June 27th, 2013, 04:38 AM  #1 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  (p, p+4)Primes
Are there any prime tuple (n^5  n  1, n^5  n + 3)? I don't see any obvious reason to conclude anything, but I have checked up to 10^6 and there are none. 
June 27th, 2013, 05:11 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: (p, p+4)Primes
n^5  n + 3 is always divisible by 3, so there are no such primes. Generally you need to check for fixed prime divisors up to the degree of the polynomial, so 2, 3, and 5 in this case. 
June 27th, 2013, 05:16 AM  #3 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: (p, p+4)Primes
Darn, I have been proved to be a stupid two times today 
June 27th, 2013, 05:33 PM  #4  
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: (p, p+4)Primes Quote:
 

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