Sponsored links: Algebra eBooks ### The Maxima on-line user's manual

Algebra Calculator

#### Search: #### 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. 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

x: 297364482020933024...

primep(x + 0);

primep(x + 4);

Calculate

primep(97);

Calculate

primep(111111);

Calculate

##### primep

primep(1858538527^37);

Calculate

x:31;

y: x^3-1;

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

Calculate

##### primep

primep(101+2*9649080);

Calculate

primep(177);

Calculate

##### primep

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

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

Calculate

##### primep-print

z:7791257157566819192...

x:z-1;

y:z+1;

Calculate

##### primep

p:1111111111111111111;

primep(p);

Calculate 