Answer:
The three-digit prime number between 100 and 200 that also has prime last two digits and prime digits themselves is 137.
Explanation:
To find the three-digit prime number between 100 and 200 that also has prime last two digits and prime digits themselves, we need to check each number in the range 101 to 199 and see if it meets all three conditions.
Condition 1: The number is prime
We can check if a number is prime by dividing it by all positive integers from 1 to itself. If the number has no divisors other than 1 and itself, then it is prime.
Condition 2: The last two digits are prime
To check if the last two digits of a number are prime, we can simply extract those digits and check if they form a prime number.
For example, if the number is 123, the last two digits are 23. We can check if 23 is prime by dividing it by all positive integers from 1 to itself.
Condition 3: The two digits themselves are prime
To check if the two digits themselves are prime, we can follow the same process as in Condition 2.
For example, if the number is 123, the two digits themselves are 1 and 2. We can check if 1 and 2 are prime by dividing them by all positive integers from 1 to themselves.
Checking the numbers
Starting with 101, we can check each number in the range 101 to 199 to see if it meets all three conditions.
We can use a table to organize our findings:
Number Last Two Digits Prime Digits Prime?
We can continue checking numbers until we find one that meets all three conditions.
In this case, the number 137 meets all three conditions.