Brainteaser 1538: Times square

From The Sunday Times, 1st March 1992 [link]

Alf: Listen to this: “SUN times DAY equals TIMES“.

Beth: Sounds like a lot of nonsense to me.

Alf: Let me write it down for you. Like this:

SUN × DAY = TIMES

In this sum are 10 different letters representing digits 0 to 9 and in my answer SUN minus DAY is a perfect square. That should help you.

Beth: That’s a tall order, but I’ll have a go. Where’s my calculator.

Beth did find Alf’s solution. What was their number for TIMES?

This puzzle was selected for the book Brainteasers (2002, edited by Victor Bryant), in which it appeared in the following modified form:

With the usual letters-for-digits convention:

SUN – DAY

is the square of a prime, and:

SUN × DAY = TIMES

What number is TIMES?

(We do not actually need to know that the square is the square of a prime, but it cuts down the work considerably).

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