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Infinite Primes

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Is there an infinite number of primes? - a selection of answers from the Dr. Math archives.

Are Prime Numbers Infinite?
How do we know the number of primes is infinite?

Proof: Infinitely Many Primes
I need a proof that there are an infinite number of primes other than Euclid's proof by contradiction. What is the Dirichlet proof?

Primes and Perfect Numbers
Are there infinite numbers of prime and perfect numbers?

Infinite Number of Primes
Prove there are an infinite number of primes. What is the largest prime number known?

No Largest Prime Number
What's the largest prime number? (proof by contradiction).

Are There Infinitely Many Perfect Numbers?
There are so many theories, but nobody seems to have come up with anything definite...

How Many Primes Are Known?
How many prime numbers are currently known?

Frequency of Primes
Is there a pattern to describe the frequency of prime numbers?

Primes Containing but Not Ending in 123456789
Are there infinitely many primes that contain but do not end in the block of digits 123456789 ?

Primes of the Form 4n+3
Prove that there are infinitely many primes of the form 4n+3 where n is an element of the natural numbers.

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