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| Odd primes never die (Posted on 2010-05-20) |
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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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No Solution Yet
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Submitted by Ady TZIDON
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Rating: 3.6667 (3 votes)
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further study
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 | Comment 2 of 11 | 
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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.
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Posted by Daniel
on 2010-05-20 13:22:00 |
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