Sieve of Atkin information

mathematics, the sieve of Atkin is a modern algorithm for finding all prime numbers up to a specified integer. Compared with the ancient sieve of Eratosthenes...

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...

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

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

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...

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)...

actress Wendy Atkin (1947–2018), British professor Atkin & Low family tree, showing the relationship between some of the above Sieve of Atkin, mathematical...

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

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 same problem is the sieve of Atkin. In advanced mathematics, sieve theory applies similar methods to other problems. Some of the fastest modern tests...

the sieve of Pritchard. Runciman provides a functional algorithm inspired by the sieve of Pritchard. Sieve of Eratosthenes Sieve of Atkin Sieve theory...

up to 655372 = 4,295,098,369. Preparing such a table (usually via the Sieve of Eratosthenes) would only be worthwhile if many numbers were to be tested...

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

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...

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...

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 by A. O. L. Atkin the same year. The algorithm was altered and improved by several collaborators subsequently, and notably by Atkin and François Morain [de]...

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...

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...

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...

from sieve theory to O ~ ( log ⁡ ( n ) 7.5 ) {\displaystyle {\tilde {O}}(\log(n)^{7.5})} . In 2005, Pomerance and Lenstra demonstrated a variant of AKS...

computes, in addition to the greatest common divisor (gcd) of integers a and b, also the coefficients of Bézout's identity, which are integers x and y such that...

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...