- Dec 5, 2003Hi 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@...>

Yes Many possiblt infinite. But watch out

>To: primenumbers@yahoogroups.com

>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??

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

download the binary

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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