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I would like to know why if the Hardy Littlewood conjecture is true, this could explain the position of the prime numbers on the diagonal of Ulam spiral. Thanks.

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The wiki on Ulam spiral mentions the connection. Did you read it? –  Aryabhata Mar 13 '12 at 17:50
    
I don't know what it would mean to "explain the position of the prime numbers on the diagonal of the Ulam spiral". Before a mathematical answer can be offered, the question has to be made more precise. –  Greg Martin Mar 13 '12 at 18:04
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