603, 604, and 605 are the first 3 consecutive integers that are the product of a prime and another prime squared.

603=3²*67
604=2²*151
605=5*11²

1. What is the first set of 4 consecutive integers that are the product of a prime and another prime squared?
2. What is the first set of 5 consecutive integers that are the product of a prime and another prime squared?

One of the 6 must be divisible by 2*3, so it can only be 2*2*3 = 12 or 2*3*3 = 18, and we know that there is no string of 6 involving those numbers that works.

Posted by Steve Herman on 2017-04-02 20:01:20