If a prime number is prime after adding 6, 8, 12 and 14, then the prime number is______ ．

If a prime number is prime after adding 6, 8, 12 and 14, then the prime number is______ ．

Let this prime number be x, divide X by 5, and divide the remainder into the following five cases: when x = 5K + 1, then x + 14 = 5 (K + 3) is a composite number; when x = 5K + 2, then x + 8 = 5 (K + 2) is a composite number; when x = 5K + 3, then x + 12 = 5 (K + 3) is a composite number; when x = 5K + 4, then x + 6 = 5 (K + 2) is a composite number, so only x = 5K

A prime number and the sum of 6, 8, 12 and 14 are still prime numbers. How many prime numbers satisfy the above conditions?
A prime number and the sum of 6, 8, 12 and 14 are still prime numbers. How many prime numbers satisfy the above conditions?
The answer in the book is 1, and this prime number is 5. How to prove that other prime numbers are not OK?

5 divided by 1 and 14 can be divided by 5
5 divided by 2 plus 8 can be divided by 5
5 divided by 3 plus 12 can be divided by 5
5 divided by 4 and 6 can be divided by 5

Which prime numbers can be written as the sum of 26 () + () = () + () = () + () + () 30) + () = () + ()

26（13）+（13）=（3）+（23）=( 2)+( 7)+(17 )
30 （13）+（ 17）=（11 ）+（19 ）