perplexus.info :: Numbers : Inverted Primes

Inverted Primes (Posted on 2006-12-15)

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.

Submitted by Josie Faulkner

Rating: 3.7778 (9 votes)

Solution: (Hide)

The two numbers are: 158269, 692851
Digits 3,4 and 7 do not make any sense while seen upside down and the number was made up of non-zero and distinct digits so that in all only 48 numbers need to be checked - Numbers of the form 1****9 or 6****9. The latter does not have any number which satisfies the given conditions of primality while the former gives 158269 which seen upside down on a calculator is 692851 . Both these numbers along with 8269, 2851 & 269 are prime.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-08-08 01:36:42
solution without computer programming or internet search or excel (LOL)	jduval	2007-05-30 16:26:46
Solution without Computer Programming (spoiler)	Dej Mar	2006-12-15 14:03:35
re: Solution without Internet search or Excel	Leming	2006-12-15 11:40:57
Solution without Internet search or Excel	Charlie	2006-12-15 11:15:45
Solution (spoiler)	Leming	2006-12-15 10:51:06
not a Solution	Leming	2006-12-15 10:23:28

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