PrimeQ

PrimeQ(n)

returns True if n is a integer prime number.

PrimeQ(n, GaussianIntegers->True)

returns True if n is a Gaussian prime number.

For very large numbers, PrimeQ uses probabilistic prime testing, so it might be wrong sometimes (i.e. a number might be composite even though PrimeQ says it is prime).

See

• Wikipedia - Prime number
• Wikipedia - Gaussian primes

Examples

>> PrimeQ(2)
True
>> PrimeQ(-3)
True
>> PrimeQ(137)
True
>> PrimeQ(2 ^ 127 - 1)
True
>> PrimeQ(1)
False
>> PrimeQ(2 ^ 255 - 1)
False

All prime numbers between 1 and 100:

>> Select(Range(100), PrimeQ)
{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}

PrimeQ has attribute Listable:

>> PrimeQ(Range(20))
{False, True, True, False, True, False, True, False, False, False, True, False, True, False, False, False, True, False, True, False}

The Gaussian integer 2 == (1 + i)*(1 − i) isn’t a Gaussian prime number:

>> PrimeQ(2, GaussianIntegers->True)
False

>> PrimeQ(5+2*I, GaussianIntegers->True)
True

Implementation status

• ✅ - full supported

Github

• Implementation of PrimeQ