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Purely prime (Posted on 2013-02-19) Difficulty: 2 of 5
Twenty-one prime numbers are in arithmetic sequence with difference d. Prove that d is divisible by 9699690.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 5.0000 (1 votes)

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Solution Just the proof (spoiler) | Comment 1 of 3
Well, d must be divisible by 2, in order that none of the numbers are divisible by 2.  Similarly, d must be divisible by 3, in order that none of the numbers are divisible by 3.  Same for 5, 7, 11, 13, 17 and 19.

Thus, d is divisible by 2*3*5*7*11*13*17*19 = 9699690.  

(As noted in relation to another puzzle recently, this proof is complete, with no need to find 21 numbers prime numbers in arithmetic sequence)

  Posted by Steve Herman on 2013-02-19 14:45:47
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