20170224, 05:07  #23 
"Rashid Naimi"
Oct 2015
Remote to Here/There
3·661 Posts 
Note:
The allocatemem()s are commented out. Code:
print("\nBMT300AAlternativeFactorials=FalsorialsPRPs.gp\n") /* allocatemem() allocatemem() allocatemem() allocatemem() allocatemem() allocatemem() allocatemem() allocatemem() allocatemem() allocatemem() allocatemem()*/ for(n= 3,3,{ forstep (i=3,3,1, falsorial=i; while(falsorial<10^1000000, falsorial=falsorial*(falsorial1);\\print(falsorial); print(#digits(falsorial)," decimal digits."); ); ) }) print("**** End of Run ****") Code:
BMT300AAlternativeFactorials=FalsorialsPRPs.gp 1 decimal digits. 2 decimal digits. 3 decimal digits. 6 decimal digits. 12 decimal digits. 24 decimal digits. 48 decimal digits. 95 decimal digits. 189 decimal digits. 377 decimal digits. 753 decimal digits. 1505 decimal digits. 3010 decimal digits. 6020 decimal digits. 12040 decimal digits. 24079 decimal digits. 48157 decimal digits. 96314 decimal digits. 192628 decimal digits. *** at toplevel: ...ial*(falsorial1);print(#digits(falsorial)," *** ^ *** digits: the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() **** End of Run **** 
20170224, 05:10  #24 
"Rashid Naimi"
Oct 2015
Remote to Here/There
3×661 Posts 
My 80k dd estimate was way off, but the point is Pari can handle arithmetic on far larger integers than its #digits() function can be used to count digits for.

20170224, 12:11  #25 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 

20170224, 12:24  #26 
Sep 2002
Database er0rr
DCE_{16} Posts 

20170224, 12:30  #27 
"Forget I exist"
Jul 2009
Dumbassville
20300_{8} Posts 
another possibility is using digits with a base other than 10 in theory you could square a number and square the base the digits are counted in and end up with the same amount of digits roughly.

20170225, 01:35  #28 
"Rashid Naimi"
Oct 2015
Remote to Here/There
11110111111_{2} Posts 

20170302, 15:03  #29 
"Rashid Naimi"
Oct 2015
Remote to Here/There
3677_{8} Posts 
The title of this thread is too huge to let it sink.
Wouldn't n1 and n+1 test be ideal for getting large primes using falserials? You start with known prime factors for 30, see if 301 is prime and get 30*29., Know it's prime factors, see if 869 is prime,... All using n1 lucas test. 
20190325, 03:44  #30 
"Rashid Naimi"
Oct 2015
Remote to Here/There
3×661 Posts 
The following 36716 dd Falserial has been proven Prime using PFGW:
There is currently no established way of showing the integer in a reduced form, but it would be quite easy to invent one. 
20190325, 04:07  #31 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3×11×281 Posts 
Are you sure that this is a Falserial and not a Ulshmartragorian?
We don't know what either of these words mean. Your attached document shows nothing pertaining to PFGW. Could you please attach the full output of PFGW, where it says "is prime"? 
20190325, 04:23  #32 
"Rashid Naimi"
Oct 2015
Remote to Here/There
3·661 Posts 
The number is added to pfgwprime.log using the t flag which I believe it means it is a deterministic Prime.
I could PM you the the helper file where every Prime is proven Prime by smaller found primes. The reason I did not post it in the open is to make a point that it can be proven prime if you have the structure in seconds but without it would take months or years. If the proper notation is invented/used it can also be proven prime in seconds since the structure would be known. If you would like to verify the primality please add the primes in the PM to a helper file as they are proven prime and move up to the last term. 
20190325, 04:32  #33 
"Rashid Naimi"
Oct 2015
Remote to Here/There
3×661 Posts 
Turns out I don't know how to add an attachment to the PM so I will attach it to this post.
Please see the PFGW pfgwprime.log. You will have to prove each lower prime 1st and then add it to the helper file for proving the subsequent primes using the N1 method. The last 2 primes are of the same order. 