In the window of my pocket calculator, I can see a six-figure number, abcdef, with distinct digits between 1 and 9. A close inspection of the digits reveals that abcdef, cdef, and def are all prime numbers.

If I turn the calculator upside-down, I see that uvwxyz and wxyz are also prime numbers.

Which number is displayed in the window of my pocket calculator and what is the upside-down version of it?

Full credit for this problem goes to Ajit Athle who has very kindly given his permission for the puzzle to be posted here.

The numbers that flip in a calculator are 1, 2, 5, 6, 8, and 9.

Primes only end in 1, 3, 7, and 9 - so the number must end in 1 or 9.

When flipped 1 remains the same but 9 becomes a 6. So the numbers must be 1xxxx9 and 6yyyy1.

I went to http://primes.utm.edu and transferred all the primes between 620000 and 699999 to excel. Doing some sorting I found 7 primes with the appropriate numbers:

628591, 682651, 692581, 692851, 695281, 698251, and 698521. Of these, only 692851 works for all the rules.

abcdef = 158269, cdef = 8269, def=269

uvwxyz = 692851, wxyz = 2851

Edited on December 15, 2006, 10:52 am

Posted by Leming on 2006-12-15 10:51:06