Table of Contents
What is the best algorithm for finding a prime number?
Sieve of Eratosthenes
Sieve of Eratosthenes is a simple and ancient algorithm used to find the prime numbers up to any given limit. It is one of the most efficient ways to find small prime numbers.
How does Miller Rabin test work?
The Miller-Rabin test picks a random a ∈ Z n . If the above sequence does not begin with , or the first member of the sequence that is not is also not then is not prime. If fails the Miller-Rabin test with a sequence starting with 1, then we have a nontrivial square root of modulo , and we can efficiently factor .
How accurate is Miller-Rabin test?
5 Answers. Miller–Rabin is indeed probabilistic, but you can trade accuracy for computation time arbitrarily. If the number you test is prime, it will always give the correct answer. The problematic case is when a number is composite, but is reported to be prime.
Is Sieve of Eratosthenes efficient?
Sieve of Eratosthenes is a simple and ancient algorithm used to find the prime numbers up to any given limit. It is one of the most efficient ways to find small prime numbers. For a given upper limit n the algorithm works by iteratively marking the multiples of primes as composite, starting from 2.
What is Sieve of Eratosthenes algorithm?
In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. One of a number of prime number sieves, it is one of the most efficient ways to find all of the smaller primes. It may be used to find primes in arithmetic progressions.
Is primality testing in P?
Primality testing in polynomial time. From randomized algorithms to PRIMES is in P.
How fast is AKs compared to ECPP?
( n)) (“fastECPP”) time, but there may be numbers that take longer. So our expectation is that standard AKS will always be slower than ECPP for almost all numbers (it certainly has shown itself so for numbers up to 25k digits). AKS may have more improvements waiting to be discovered that makes it practical.
Is trial division faster than the sieve of Eratosthenes?
Both of these tests are vastly faster than any kind of trial division. If you are just trying to find if a number is prime or not it’s good enough, but if you’re trying to find all primes from 0 to n a better option will be the Sieve of Eratosthenes But it will depend on limitations of java on array sizes etc.
Is there a sieve of Eratosthenes in Java?
When you follow this reasoning to its conclusion, you get the Sieve of Eratosthenes. Take a look at the AKS primality test (and its various optimizations). It is a deterministic primality test that runs in polynomial time. There is an implementation of the algorithm in Java from the University of Tuebingen (Germany) here
What is the best method to generate a list of primality tests?
Like mentioned in other answers the Sieve of Eratosthenes is the preferred method to generate such a precomputed list. If your numbers are larger than this, you can use the primality test of Rabin. Rabin primality test