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The Maxima on-line user's manual

Algebra Calculator

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Primep

Function: primep (<n>) Primality test. If primep (<n>) returns false, <n> is a composite number and if it returns true, <n> is a prime number with very high probability.

product(sum(f(n,(10*k+1),10*n-(2*k+1))*(is(equal(primep((2*k+1))*primep(2*n-(2*k+1)),true^2))-unknown)/(true-unknown),k, 18000, 19000),n,10^30,10^30);

For <n> less than 341550071728321 a deterministic version of Miller-Rabins test is used. If primep (<n>) returns true, then <n> is a prime number.

For <n> bigger than 341550071728321 primep uses primep_number_of_tests Miller-Rabins pseudo-primality tests and one Lucas pseudo-primality test. The probability that <n> will pass one Miller-Rabin test is less than 1/4. Using the default value 25 for primep_number_of_tests, the probability of <n> beeing composite is much smaller that 10^-15.

There are also some inexact matches for primep. Try ?? primep to see them.

(%o1)                                true
(%i2) 

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