1061

This number is a prime.

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If we are to append to prime 1061 another smallest prime so that the concatenation would yield a square then this second prime would be 10601. Note that 10601 is 1061 with just an extra zero inserted. Also the square root of 106110601 is 10301. Both 10301 and 10601 are palindromic primes! [De Geest]