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Problem 200


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。