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Randomly pick a number a. Check equality (corresponding to the chosen test) involving a and the given number n. If the equality fails to hold true, then n is a composite number and a is a witness for the compositeness, and the test stops. Get back to the step one until the required accuracy is reached.
Input #1: b, the number of bits of the result Input #2: k, the number of rounds of testing to perform Output: a strong probable prime n while True: pick a random odd integer n in the range [2 b −1 , 2 b −1] if the Miller–Rabin test with inputs n and k returns “ probably prime ” then return n
Starlark: Starlark is a dialect of Python created by Google for Bazel. Model checkers like FizzBee uses Starlark/Python as the modeling language. TLA+: General-purpose specification language based on the Temporal Logic of Actions, originally used for distributed and concurrent systems. The language for the specifications and their properties is ...
A strong pseudoprime is a composite number that passes the Miller–Rabin primality test. All prime numbers pass this test, but a small fraction of composites also pass, making them " pseudoprimes ". Unlike the Fermat pseudoprimes , for which there exist numbers that are pseudoprimes to all coprime bases (the Carmichael numbers ), there are no ...
Using fast algorithms for modular exponentiation and multiprecision multiplication, the running time of this algorithm is O(k log 2 n log log n) = Õ(k log 2 n), where k is the number of times we test a random a, and n is the value we want to test for primality; see Miller–Rabin primality test for details.
There is also overlap among strong pseudoprimes to different bases. For example, 1373653 is the smallest strong pseudoprime to bases 2 through 4, and 3215031751 is the smallest strong pseudoprime to bases 2 through 10. Arnault [11] gives a 397-digit Carmichael number N that is a strong pseudoprime to all prime bases less than 307.
To find any of a large number, say k, fixed length patterns in a text, a simple variant of the Rabin–Karp algorithm uses a Bloom filter or a set data structure to check whether the hash of a given string belongs to a set of hash values of patterns we are looking for:
the use of 2 to check whether a number is even or odd, as in isEven = (x % 2 == 0), where % is the modulo operator the use of simple arithmetic constants, e.g., in expressions such as circumference = 2 * Math.PI * radius , [ 1 ] or for calculating the discriminant of a quadratic equation as d = b^2 − 4*a*c