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April 22nd, 2011, 02:35 AM  #1 
Member Joined: Jun 2010 Posts: 64 Thanks: 0  Are there infinitely many primes of the form (n!)/2+1 ?
Are there infinitely many primes numbers of the form (n!)/2+1 , Thank you ..

April 22nd, 2011, 06:32 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Are there infinitely many primes of the form (n!)/2+1 ?
It's not known. See A082672 for a list of the known primes of this form (or rather, their n values). Generally no 'natural' sequence with a growth rate that high is known to contain infinitely many primes. 
April 22nd, 2011, 11:05 AM  #3 
Member Joined: Jun 2010 Posts: 64 Thanks: 0  Re: Are there infinitely many primes of the form (n!)/2+1 ?
Are there infinit primes numbers of the form (n!)/2+1 ?

April 22nd, 2011, 11:13 AM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,209 Thanks: 517 Math Focus: Calculus/ODEs  Re: Are there infinitely many primes of the form (n!)/2+1 ?
You must have somehow missed the reply from [color=#008000]CRGreathouse[/color]. He stated this is unknown, but generally thought not to be the case.

April 22nd, 2011, 11:57 AM  #5  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Are there infinitely many primes of the form (n!)/2+1 ? Quote:
 
April 28th, 2011, 04:58 PM  #6 
Member Joined: Jun 2010 Posts: 64 Thanks: 0  Re: Are there infinitely many primes of the form (n!)/2+1 ?
n=5 we have (5!)/2+1=61 is prime number,, (7!)/2+1=2521 is prime number, (19!)/2+1=60822550204416001 IS PRIME NUMBER.Are there infinitely primes number of this form???.ca you help me please..

April 28th, 2011, 09:47 PM  #7 
Senior Member Joined: Nov 2010 Posts: 502 Thanks: 0  Re: Are there infinitely many primes of the form (n!)/2+1 ?
I don't know. No one does. But I have a question for you  n = 2 we have, a prime number. Do you think that there might be infinitely many primes of the form as well?

April 28th, 2011, 10:16 PM  #8 
Newbie Joined: Oct 2009 Posts: 26 Thanks: 0  Re: Are there infinitely many primes of the form (n!)/2+1 ?
Friendlander and Iwaniec were able to prove there are infinitely many primes of the form a^2 + b^4, which is a fairly sparse set within the natural numbers. The set you're asking about is orders of magnitude more sparse than what can be proven at this time, unless there's some kind of proof trick that is unique to that set.

April 29th, 2011, 09:45 AM  #9  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Are there infinitely many primes of the form (n!)/2+1 ? Quote:
 

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