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| Consecutive Odd and Prime (Posted on 2006-11-08) |
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How many sets of 3 or more consecutive positive odd numbers greater than 1 exist such that all of the numbers are prime?
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Submitted by Richard
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Rating: 2.2500 (4 votes)
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Solution:
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{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. |
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