20200519, 18:11  #12 
"Rashid Naimi"
Oct 2015
Remote to Here/There
1856_{10} Posts 
DHS170A For any given factorial n! greater than 4!, let v be the valuation of prime factor q of n!, where q >=5
Then we know that one of the (n! +/ q^v)/(q^v) will have a valuations of q that is 0 and the other will have a valuations of q that is greater than or equal to 0. Other than for q (for perhaps only one of the pair) the expressions will have no other common prime factors with n!. Tobecontinued ... 
20200519, 18:29  #13 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2^{6}·29 Posts 
DHS180A For any given factorial n! if (n! +/ k)/(k) are both positive integers which are both coprime to n! & (n! +/ k)/(k) < n^2, then (n! +/ k)/(k) are twin primes
Tobecontinued ... Last fiddled with by a1call on 20200519 at 19:23 
20200520, 02:59  #14 
"Rashid Naimi"
Oct 2015
Remote to Here/There
740_{16} Posts 

20200520, 03:56  #15 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2^{6}×29 Posts 
DHS200A Any given pair of twin primes q & p where p = q+2 can be expressed as (n! +/ k)/(k) for infinite integers n such that:
n >= r where r is the greatest prime factor of (q+1) & k = n!/(q+1) It follows that there are infinite (not necessarily distinct) twin primes of the form (n! +/ k)/(k) Tobecontinued ... Last fiddled with by a1call on 20200520 at 04:25 
20200520, 05:53  #16  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2^{6}·29 Posts 
Quote:
Will see of I can come up with a correct version. To be continued ... Last fiddled with by a1call on 20200520 at 05:54 

20200520, 06:21  #17  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2^{6}·29 Posts 
Quote:
DHS200B Any given pair of twin primes q & p where p = q+2 can be expressed as (n! +/ k)/(k) for infinite integers n such that: n >= r where r = (q+1) & k = n!/r It follows that there are infinite (not necessarily distinct) twin primes of the form (n! +/ k)/(k) Tobecontinued ...[/QUOTE] Last fiddled with by a1call on 20200520 at 06:22 

20200530, 22:41  #18 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2^{6}×29 Posts 
A 79820 dd Prime example found using PFGW:
(20577!2652)/2652 Currently waiting for FactorDB to process the number. Stay tuned if not done. Last fiddled with by a1call on 20200530 at 22:44 
20200531, 04:16  #19  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2^{6}×29 Posts 
Quote:


20200531, 04:23  #20 
Sep 2002
Database er0rr
2^{3}·3·139 Posts 

20200531, 04:30  #21 
"Rashid Naimi"
Oct 2015
Remote to Here/There
11101000000_{2} Posts 
Thank you Paul. I know it is small potatoes, but the size would be a top 10 (20 counting twins as double) if it were a twin prime which is what I am aiming for.
I have a virtualbox instance which I run on 4 cores when I can, so in a few months who knows. Keeps me dreaming. 
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