603, 604, and 605 are the first 3 consecutive integers that are the product of a prime and another prime squared.
603=3^{2}*67
604=2^{2}*151
605=5*11^{2}
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?
(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 20170402 09:56:47 