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isprime

primality test

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

isprime(n)

Parameters

n

-

integer

Description

• 

The isprime command is a probabilistic primality testing routine. (See prime number.)

• 

It returns false if n is shown to be composite within one strong pseudo-primality test and one Lucas test. It returns true otherwise.

• 

If isprime returns true, n is very probably prime - see References section. No counterexample is known and it has been conjectured that such a counter example must be hundreds of digits long.

Examples

isprime1

false

(1)

isprime2

true

(2)

isprime17

true

(3)

isprime21

false

(4)

isprime11!+1

true

(5)

isprime230330+7

true

(6)

The Tabulate command can be used to display prime numbers in a grid. The following table highlights any prime numbers with a pink background.

Vr,c→DocumentTools:-TabulateMatrixr,c,i,j→c*i1+j,fillcolor=T,i,j→`if`isprimec*i1+j,Pink,White:

V10,30

Tabulate

(7)

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Note that this procedure can be modified to show tables for various values of r and c.

References

  

Knuth, Donald E. The Art of Computer Programming. 2nd ed. Reading, Mass.: Addison-Wesley, 1997. Vol. 2 Section 4.5.4: Algorithm P.

  

Riesel, H. Prime Numbers and Computer Methods for Factorization. Basel: Birkhauser, 1994.

See Also

ithprime

nextprime

prevprime

type[prime]

 


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