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 Odd primes never die (Posted on 2010-05-20)
I 've found an interesting table of numbers in an old issue of JMR, dedicated to astounding trivia regarding primes.
Erasing all the digits in the table's footnotes I got a challenging, albeit solvable puzzle:
The XX consecutive primes from X to XX sum up to the prime number XXX.
Also when arranged in groups of three, each group sums up to a prime number.
Furthermore, those partial sums with their digits reversed, also sum up to the same sum as before the reversal!

Try to reconstruct the trivia : both the table and the text.

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 perhaps some clarification | Comment 1 of 11
based on the first criteria of XX consecutive primes from X to XX sum up to the prime XXX
I found 9 lists that work and they are
{2,3,5,7,11,13,17,19,23,29,31,37}

{2,3,5,7,11,13,17,19,23,29,31,37,41,43}

{3,5,7,11,13,17,19,23,29,31,37,41,43,47,53}

{3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61}

{5,7,11,13,17,19,23,29,31,37,41}

{5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67}

{7,11,13,17,19,23,29,31,37,41,43}

{7,11,13,17,19,23,29,31,37,41,43,47,53,59,61}

{7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89}

however the way I interpret the next criteria, I take it to mean that all subsets of 3 sum to a prime.  Unfortunately none of these sets fit that criteria.  So perhaps somebody could propose another possible interpretation.

 Posted by Daniel on 2010-05-20 12:16:40

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