0
$\begingroup$

An integer is said to be palindrome if it reads the same forward or backward. For example, the integer 14541 is a 5 digit palindrome and 12345 is not a palindrome. How many 8-digit palindromes are prime?

$\endgroup$

closed as off-topic by Did, Matthew Conroy, user91500, steven gregory, Namaste Apr 28 '17 at 23:47

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, Matthew Conroy, user91500, steven gregory, Namaste
If this question can be reworded to fit the rules in the help center, please edit the question.

6
$\begingroup$

Let the digits of our 8-digit palindrome $n$ be $d_1d_2d_3d_4d_4d_3d_2d_1$. Then the palindrome has the form $$ n=10000001\cdot d_1 + 1000010\cdot d_2 + 100100\cdot d_3 + 11000\cdot d_4. $$ Such $n$ cannot be prime because $$ \gcd(10000001,1000010,100100,11000)=11. $$ So there are no 8-digit prime palindromes. (However, there are prime palindromes with an odd number of digits, e.g. $101$, $10301$, $98689$, $9801089$.)

$\endgroup$
3
$\begingroup$

I think palindrome is divisible by 11 because division by 11requires addition of alternate digits should be equal let the 8 digit palindrome number be (abcddcba) then a+c+d+b=b+d+c+a hence it cannot be a prime so that means the palindrome having even no of digits cannot be prime number of course 11 is an exception

$\endgroup$
  • $\begingroup$ Of course Alex what you said is correct . $\endgroup$ – Ch.Siva Ram Kishore Apr 28 '17 at 5:48

Not the answer you're looking for? Browse other questions tagged or ask your own question.