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Consecutive Odd and Prime (Posted on 2006-11-08) Difficulty: 1 of 5
How many sets of 3 or more consecutive positive odd numbers greater than 1 exist such that all of the numbers are prime?

  Submitted by Richard    
Rating: 2.2500 (4 votes)
Solution: (Hide)
{3,5,7} is the unique set of 3 or more consecutive odd numbers that are primes. Suppose x,y,z are 3 consecutive odd numbers in order and suppose that x is a prime that exceeds 3. Then x equals either 1 or 2 mod 3. If x equals 1 mod 3, then y is a multiple of 3. If x equals 2 mod 3, then z is a multiple of 3.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle SolutionK Sengupta2008-11-09 05:33:03
re: TrivialRichard2006-11-08 23:21:22
SolutionTriviale.g.2006-11-08 19:08:10
a solutionDennis2006-11-08 09:25:03
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