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June 27th, 2013, 04:38 AM   #1
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(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.
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June 27th, 2013, 05:11 AM   #2
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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.
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June 27th, 2013, 05:16 AM   #3
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Re: (p, p+4)-Primes

Darn, I have been proved to be a stupid two times today
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June 27th, 2013, 05:33 PM   #4
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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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