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Find the 200th prime-proof sqube containing the contiguous sub-string "200"

Problem 200

Published on 28 June 2008 at 10:00 am [Server Time]

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".


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