A 4-digit number is formed by repeating a 2-digit number such as 2525, 3232 etc. Any number of this form is exactly divisible by

Assume the unit digit to be x and ten’s digit to be y respectively.

Number = 1000y + 100x + 10y + x

⇒1010y + 101x

⇒101 (10y + x)

The number is divisible by 101, which is the required smallest three-digit prime number.

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