Needed: gaps between large primes

[cino hilliard]

Hi,
The gaps between consecutive prime can be arbitrarily large. For example 5! 
= 120 thus between
5! and 5!+5  we have  5!+2,5!+3,5!+4,5!+5  = 4 composit numbers. so between
precprime(5!) and nextprime(5!+5) there are at least 4 composites. If we 
generalize this for n! then
there are at least n-1 composits between precprime(n!) and nextprime(n!+n). 
for another example,
there are at least a googolplex-1 composit numbers between 
precprime(googolplex!) and
nextprime(googolplex!+googolplex). This is a large gap indeed!

I think this information may be more useful to the class than a list. of 
course you could make a list
from this.

I submitted a sequence to this effect.

factgaps2(m) =
         {
         for(n=3,m,
         c=0;
         nf=n!;
         for(x=precprime(nf),nextprime(nf+n),if(!isprime(x),c++));
         print1(c",")
         )
         }




>From: "Pfoertner, Hugo" <Hugo.Pfoertner at muc.mtu.de>
>To: "'matuszyk at ltk.com.pl'" <matuszyk at ltk.com.pl>
>CC: seqfan at ext.jussieu.fr, "'njas at research.att.com'" 
><njas at research.att.com>
>Subject: RE: Needed: gaps between large primes
>Date: Mon, 3 Nov 2003 14:33:49 +0100
>
>Dear Marian,
>
>you asked Neil Sloane for examples of gaps between large prime numbers to
>test
>programs developed by yourself and your students.
>It's extremely easy to create such numbers using OpenPFGW
>which was available at http://www.primeform.net/openpfgw/ ,
>but this address currently? seems to be offline.
>OpenPFGW can handle numbers of several 10000 digits.
>Here are the first entries: (differences computed with Excel)
>
>             Primes                             Gap
>
>         39+         10^20            129        90
>        129+         10^20            151        22
>        151+         10^20            193        42

Cino

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