perplexus.info :: Numbers : Primed Palindromes

Primed Palindromes (Posted on 2008-12-27)

A prime number less than 100 is increased by 1 and squared.
This square is incremented by 1 to yield a prime which is then squared.
The digits of this second square are reversed and added to that square resulting in a palindrome.

For which primes does this occur?

See The Solution Submitted by brianjn

Rating: 5.0000 (1 votes)

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Puzzle Answer

Comment 3 of 3 |

There are precisely 2 primes which satisfy the given conditions. These are:

19 and 89, since:

1) 19+1=20, 20^2+1=401, 401 ^2=160801 and, 160801+108061= 268862, which is a palindrome.

2) 89+1=90, 90^2+1=8101, 8101^2=65626201 and:

65626201+10262656= 75888857

Edited on May 17, 2022, 2:18 am

Posted by K Sengupta on 2022-05-17 02:12:36

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