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Prime Squares (Posted on 2009-04-09)

Consider two 5-digit perfect squares, the first two digits of each of which form a 2-digit prime number, and the last three digits form a 3-digit prime number.

For sake of discussion, let the digits be called ABCDE and VWXYZ. The two squares I'm thinking of can form, from those digits, another 5-digit square: ABXYZ. It is of the same type as the other two as AB is prime as is XYZ.

The use of different letters does not imply that all the letters represent different digits; any two may be the same or different, but the combined square does share its first two digits with those of one of the two original squares and its last three with the last three of the other.

What are the three squares?

Submitted by Charlie

Rating: 4.0000 (1 votes)

Solution: (Hide)

The following lists those 5-digit perfect squares that consist of a 2-digit prime concatenated with a 3-digit prime:

square square of: 11449 107 11881 109 19881 141 23409 153 29241 171 29929 173 83521 289 89401 299

11881 shares its first two digits with 11449 and its last three digits with 19881.

10 for I=100 to 316 20 Sq=I*I 30 Pr1=Sq\1000:Pr2=Sq@1000 40 if Pr1>9 and Pr2>99 then 50 :if prmdiv(Pr1)=Pr1 and prmdiv(Pr2)=Pr2 then 60 :print Sq,I 70 next

Adapted from Enigma No. 1527, "Square from primes", by Richard England, New Scientist, 10 January 2009.

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

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-09-10 21:34:16
re(2): computer solution (spoiler)	Daniel	2009-04-09 16:59:59
Solution	Dej Mar	2009-04-09 16:48:55
re: computer solution (spoiler)	Charlie	2009-04-09 12:28:07
computer solution (spoiler)	Daniel	2009-04-09 11:42:29

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