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 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

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Re: (p, p+4)-Primes

Quote:
 Originally Posted by mathbalarka Darn, I have been proved to be a stupid two times today
Nope. People who factor quintics for fun are by definition the very opposite of stupid. The real lesson here is that ANYONE can make an inattentive mistake.

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