there are two prime numbers between 100 and 199 such that the ten digits is a prime number, the ones digit is a prime number and the tens and ones digits taken together are a 2 digit prime number. find the sum of these 2 prime number.

1ab

a prime = 2,3,5,7
b prime = 2,3,5,7

ab = 23,37,53,73

numbers are 137 and 173
sum = 310

nu uh

Apologies for the mistake. Let's go through the given conditions step by step.

1. The ten digit is a prime number: The only prime numbers between 100 and 199 that satisfy this condition are 1, 2, 3, 5, 7.

2. The ones digit is a prime number: The prime numbers between 0 and 9 are 2, 3, 5, 7.

3. The tens and ones digits taken together are a 2-digit prime number: The 2-digit prime numbers are 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Now, let's find the prime numbers that satisfy all three conditions:
- The tens digit can be either 1 or 7.
- The ones digit can be either 3 or 7.

Combining the options, we get the following two possible prime numbers:
1. 137
2. 173

The sum of these two prime numbers is 137 + 173 = 310.

Well, you've certainly set up quite a prime puzzle for me! Let's go on a prime adventure, shall we?

After some mathematical clowning around, I found out that the two prime numbers that meet your criteria are 113 and 157. The ten digit, one digit, and combination of tens and ones digits are all prime numbers in both cases. So, the sum of these two prime numbers is 113 + 157 = 270.

Now, you can say you've cracked the prime code and discovered the sum of these hilarious prime numbers!

To solve this problem, we need to identify the prime numbers that satisfy the given conditions between 100 and 199.

Let's break down the conditions:

1. The ten digits (the digit in the tens place) must be a prime number.
2. The ones digit must be a prime number.
3. When the tens and ones digits are taken together, they must form a two-digit prime number.

First, we will list all the prime numbers between 100 and 199:

101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.

Then, we will apply the conditions one by one.

Condition 1: The ten digits must be a prime number.
This condition narrows down our list to: 103, 107, 109, 113, 127, 131, 137, 139, 149, 157, 163, 167, 173, 179, 181, 191, 193, 197.

Condition 2: The ones digit must be a prime number.
This condition further narrows down our list to: 103, 107, 109, 113, 127, 131, 137, 139, 149, 157, 163, 167, 173, 179, 181, 191, 193, 197.

Condition 3: The tens and ones digits together must form a two-digit prime number.
To check this condition, we need to find all the two-digit prime numbers and see if they exist in our list.

The two-digit prime numbers are: 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Cross-referencing the two-digit prime numbers with our list, we find that the prime numbers satisfying all the conditions are 13 and 37.

Finally, we can calculate the sum of these two prime numbers:
13 + 37 = 50.

Therefore, the sum of the two prime numbers between 100 and 199 that satisfy the given conditions is 50.