theorem on prime gaps conditional to Elliott-Halberstam
- Goldston-Pintz-Yildirim theorem on prime gaps relative to logarithm of prime
- Goormaghtigh conjecture
- Green-Tao theorem
- Heath-Brown's conjecture on the first Dirichlet prime
- Heath-Brown theorem on Artin's conjecture
- Highly composite number
- Hilbert number
- Infinitude conjecture for Mersenne primes
- Infinitude conjecture for regular primes
- Infinitude of Poulet numbers
- Infinitude of primes
- Irregular prime
- Lagrange's four-square theorem
- Landau's function
- Large set
- Largest prime divisor
- Largest prime power divisor
- Lcm of all numbers so far
- Least primitive root
- Legendre symbol
- Lehmer's totient problem
- Limit inferior of least primitive root is finite
- Linnik's theorem
- Logarithmic integral function
- Lower asymptotic density
- Lucky number of Euler
- Main Page
- Mann's theorem
- Maximum-so-far
- Mersenne number
- Mersenne number for prime or Poulet implies prime or Poulet
- Mersenne number is prime implies number is prime
- Mersenne prime
- Mertens function
- Minimum-so-far
- Mobius function
- Modular first Chebyshev function
- Modular prime-counting function
- Mordell equation
- Multiplicative function
- Multiplicative functions form abelian group under Dirichlet product
- Multiplicative group of a prime field is generated by all primes less than square root plus one
- Near-square prime
- Number of groups of given order
- Odd perfect number conjecture
- Ore's conjecture
- Perfect number
- Perfect square
- Pillai's lower bound on the least primitive root
- Polignac's conjecture
- Polynomial Diophantine equation
- Polynomial Diophantine equation that has a solution modulo every prime may have no integer solution
- Poulet number
- Prime-between-squares conjecture
- Prime-counting function
- Prime divisor count function
- Prime divisor of Fermat number is congruent to one modulo large power of two
- Prime gap
- Prime number
- Prime number theorem
- Primitive Pythagorean triple
- Primitive root
- Primorial
- Primorial prime
- Product of successive primes in Cunningham chain of the second kind satisfying congruence conditions is Poulet number
- Proth's theorem
- Proth number
- Proth prime
- Pseudoperfect number
- Pythagorean triple
- Quadratic Diophantine equation in one variable that has a solution modulo every prime has an integer solution
- Quadratic nonresidue
- Quadratic nonresidue equals primitive root for Fermat prime
- Quadratic nonresidue that is not minus one is primitive root for safe prime
- Quadratic reciprocity
- Quasiperfect number
- Refactorable number
- Regular prime
- Riemann hypothesis
- Riemann prime-counting function
- Riemann zeta-function
- Riesel number
- Safe prime
- Safe prime has plus or minus two as a primitive root
- Schinzel's hypothesis H
- Schinzel-Sierpinski conjecture
- Schnirelmann's theorem on Goldbach's conjecture
- Schnirelmann density
- Second Chebyshev function
- Semiprime
- Set of prime divisors of values of nonconstant polynomial with integer coefficients is infinite
- Set of primes is large
- Sierpinski number
- Small set
- Smallest quadratic nonresidue
- Smallest quadratic nonresidue is less than square root plus one
- Smooth number
- Sophie Germain prime
- Square-free kernel
- Square of Wieferich prime is Poulet number
- Squareroot prime gap conjecture
- Strict maximum-so-far
- Strict minimum-so-far
- Strong pseudoprime
- Strongly smooth number
- Sum of squares function
- Superabundant number
- Supersingular prime
- There are infinitely many primes that are one modulo any modulus
- There exist arbitrarily large prime gaps
- Totient summatory function
- Twin prime conjecture
- Twin primes
- Universal exponent
- Upper asymptotic density
- Von Mangoldt function
- Weak Goldbach conjecture
- Wieferich prime
- Wilson prime
- Wolstenholme's theorem
- Wolstenholme prime
- Zeta constant
- Zhou's theorem on arbitrarily large arithmetic progressions of Chen primes