Quote:
Originally Posted by LaurV
Do you mean like they are all stored in a list, somewhere, or that we can produce them on request? If you read a bit about how the small primes are found, and how their primality is proven, you will find out that generating small primes is faster than reading them from an external memory support (like a hard disk) and due to that fact, nobody bother to "store" them. And about producing them, well, we can "produce" any sequence of primes in order below the limit where we can prove primality for general form (thousands of digits). So, I guess, we "know" all primes smaller than the "record" of primo or ecpp, just that they are not "stored" anywhere, and no human have seen most of them yet... (ha, is the prime "found" when a human sees it? who made this rule? )

That is a good answer but more in the spirit of the questioner Tomas Oliveira e Silva fron the University of Aveiro Portugal calculated all primes below 4*10
^{18} in July 2014
The article in Mathematics of Computation is entitled
Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4ยท10^{18}
As to the second question of the OP that would be Primorial (4*10
^{18}) or (4x10
^{18})# approximately e
^{4*10^18}