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.
(In reply to
re: update MORE DETAILS - not a spoiler by Ady TZIDON)
I have just completed an exhaustive search of the set of 21 primes starting at 7 and did not find any in which all the reversed sums were prime (adding this criteria significantly sped up the search process as would be expected). I am going to start a search tonight that will expand the search for a different set of primes that might work. I'm interpreting the more general case being being a set of consecutive primes that satisfy the following criteria
(a) their sum is a prime number
(b) there exists a disjoint partition of equal sized subsets each of whose total is prime and the reverse of that total is also prime and the sum of the reversals gives the original total
My knee jerk reaction is that there probably is such a set given the vast number of sets that satisfy all but the last criteria, but while my search is running I will work on an analytical proof that no such set exists.
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Posted by Daniel
on 2010-05-22 20:36:07 |
re(2): update MORE DETAILS - not a spoiler
