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√103 is more than 10 and less than 11. The primes less than 11 are 2, 3, 5, and 7.
The units digit (3) is not even, so 103 is not divisible by 2.
The sum of the digits (4) is not a multiple of 3, so 103 is not divisible by 3.
The units digit (3) is not 0 or 5, so 103 is not divisible by 5.
When 103 is divided by 7, the remainder is 5 (not 0), so 103 is not divisible by 7.
103 has no divisors less than its square root, so 103 is prime.
The units digit (3) is not even, so 103 is not divisible by 2.
The sum of the digits (4) is not a multiple of 3, so 103 is not divisible by 3.
The units digit (3) is not 0 or 5, so 103 is not divisible by 5.
When 103 is divided by 7, the remainder is 5 (not 0), so 103 is not divisible by 7.
103 has no divisors less than its square root, so 103 is prime.
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