20161214, 19:16  #1 
"Rashid Naimi"
Oct 2015
Remote to Here/There
4176_{8} 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. 
20161214, 19:22  #2 
Sep 2002
Database er0rr
2·7·281 Posts 

20161214, 19:41  #3 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2·1,087 Posts 
Neat, thank you very much for the links.

20161214, 19:49  #4 
"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?

20161214, 19:53  #5 
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 N1 test  is has 100% factorisation when only 33.33% is needed.

20161214, 20:01  #6  
"Ben"
Feb 2007
110111111011_{2} Posts 
Quote:
This took about 30 seconds to compute: Code:
>> size(100000000#) 43424120 digits, 144251803 bits 

20161214, 20:07  #7 
"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. 
20161214, 20:09  #8  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2·1,087 Posts 
Quote:
So back to the fact that it is easier to compute than store, there is no highest known primorial record. Is that correct? 

20161214, 20:14  #9  
(loop (#_fork))
Feb 2006
Cambridge, England
2^{2}×3^{2}×179 Posts 
Quote:


20161214, 20:34  #10 
"Rashid Naimi"
Oct 2015
Remote to Here/There
100001111110_{2} 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. 
20161214, 20:38  #11  
Aug 2006
1011101011011_{2} Posts 
Quote:
Does anyone have actual numbers on how long GMP or something else takes to do multiGB multiplications? Last fiddled with by CRGreathouse on 20161214 at 20:39 

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