p, p+8, p+22 Not PrimeDate: 10/16/2001 at 07:37:17 From: Scott S Subject: Proof On Prime Numbers Could you help me with this question?: Prove that there is no positive integer p such that each of the numbers: p p+8 p+22 is prime. Any help would be much appreciated. Cheers, Scott Date: 10/16/2001 at 08:38:49 From: Doctor Paul Subject: Re: Proof On Prime Numbers If p is not prime, we're done. So assume p is prime. Then p is either one more than a multiple of three, or p is two more than a multiple of three. In other notation: p = 1 mod 3 or p = 2 mod 3. If p = 1 mod 3 then p+8 = 0 mod 3 and is therefore divisible by three and is hence not prime. If p = 2 mod 3 then p+22 = 0 mod 3 and is therefore divisible by three and is hence not prime. Write back if you want to talk about this some more. - Doctor Paul, The Math Forum http://mathforum.org/dr.math/ |
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