# pseudoprime

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## pseudoprime

A backgammon prime (six consecutive occupied points) with one point missing. This term is an esoteric pun derived from a mathematical method that, rather than determining precisely whether a number is prime (has no divisors), uses a statistical technique to decide whether the number is "probably" prime. A number that passes this test is called a pseudoprime. The hacker backgammon usage stems from the idea that a pseudoprime is almost as good as a prime: it does the job of a prime until proven otherwise, and that probably won't happen.
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Let [member of] be a randomly chosen [l.sub.e]-bit pseudoprime which is not a prime with the probability [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Note that, in our protocol, we use a pseudoprime which is not prime with probability [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Our protocol uses a 52-bit pseudoprime [member of] which is indeed prime with probability [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and so it suffices to perform the primary tests 37 times according to the formula given in [12].
Numbers like 341 that pass the test but are not prime are said to be pseudoprime. The fortunate thing about them is that they are quite rare, so if a number p satisfies the condition that [2.sup.p] - 2 is divisible by p, then we can be reasonably confident that it is prime.
In order to accomplish the first task, one standard method is to use pseudoprimes. It has been known for hundreds of years that if p is prime, then [2.sup.p] - 2 is divisible by p; this is a consequence of Fermat's Little Theorem.
Jiang and Shi [15] discussed characterizations of pseudoprimes and studied strong retracts of (stable) semicontinuous lattices.

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