ISPR - Rapidly determine whether an arbitrarily large positive integer is a probable prime.

USAGE: q = ispr(n)
q = ispn(n,1)

n = positive integer, either as a numeric or string datatype

q = 1 if n is prime, 0 if n is composite

1 = any second input will cause the function to output a message describing the result in plain language, including (if n is probably prime) a statement about the certainty with which n is claimed to be prime.

Notes: Probable primes are also known as "industrial strength" primes because of the exceedlingly high probability -- but not certainty -- of primality. This function utilizes the Java class "BigInteger" with its method
"isProbablePrime."

For small integers, you can use numeric inputs; however, for abitrarily large integers, you must input the number as a string in order to avoid an overflow. Note the overflow error in the second to last example below.

Examples:

>>ispr(314159,1)
I believe that 314159 is prime, but there is a 1 in 590295810358705650000 chance that I am mistaken.

>>ispr('338327950288419716939',1)
I believe that 338327950288419716939 is prime, but there is a 1 in  64613997892457940000000000000000000 chance that I am mistaken.

>>ispr(338327950288419716939,1)
338327950288419680000 is definitely not prime.

>> for i=1:1000;if ispr(i);fprintf('%i ',i);end;end;fprintf('')

Michael Kleder, September 2004