Largest Known Primorial

[a1call]

Hi,
Considering that calculation of primorials is subject to calculating consecutive primes, are there any records kept in regards to largest known/calculated primorial?

Thanks in advance.

[paulunderwood]

Top20 primorials and PrimeGrid's primorial server

HTH

[a1call]

Neat, thank you very much for the links.

[a1call]

Is it logical to assume that lager primorials have been calculated which have not resulted in primorial primes or PRPs, or are primorial PRPs so common that they basically are associated with the highest known primorials?

[paulunderwood]

A primorial PRP can easily be converted into a prime using a either BLS N+1 or N-1 test -- is has 100% factorisation when only 33.33% is needed.

[bsquared]

Originally Posted by a1call

Is it logical to assume that lager primorials have been calculated which have not resulted in primorial primes or PRPs, or are primorial PRPs so common that they basically are associated with the highest known primorials?

It is trivial to compute larger primorials. It takes GMP a few milliseconds to compute the largest one on that page and a second or so to print it.

This took about 30 seconds to compute:

>> size(100000000#)

43424120 digits, 144251803 bits

[a1call]

Ok, but basically once you calculate the largest known (to you) primorial, you have couple of primorial PRPs (since not divisible by any of the calculated prime constituents) which can easily be proven/disproven prime. This seems like an unofficial record of the (near)-largest known primorial (independent of if it is associated with a primorial prime or not).
In other words the links provided are basically very near the extent of the largest known primorial.

[a1call]

Originally Posted by bsquared

It is trivial to compute larger primorials. It takes GMP a few milliseconds to compute the largest one on that page and a second or so to print it.

This took about 30 seconds to compute:

>> size(100000000#)

43424120 digits, 144251803 bits

We cross posted.
So back to the fact that it is easier to compute than store, there is no highest known primorial record. Is that correct?

[fivemack]

Originally Posted by a1call

Ok, but basically once you calculate the largest known (to you) primorial, you have couple of primorial PRPs (since not divisible by any of the calculated prime constituents) which can easily be proven/disproven prime. This seems like an unofficial record of the (near)-largest known primorial (independent of if it is associated with a primorial prime or not).

I don't see what you mean. A primorial is not a probable-prime; 67#+1 is composite with smallest factor 54730729297, you rule out only prime divisors up to about the logarithm of the number and there are an awful lot more candidate prime divisors than that!

[a1call]

Yes I do realize it might divide primes that are larger than the constituting primes.
In any case the bottom line answer to my OP question seems to be that there are no records kept due to ease of computation vs large sizes not cost worthy to store records.

[CRGreathouse]

Originally Posted by a1call

So back to the fact that it is easier to compute than store, there is no highest known primorial record. Is that correct?

Right, no one keeps track of that. You should pretty much be able to fill up as much memory as you like with a primorial. It shouldn't take more than, say, a day to sieve out a bunch of primes filling half your RAM and then multiply them together in the other half. (With more care you could fill 3/4 of your RAM and improve on the speed.)

Does anyone have actual numbers on how long GMP or something else takes to do multi-GB multiplications?