Many fast primality tests are known that work only for numbers with certain properties.

Any primality test can be used as the basis for a prime number formula.

Repeat step 4 until the largest number to be tested for primality.

The official proof of a prime is through its primality certificate.

It has preliminary primality testing, finding small factors, and powers.

We can use a primality testing algorithm to make sure that is indeed composite.

Prime integers can be efficiently found using a primality test.

He also called those who proved their primality titans.

He devised methods for testing the primality of numbers.

For some forms of numbers, it is possible to find 'short-cuts' to a primality proof.

The property of being prime is called primality.

Many mathematicians have worked on primality tests for large numbers, often restricted to specific number forms.

Composite numbers that do pass a given primality test are referred to as pseudoprimes.

An example of a decision problem is primality testing:

These are the key facts that make Lucas sequences useful in primality testing.

There are algorithms that prove the primality of an integer.

For example, there is a definition of primality using only bounded quantifiers.

For example, consider the problem of primality testing.

This is a bad way to prove primality.

Moreover, a and q are the certificate of primality.

It is not a proof of primality until we know our factors of A are prime as well.

If we get a factor of A where primality is not certain, the test must be performed on this factor as well.

Consequently, this can be considered a deterministic primality test on numbers below that bound.

Let n be the odd positive integer that we wish to test for primality.

At that time, no practical deterministic algorithm for primality was known.