Off the top of my head, 1001 is the answer. Check it out and see . . .
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1001 is not prime. 7 X 143 equals 1001.
There is 11, which is prime and which has 2 digits.
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No, 11 is the only palindromic prime with an even number of digits.
It is 2 which also is the only even prime number
The only two digit numbers whose digits add up to 17 are 89 and 98. Since 98 is an even number, 89 is prime.
It is composite, as are all whole numbers whose last digits are even.
The two-digit primes less than 50 are 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47. For each prime on this list whose tens digit is odd, check whether or not the number formed when the digits are reversed is also prime. (Note that if the tens digit is even, then the ``reversed'' number is even and hence not prime.) The palindromic primes less than 50 are 11, 13, 17, 31, and 37, whose sum is 109.