Not necessarily. Consider 444.
The digits are not different.
The first and second digits are not multiples of 3
The first digit is not greater than the second digit.
In spite of all that, 444 is a 3-digit number
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117. All multiples of 9 have digits that add up to something divisible by 9. Examples, 117, 36, 45, 54 all have digits that add up to 9.
Integers of 6 digits are normally greater than integers of 5 digits
4 x 578 = 2312 8 x 754 = 6032
Any 5-digit number is greater than a 4-digit one.
Prime number between 196 and 289 whose digits add to 14? Possibles 239, 248, 257, 266, 275, 284. 248, 266 and 284 are multiples of 2, 275 is a multiple of 5. This leaves 239 and 257. Only 239 has one digit which is the square of another. So there you have it.