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 2016-12-14, 19:16 #1 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 41768 Posts Largest Known Primorial 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.
 2016-12-14, 19:22 #2 paulunderwood     Sep 2002 Database er0rr 2·7·281 Posts Top20 primorials and PrimeGrid's primorial server HTH
 2016-12-14, 19:41 #3 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2·1,087 Posts Neat, thank you very much for the links.
 2016-12-14, 19:49 #4 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2×1,087 Posts 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?
 2016-12-14, 19:53 #5 paulunderwood     Sep 2002 Database er0rr 2·7·281 Posts 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.
2016-12-14, 20:01   #6
bsquared

"Ben"
Feb 2007

1101111110112 Posts

Quote:
 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:
Code:
>> size(100000000#)

43424120 digits, 144251803 bits

 2016-12-14, 20:07 #7 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2×1,087 Posts 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.
2016-12-14, 20:09   #8
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

2·1,087 Posts

Quote:
 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: Code: >> 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?

2016-12-14, 20:14   #9
fivemack
(loop (#_fork))

Feb 2006
Cambridge, England

22×32×179 Posts

Quote:
 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!

 2016-12-14, 20:34 #10 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 1000011111102 Posts 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.
2016-12-14, 20:38   #11
CRGreathouse

Aug 2006

10111010110112 Posts

Quote:
 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?

Last fiddled with by CRGreathouse on 2016-12-14 at 20:39

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