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 Prime it remains (Posted on 2013-01-15)
What is the smallest prime remaining prime when added to its reverse?

Analytical solution preferred.

 No Solution Yet Submitted by Ady TZIDON Rating: 4.0000 (2 votes)

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 Some observations and an answer | Comment 2 of 4 |
observation 1) It can't be a single digit, because the resulting sum is divisible by 2

observation 2) It can't have an even number of digits, because the resulting sum is divisible by 11.  Using a mod 11 test, the number and its reverse necessarily have opposing signs.  For instance, consider 1019. The odd digits minus the even ones = 7.  Its reverse is 9101, for which the odd digits minus the even ones = -7 .  So the sum, 10120, is necessarily divisible by 11.

observation 3) It can't have an initial odd digit, because the resulting sum is necessarily divisible by 2.

Using a prime number table, that makes the first 4 candidates 211 223 227 229 .

211 + 112 = 323, which is a multiple of 17
223 + 322 = 545, which is a multiple of 5
227 + 722 = 949, which is a multiple of 13
229 + 922 = 1151, which is prime number, so our answer is 229

Edited on January 15, 2013, 6:09 pm
 Posted by Steve Herman on 2013-01-15 18:08:25

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