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Q: What number has a 4 in the tens place that is 2 less than a perfect square?

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3 is prime, 1 less than the perfect square of 4 (2x2)

It is: 4

A square number, or perfect square, is the square of an integer. 232 is less than 572, 242 is more, so it is not the square of an integer.

It is 64 which is also a square number

One way is to get the prime factorization of the number. If every prime occurs an even number of times, it is a square, otherwise, not. Another is to estimate the square root of the number, and square it. If you get more than the number, try a lower estimate; if less, a higher one. Using interval bisection you very quickly zero in on the square root, if it is a whole number. If so, the number is a perfect square. Otherwise, you find 2 consecutive whole numbers between which is the square root, in which case it is not a perfect square.

Any number squared except 0 is a perfect square so it follows that prime numbers are less common than perfect squares.

Actually it can, if it's not the square of a prime number. For example, 144 is the square of 12; but you can also factor it as 6 x 24.

5040 is not a perfect square. The greatest perfect square less than 5040 is 4900.

8, 10 24, 26

1,0002 = 1,000,000 so 1 less is 9992 = 998,001

A beprisque number nnn is an integer which is either one more than a prime number and one less than a perfect square, or one more than a square and one less than a prime. The 5th such number is 10.

324

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