A question about perfect squares

[Ore4444]

Homework Statement

I've been given a task to find "A 4-digit perfect square whose digits are all unique, and whose square root is a prime number".
That's all. I know that there are about 10 possible answers and I need them all.
Thanks a lot for any future help.

 

[HallsofIvy]

Did you really mean to put this in the physics section?

Square root of 1000 is 31 point something so that would be too small. Square root of 1000 is, of course, 100 so you are looking for prime numbers between 32 and 100.
Seems to me, squaring all primes between 32 and 100 would do it would give you the answer.

 

[Ore4444]

I wasn't sure if this was the right forum either but I thank you for your answer.
I'll try to do what you said. :)

 

[CompuChip]

And there are exactly 9 of them.

 

[asd1249jf]

Did you really mean to put this in the physics section?

Square root of 1000 is 31 point something so that would be too small. Square root of 1000 is, of course, 100 so you are looking for prime numbers between 32 and 100.
Seems to me, squaring all primes between 32 and 100 would do it would give you the answer.

Why is square root of 1000, 100? Why only up until 1000? The maximum value possible for 4 digit number is 9999

[EDIT]

Oh I just realized you meant to put 10000 lol, ok fair enough

 

[Ore4444]

Thank you.
I solved it. The answer was 5329.

 

[asd1249jf]

Thank you.
I solved it. The answer was 5329.

That's one answer. There are more answers, just to let you know.

 

[CompuChip]

And there are exactly 9 of them.

As I said

But the question was

I've been given a task to find "A 4-digit perfect square [...]

so I guess one is enough.

 

[Ore4444]

Oh yes, but I needed only this one.

 

[CompuChip]

Mathematica is cool

Table[If[PrimeQ[n] && Length[Union[IntegerDigits[n^2]]] == 4, 
   Print["n = ", n, "; n^2 = ", n^2]], 
     {n, Floor[Sqrt[999]], Sqrt[10000]}];

n = 37; n^2 = 1369
n = 43; n^2 = 1849
n = 53; n^2 = 2809
n = 59; n^2 = 3481
n = 61; n^2 = 3721
n = 71; n^2 = 5041
n = 73; n^2 = 5329
n = 79; n^2 = 6241
n = 89; n^2 = 7921