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 Prime power puzzle (Posted on 2017-04-01)
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?

 See The Solution Submitted by Math Man Rating: 5.0000 (1 votes)

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 re: computer so far | Comment 2 of 9 |
(In reply to computer so far by Charlie)

By now the program has gotten up to 681940994 for n, but has still not found 4 in a row, much less 5 in a row.

I was trying to find a proof that four in a row was impossible, something along the lines of every group of four needs two even numbers, one of which is a multiple of 4. The multiple of 4 is 2^2 times some other prime. The other even number would have to be a multiple of 2 (obvious) times the square of some other prime number. I don't know if this is somehow impossible.

 Posted by Charlie on 2017-04-02 09:56:47

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