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 update by Daniel)

Daniel,
Apparently, all your solutions are valid. It looks like the existence of such a huge quantity was not known prior to your research.
For me it was a genuine surprise.

The table in the article - which was the base for my riddle- was your solution #1, i.e.the sequence as is, subsets of 3 arranged in ascending order.

If you are interested to view the source  or to communicate with the researcher-   it will  be my pleasure  to Email the details to you.

BTW, when you get the final results please post them.

Is there   any partition  in which all the reversed sums are prime?
If not , can you analytically prove (maybe  by pigeon principle) that it
is impossible?

 

Posted by Ady TZIDON on 2010-05-22 05:28:57