99
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The largest two-digit prime number is 97.
99
98
The greatest two-digit odd number is 99. In a two-digit number, the first digit can range from 1 to 9, and the second digit can range from 0 to 9. Since we are looking for an odd number, the second digit must be odd, limiting our options to 1, 3, 5, 7, or 9. Among these, 99 is the greatest possible two-digit odd number.
96