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## 14133RE: [PrimeNumbers] Generalised factorial primes??

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• Dec 5 7:22 AM
Hi all,
I just joined the group. I found it searching for a solution to a prime
problem I had and am
trying to prove. This caught my interest so i though i would chime in.

>From: "julienbenney" <jpbenney@...>
>Subject: [PrimeNumbers] Generalised factorial primes??
>Date: Fri, 05 Dec 2003 11:32:54 -0000
>
>Using the ordinary equipment on my old home computer, I found that (13!
>+ 2)/2 is prime.
>
>How many primes of the form (a! + n)/n [or (a! - n)/n] are actually
>known? Do you think there might by many to be found??
Yes Many possiblt infinite. But watch out

From the Pari script below.
Here is a list n =1,2..50 and n=1,2 for sums

a n (a! + n)/n
1,1,2,
2,1,3,
2,2,2,
3,1,7,
4,2,13,
5,2,61,
7,2,2521,
8,2,20161,
11,1,39916801,
13,2,3113510401,
16,2,10461394944001,
27,1,10888869450418352160768000001,
30,2,132626429906095529318154240000001,
37,1,13763753091226345046315979581580902400000001,
41,1,33452526613163807108170062053440751665152000000001,
43,2,30207631531686917818677566034256998753632256000000001,
49,2,304140932017133780436126081660647688443776415689605120000000001,

Another list for n = 1,2..50 for diff
a n (a! - n)/n
3,1,5,
3,2,2,
4,1,23,
4,2,11,
5,2,59,
6,1,719,
6,2,359,
7,1,5039,
9,2,181439,
12,1,479001599,
14,1,87178291199,
30,1,265252859812191058636308479999999,
31,2,4111419327088961408862781439999999,
32,1,263130836933693530167218012159999999,
33,1,8683317618811886495518194401279999999,
38,1,523022617466601111760007224100074291199999999,
41,2,16726263306581903554085031026720375832575999999999,

Pari Script.
nfactp2d2(n,m) =
{
for(x=1,n,
for(k=1,m,
y=floor((x!+ k)/k);
if(isprime(y),print(x","k","y","))
)
)
}
nfactm2d2(n,m) =
{
for(x=1,n,
for(k=1,m,
y=floor((x!- k)/k);
if(isprime(y),print(x",",k","y","))
)
)
}
If you dont have Pari I recommend it over all the expensive programs
Maple,Mathematica etc
it is free and available at

http://pari.math.u-bordeaux.fr/

Also, it has prime proving capability isprime() in addition to the much
faster ispseudoprime.
The script language is c-like but much better than c in terms of use and of
course number
theory capability.

I don't know what your system is but if it is windows, I recommend you
executable Pari.exe that will build all the files and folders for you. You
will need to modify the
environment path to include c:\program files\pari; This will enable you to
call gp.exe from other
folders.

I submitted some sequences to sloane's and referenced this email and your
question.

Have fun in Primelandia
Cino

Behind some primes are other primes
with other primes behind um.
And behind these primes
are still more primes
and so ad infinitum.

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