A pair of emirps consists of two prime numbers such that reversing the digits of one number gives the other. How many pairs of two-digit emirps exist such that each number in the pair is greater than 11?
The list of prime numbers between 11 and 100 are:
11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
So try them one at a time, say
number reversed
11 11 OK
13 31 OK
17 71 OK
19 91 is composite [pair rejected]
23 32 [rejected]
...
97 79 OK
So you'll get a list in no time.
To find the number of pairs of two-digit emirps, we need to check every two-digit prime number greater than 11 and see if the reverse of its digits is another prime number. Let's follow these steps:
Step 1: Identify all the two-digit prime numbers greater than 11.
Starting from 12, we check each consecutive two-digit number to see if it's prime. The two-digit prime numbers are: 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
Step 2: Check if the reverse of each prime number is also prime.
For example, the reverse of 13 is 31. If 31 is a prime number, then we have found a pair of emirps. If not, we move on to the next prime number.
Step 3: Count the number of pairs of emirps found.
Keep track of the prime numbers for which the reverse is also prime.
By following these steps, we can determine the number of pairs of two-digit emirps such that each number in the pair is greater than 11.
To solve this problem, we need to determine which prime numbers are emirps. An emirp is a prime number that remains prime when its digits are reversed and the resulting number is different.
To find all the prime numbers between 11 and 99, we can use a prime number generator algorithm. Here is a step-by-step guide:
1. Create a list of all numbers between 11 and 99.
2. Iterate through the list, starting from the first number.
3. Check if the number is divisible by any number between 2 and the square root of the number. If it is, remove it from the list.
4. Repeat this process until you reach the end of the list.
5. The remaining numbers in the list are prime numbers.
Once you have the list of prime numbers, check if each prime number is an emirp. To do this, reverse the digits of each prime number and check if the reversed number is also in the list of prime numbers.
Finally, count the number of pairs where both prime numbers are greater than 11 and each number in the pair is an emirp.