In mathematics, the sieve of Sundaram is a variant of the sieve of Eratosthenes, a simple deterministic algorithm for finding all the prime numbers up...

Atkin Sieve of Sundaram Sieve theory Horsley, Rev. Samuel, F. R. S., "Κόσκινον Ερατοσθένους or, The Sieve of Eratosthenes. Being an account of his method...

In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 10100. Heuristically...

the sieve of Sundaram (1934), the still faster but more complicated sieve of Atkin (2003), and various wheel sieves are most common. A prime sieve works...

range. Sieve of Eratosthenes Legendre sieve Sieve of Sundaram Sieve theory A.O.L. Atkin, D.J. Bernstein, Prime sieves using binary quadratic forms, Math...

time. The fundamental ideas of Fermat's factorization method are the basis of the quadratic sieve and general number field sieve, the best-known algorithms...

the halfway point. Sieve of Sundaram Sieve of Atkin Sieve of Pritchard Sieve theory Pritchard, Paul, "Linear prime-number sieves: a family tree," Sci...

quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second-fastest method known (after the general number field sieve)....

branch of mathematics, the special number field sieve (SNFS) is a special-purpose integer factorization algorithm. The general number field sieve (GNFS)...

completed with a highly optimized implementation of the general number field sieve run on hundreds of machines. No algorithm has been published that can...

artist V. A. Sundaram (1896 –1967), an activist in the Indian Independence movement Sieve of Sundaram, a method for finding prime numbers Sundaram (theatre...

the rational sieve is a general algorithm for factoring integers into prime factors. It is a special case of the general number field sieve. While it is...

However, none of them runs in polynomial time (in the number of digits in the size of the group). Baby-step giant-step Function field sieve Index calculus...

theory, a branch of mathematics, the baby-step giant-step is a meet-in-the-middle algorithm for computing the discrete logarithm or order of an element in...

sets of numbers General number field sieve Large sieve Quadratic sieve Sieve of Atkin Sieve of Eratosthenes Sieve of Sundaram Sieve of Pritchard Sieve, in...

divide-and-conquer algorithm that reduces the multiplication of two n-digit numbers to three multiplications of n/2-digit numbers and, by repeating this reduction...

quadratic sieve and the general number field sieve (GNFS). Because these methods also have superpolynomial time growth a practical limit of n digits is...

onto the sieve (i.e., increasing the number of equations while reducing the number of variables). The third stage searches for a power s of the generator...

giving the Sieve of Eratosthenes. One way to speed up these methods (and all the others mentioned below) is to pre-compute and store a list of all primes...

algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers (numbers), the largest number that divides them both without...

efficient known classical factoring algorithm, the general number field sieve, which works in sub-exponential time: O ( e 1.9 ( log ⁡ N ) 1 / 3 ( log...

The Trachtenberg system is a system of rapid mental calculation. The system consists of a number of readily memorized operations that allow one to perform...

over a modulus. It is useful in computer science, especially in the field of public-key cryptography, where it is used in both Diffie–Hellman key exchange...

by p and see whether the congruence holds. If it does not hold for a value of a, then p is composite. This congruence is unlikely to hold for a random a...

symbol can be computed in time O((log n)²) using Jacobi's generalization of the law of quadratic reciprocity. Given an odd number n one can contemplate whether...

root (isqrt) of a non-negative integer n is the non-negative integer m which is the greatest integer less than or equal to the square root of n, isqrt ⁡...

Mp = 2p − 1 be the Mersenne number to test with p an odd prime. The primality of p can be efficiently checked with a simple algorithm like trial division since...

second-fastest is the multiple polynomial quadratic sieve, and the fastest is the general number field sieve. The Lenstra elliptic-curve factorization is named...

theorem Brun sieve Function field sieve General number field sieve Large sieve Larger sieve Quadratic sieve Selberg sieve Sieve of Atkin Sieve of Eratosthenes...

the year of his death. As shown in the example, the multiplicand and multiplier are written above and to the right of a lattice, or a sieve. It is found...