Find the smallest palindrome number which is prime too and greater then given number N.
Input : N = 7 Output :11 11 is the smallest palindrome prime which is greater than N. Input : N = 112 Output : 131
An efficient solution is based on below observations. All palindrome with even digits is multiple of 11.
We can prove as follow:
11 % 11 = 0
1111 % 11 = 0
111111 % 11 = 0
11111111 % 11 = 0
1001 % 11 = (1111 – 11 * 10) % 11 = 0
100001 % 11 = (111111 – 1111 * 10) % 11 = 0
10000001 % 11 = (11111111 – 111111 * 10) % 11 = 0
For any palindrome with even digits:
abcddcba % 11
= (a * 10000001 + b * 100001 * 10 + c * 1001 * 100 + d * 11 * 1000) % 11
All palindrome with even digits is multiple of 11.
So among them, 11 is the only one prime
if (8 <= N <= 11) return 11
For other, we consider only palindrome with odd digits.
=N and it is a prime number
// then return it.
if ($y >= $N && isPrime($y) == true)
// Driver code
// This code is contributed by mits
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