How many known prime numbers are there?

Question

Also, is there a website that lists all of the known prime numbers?

Yes, I know there are infinite prime numbers. No, it is not that easy to produce new ones, if it was that easy there would already be primes that are 10 million digits, which there is a reward for.

Answer 1

The prime number theorem can give you a rough estimate on how many prime numbers are there which are less than a given integer. If you happen to know which is the largest known prime number, you can manage to have a rough upper bound on how many prime numbers are known till today. You can proceed as follows:

Largest prime number till today: (2^32,582,657)-1
from wikipedia: http://en.wikipedia.org/wiki/Largest_known_prime

Rough estimate of prime numbers less than n: n/(ln n)

To calculate n/(ln n) for n=(2^32,582,657)-1 you can happily forget the minus one (since we are giving a rough estimate), so the denominator reads as

ln (2^32,582,657) = 32,582,657*(ln 2)

Since 32,582,657 is roughly 2^25, we obtain:

"prime numbers less than the largest one" ~ 1.4*(2^32,582,632) ~ 1.4*(10^9,808,350)

which maybe suggests why there seems to be no list of all the prime numbers known. Anyway remember that, in the search for the largest one, people consider special forms of numbers (Mersenne numbers for instance) so many primes less than the largest are actually left behind (and the rough estimate above is just an upper bound).

Bye!

Answer 2

It would be hard to make a list of all the known primes, since simply by taking the two largest on the list, multiplying them together, and then adding 1, you would ALWAYS get another prime that is not on the list. So you could say it is then "known", so to speak. (This is similar to the proof of why we know there are infinitely many primes.)

Answer 3

The answer is infinite. There was one mathematician that wrote volumes of prime numbers--of course his work will never be completed.

Answer 4

It has been proven long ago that there is an infinite number of prime numbers.

Answer 5

there are MANY prime numbers, so this site lists the first 500 and breaks them down into different lists by "prime number type".

http://en.wikipedia.org/wiki/List_of_prime_numbers

Answer 6

advise you to go to wikipedia - I just did. You'll learn lot.