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The Miller–Rabin primality test or Rabin–Miller primality test is a probabilistic primality test: an algorithm which determines whether a given number is likely to be prime, similar to the Fermat primality test and the Solovay–Strassen primality test. It is of historical significance in the search for a polynomial-time deterministic ...
The Miller–Rabin and the Solovay–Strassen primality tests are simple and are much faster than other general primality tests. One method of improving efficiency further in some cases is the Frobenius pseudoprimality test ; a round of this test takes about three times as long as a round of Miller–Rabin, but achieves a probability bound ...
Hence, the probability of failure is at most 2 −k (compare this with the probability of failure for the Miller–Rabin primality test, which is at most 4 −k). For purposes of cryptography the more bases a we test, i.e. if we pick a sufficiently large value of k, the better the accuracy of test.
The earliest known reference to the sieve (Ancient Greek: κόσκινον Ἐρατοσθένους, kóskinon Eratosthénous) is in Nicomachus of Gerasa's Introduction to Arithmetic, [3] an early 2nd century CE book which attributes it to Eratosthenes of Cyrene, a 3rd century BCE Greek mathematician, though describing the sieving by odd ...
"The Miller-Rabin test is stronger than the Solovay-Strassen primality test in the sense the set of strong liars of the Miller-Rabin test is a subset of the set of the Solovay-Strassen primality test." If there's no feedback, I'm going to make one of these changes in a few days. CRGreathouse (talk • contribs) 17:01, 5 August 2006 (UTC)
Rabin was born in 1931 in Breslau, Germany (today Wrocław, in Poland), the son of a rabbi.In 1935, he emigrated with his family to Mandatory Palestine.As a young boy, he was very interested in mathematics and his father sent him to the best high school in Haifa, where he studied under mathematician Elisha Netanyahu, who was then a high school teacher.
Even so, this is a quite satisfactory method, considering that even the best-known algorithms have exponential time growth. For a chosen uniformly at random from integers of a given length, there is a 50% chance that 2 is a factor of a and a 33% chance that 3 is a factor of a, and so on. It can be shown that 88% of all positive integers have a ...
The Miller test, also called the three-prong obscenity test, is the United States Supreme Court's test for determining whether speech or expression can be labeled obscene, in which case it is not protected by the First Amendment to the United States Constitution and can be prohibited.