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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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 further study | Comment 2 of 11 |
in an attempt to determine the nature of the groupings being asked for I took each of the lists given before and determined what groups of 3 fit the last 2 criteria of summing to a prime and the reverse of their digits summing to the same prime.  Furthermore I eliminated the lists that contain 2 as any group of 3 primes that includes 2 will add to an even number greater than 2 and thus not be prime.

This is what I got:
The 15 consecutive primes from 3 to 53 sum up to the prime number 379

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

Viable Groups of 3:

{3,5,11} Sum: 19

{3,13,31} Sum: 47

{5,7,11} Sum: 23

{5,13,53} Sum: 71

{5,23,43} Sum: 71

{7,13,53} Sum: 73

{7,23,43} Sum: 73

The 17 consecutive primes from 3 to 61 sum up to the prime number 499

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

Viable Groups of 3:

{3,5,11} Sum: 19

{3,13,31} Sum: 47

{5,7,11} Sum: 23

{5,13,53} Sum: 71

{5,23,43} Sum: 71

{7,13,53} Sum: 73

{7,23,43} Sum: 73

{17,41,61} Sum: 119

The 11 consecutive primes from 5 to 41 sum up to the prime number 233

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

Viable Groups of 3:

{5,7,11} Sum: 23

The 17 consecutive primes from 5 to 67 sum up to the prime number 563

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

Viable Groups of 3:

{5,7,11} Sum: 23

{5,13,53} Sum: 71

{5,23,43} Sum: 71

{5,43,47} Sum: 95

{7,13,53} Sum: 73

{7,23,43} Sum: 73

{17,41,61} Sum: 119

The 11 consecutive primes from 7 to 43 sum up to the prime number 271

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

Viable Groups of 3:

{7,23,43} Sum: 73

The 15 consecutive primes from 7 to 61 sum up to the prime number 491

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

Viable Groups of 3:

{7,13,53} Sum: 73

{7,23,43} Sum: 73

{17,41,61} Sum: 119

The 21 consecutive primes from 7 to 89 sum up to the prime number 953

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

Viable Groups of 3:

{7,13,53} Sum: 73

{7,23,43} Sum: 73

{7,43,89} Sum: 139

{7,53,59} Sum: 119

{7,53,79} Sum: 139

{7,59,73} Sum: 139

{17,41,61} Sum: 119

I am out of time to work on this for now, so perhaps somebody could work on finding a way to use these groupings to fit the problem criteria.

 Posted by Daniel on 2010-05-20 13:22:00

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