Template:Number-theoretic algorithms

v t e Number-theoretic algorithms
Primality tests	AKS APR Baillie–PSW ECPP Elliptic curve Pocklington Fermat Lucas Lucas–Lehmer Lucas–Lehmer–Riesel Proth's theorem Pépin's Solovay–Strassen Miller–Rabin Trial division
Prime generating algorithms	Sieve of Atkin Sieve of Eratosthenes Sieve of Sundaram Wheel factorization
Integer factorization algorithms	CFRAC Dixon's ECM Euler's Pollard's rho p − 1 p + 1 QS GNFS SNFS rational sieve Fermat's Shanks' square forms Trial division Shor's
Multiplication algorithms	Ancient Egyptian multiplication Karatsuba algorithm Toom–Cook multiplication Schönhage–Strassen algorithm Fürer's algorithm
Discrete logarithm algorithms	Baby-step giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve
GCD algorithms	Binary GCD Euclidean Extended Euclidean Lehmer's
Modular square root algorithms	Cipolla Pocklington's Tonelli–Shanks
Other algorithms	Chakravala Cornacchia integer relation algorithm integer square root Modular exponentiation Schoof's
Italics indicate that algorithm is for numbers of special forms; double underline indicates deterministic algorithm for primality tests.