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A palindrome is a sequence of digits which reads the same backward or forward. For example, $7447$, $1001$ are palindromes, but $7455$, $1201$ are not palindromes. How many $8$ digit prime palindromes are there?
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27 votes
I think the answer should be $0$, as any even digit palindrome(other than $11$) cannot be prime. Even digit palindromes will always be divisible by $11$ (you can check the divisibility test by $11$).
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Even no of digits cannot be prime number so no pallindromes

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Let the digits of our 8-digit palindrome n be d1d2d3d4d4d3d2d1. Then the palindrome has the form

n=10000001⋅d1+1000010⋅d2+100100⋅d3+11000⋅d4.

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. 101101, 1030110301, 9868998689, 98010899801089.)

The correct answer is 0.

–2 votes
–2 votes
i think answer will  be 9*10^3   bcz

9*10*10*10*1*1*1*1 =9000  and each no in multiplication shows the digit place
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