# Palindrome Number Calculator

Palindrome Checker
Lower Bound =
Upper Bound =

Options:
only square palindromes
only palindromes divisible by
all palindromes within range

There are palindromes.

Palindromic numbers are those which read the same forward and backward. Whether a number is a palindrome or not depends on its base representation. For example, 25152 is a palindrome in base-10, but its base-2 representation 110001001000000 is not a palindrome.

Prime palindromes are of interest to mathematicians because they are sparsely distributed in the integers. If a number is both prime and a palindrome, it must have an odd number of digits, except for the number 11. (A palindrome with an even number of digits is divisible by 11.)

The palindromic primes up to 100000 are

2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13331, 13831, 13931, 14341, 14741, 15451, 15551, 16061, 16361, 16561, 16661, 17471, 17971, 18181, 18481, 19391, 19891, 19991, 30103, 30203, 30403, 30703, 30803, 31013, 31513, 32323, 32423, 33533, 34543, 34843, 35053, 35153, 35353, 35753, 36263, 36563, 37273, 37573, 38083, 38183, 38783, 39293, 70207, 70507, 70607, 71317, 71917, 72227, 72727, 73037, 73237, 73637, 74047, 74747, 75557, 76367, 76667, 77377, 77477, 77977, 78487, 78787, 78887, 79397, 79697, 79997, 90709, 91019, 93139, 93239, 93739, 94049, 94349, 94649, 94849, 94949, 95959, 96269, 96469, 96769, 97379, 97579, 97879, 98389, 98689

You can use the calculator on the left to find palindromes that are squares of multiples of a certain number.