Two conditions
Number Theory
Level
2
A base-10 integer larger than 11 satisfies two conditions:
1) it is a palindrome
2) it is a prime number
The number of digits in the integer is...
Odd
Infinite
It can be either odd or even
Even
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1 solution
Assume the number of digits in the integer is even.
Add and subtract alternate digits. Since the number is a palindrome, every digit in the first half of the number have the matching digit in the second half of the number added or subtracted, meaning each pair will sum to zero. (For example, the number ABCDDCBA will have A - B + C - D + D - C + B - A.) This means the number is divisible by 11 and hence not prime.
So the number of digits must be odd. To prove such a number exists, 101 is prime.