Speaking of Li Bai, people all know that he was a great poet in the Tang Dynasty in China. If the word "Li Bai" is reversed into "Li Bai", it can also be a person's name. This man's surname is Li Bai. Such meaningful and backward thinking languages are called palindromes, such as "Dog Bites Wolf", "Heaven and Earth" and "Lingling loves Mao Mao". Generally speaking, palindromes are written in units of words, and palindromes are very similar to symmetry in mathematics.

If a number reads the same in both directions, it is called palindrome, such as 10 1, 32 123, 9999, etc.

There is a famous "back number conjecture" in mathematics, which has not been solved yet. Take any decimal number, turn it upside down, add these two numbers, then add this sum to the original sum in turn, and repeat this process until you get a palindrome.

For example, 68, as long as you follow the above method, you can get the palindrome number of111in three steps.

68+86 154+45 1605+506 1 1 1 1

The guess of palindrome number means that no matter what number is used at the beginning, a palindrome number can be obtained after a limited number of steps.

No one can be sure whether this conjecture is right or wrong. Three digits 196 may be a counterexample, which shows that the "palindrome conjecture" is not valid, because this number has been calculated by computer for hundreds of thousands of steps, and there is still no palindrome, but no one can prove that this number will never produce palindromes.

Mathematicians have studied palindromes that are also prime numbers. Mathematicians think that there are infinite palindromes, but no one can prove this idea right yet.

Mathematicians also suspect that when there are infinite palindrome prime numbers, such as 30 103 and 30203, their characteristics are that the middle number is continuous and the other numbers are equal. Except 1 1 must be an odd number, because every even palindrome must be a multiple of 1 1, so it is not a prime number. For example, 12552 1 is a 6-digit palindrome. According to the method of judging whether it can be divisible by 1 1: the difference between the sum of all even numbers and the sum of all odd numbers is a multiple of 1 1, then this number can be divisible by 1 1,1252/kloc. Odd digits are 2,5, 1, and the difference of their sum is

( 1+5+2)-(2+5+ 1)=0,

Is a multiple of 1 1, so 12552 1 can be divisible by 1 1, and

12552 1÷ 1 1= 1 14 1 1。

So 12552 1 is not a prime number.

For example, there are many squares in the palindrome.

12 1= 1 12,

1232 1= 1 1 12,

123432 1= 1 1 1 12,

…,

1234567898765432 1= 1 1 1 1 1 1 1 1 12,

You can find some palindromes at will, and the square number accounts for a large proportion.

A similar situation exists for the cubic number, such as1331=13,1367631=13.

There are still many mysteries about such interesting palindromes.