The sum of my ones and tens digit is 10. My tens digit is greater than my ones digit. I am a prime number. What number am I?

Using your first two sentences, I see only the following possibilities

91
82
73
64
of these only 73 is prime.

I am assuming you wanted only a 2 digit number.

but don't the following also fit all your conditions ?

191,173,1873,1973,3491, .... ?

Lala

Let's break down the given information step-by-step to find the number you are looking for.

1. The sum of the ones and tens digit is 10.
Let's consider the possible combinations for the digits:
1 + 9 = 10
2 + 8 = 10
3 + 7 = 10
4 + 6 = 10
5 + 5 = 10

2. The tens digit is greater than the ones digit.
Based on the given combinations, we can eliminate the ones where the tens digit is not greater than the ones digit.
So, we are left with the following combinations:
2 + 8 = 10
3 + 7 = 10
4 + 6 = 10

3. The number is a prime number.
Among the possible combinations, we need to determine which ones form prime numbers.
The numbers formed with the combinations 2 + 8 and 4 + 6 are not prime numbers.
However, the number formed with the combination 3 + 7 is 37, which is a prime number.

Therefore, the number you are looking for is 37.

To solve this problem, we need to break it down into steps:

Step 1: Determine the possible combinations of the ones and tens digits that sum up to 10.
Since the tens digit is greater than the ones digit and both digits must add up to 10, the possible combinations are:
1 + 9
2 + 8
3 + 7
4 + 6
5 + 5 (not valid since both digits must be different)

Step 2: Combine each combination from Step 1 to get the two-digit numbers.
The two-digit numbers we get from each combination are:
19
28
37
46

Step 3: Check if any of the two-digit numbers obtained in Step 2 are prime numbers.
To do this, we check if each number is divisible by any number from 2 to the square root of that number.
If any number has no divisors other than 1 and itself, it is a prime number.

Let's check each number:
19: It is a prime number since there are no divisors other than 1 and 19.
28: It is not a prime number since it is divisible by 2 and 4.
37: It is a prime number since there are no divisors other than 1 and 37.
46: It is not a prime number since it is divisible by 2 and 23.

Step 4: Determine which of the prime numbers found in Step 3 matches the given conditions.
Based on the conditions given in the question (the sum of ones and tens digit is 10, and the tens digit is greater than the ones digit), the number that matches is 37.

So, the number you are looking for is 37.