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Prime power puzzle (Posted on 2017-04-01) Difficulty: 3 of 5
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?

No Solution Yet Submitted by Math Man    
Rating: 5.0000 (1 votes)

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Some Thoughts A simpler proof that 6 in a row is impossible | Comment 7 of 8 |
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
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