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The Maxima on-line user's manual

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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) 

Related Examples

primep

primep(213);

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primep-sqrt

sqrt(((5+3)^4/8^2)/(1...

sqrt((3^6/(6-3)^4)/(5...

sqrt((36*4*(14+2*11))...

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primep

primep(11111111111111...

p:1111111111111111111;

b:17;

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primep

n=p+q;

primep(2);

primep(2);

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primep

next_primep(45641);

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primep

F(n):=((2^(2^n))+1);

F(3);

primep(F(3));

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primep

P:2*3*5*7*11*13;

[primep(P-1),primep(P...

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primep

fa(x):=x^3-1;

ff(x):= fa(x)-fa(x-1);

for i:2 thru 10 step ...

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primep-print

x:30;

y: x^3-1;

z: (x-1)^3-1;

Calculate

primep-sqrt

sqrt(((5+3)^4/8^2)/(1...

sqrt((3^6/(6-3)^4)/(5...

sqrt((36*4*(14+2*11))...

Calculate