Problem 200
Find the 200th prime-proof sqube containing the contiguous sub-string “200”
We shall define a sqube to be a number of the form, p2q3, where p and q are distinct primes.
For example, 200 = 5223 or 120072949 = 232613.
The first five squbes are 72, 108, 200, 392, and 500.
Interestingly, 200 is also the first number for which you cannot change any single digit to make a prime; we shall call such numbers, prime-proof. The next prime-proof sqube which contains the contiguous sub-string “200” is 1992008.
Find the 200th prime-proof sqube containing the contiguous sub-string “200”.
找出第200个拥有连续子串“200”且不可变质数的平立方数
我们定义平立方数为可以写成p2q3形式的数，其中p和q为不同质数。
例如，200 = 5223，以及120072949 = 232613。
前五个平立方数分别是72, 108, 200, 392和500。
有趣的是，200同样是第一个你无法只改变其一位数字就成为质数的数， 我们称这样的数为不可变质数的。下一个拥有连续子串“200”且不可变质数的平立方数是1992008。
找出第200个拥有连续子串“200”且不可变质数的平立方数。