17 is aprime number. When the digits are
reversed, the resultis 71, which is also a -
prime number. Findother examples of
prime numbers that produce a prime-
number when the digits are reversed.
To find prime numbers that produce a prime number when the digits are reversed, we can start by checking single-digit prime numbers (2, 3, 5, 7) and their reversed forms.
For the given example, 17, when the digits are reversed, we get 71, which is also a prime number.
Let's check other single-digit prime numbers:
1. When the digit 2 is reversed, we get 2 again, which is a prime number.
2. When the digit 3 is reversed, we get 3 again, which is a prime number.
3. When the digit 5 is reversed, we get 5 again, which is a prime number.
4. When the digit 7 is reversed, we get 7 again, which is a prime number.
So, all single-digit prime numbers and their reversals are prime numbers.
Let's continue checking two-digit prime numbers:
1. 11 is a two-digit prime number, but when its digits are reversed, we also get 11. However, 11 is not considered a prime number for this question since reversing the digits doesn't give a different prime number.
2. 13 is a two-digit prime number. When we reverse its digits, we get 31, which is also a prime number.
3. 17 (already checked) is a two-digit prime number. When we reverse its digits, we get 71, which is also a prime number.
4. 19 is a two-digit prime number. When we reverse its digits, we get 91, which is not a prime number.
Therefore, the examples of prime numbers that produce prime numbers when their digits are reversed are:
13 and 31
17 and 71
To find other examples of prime numbers that produce a prime number when the digits are reversed, we can follow a step-by-step method:
1. Start by listing all prime numbers up to a reasonable limit. Let's consider prime numbers up to 100 for simplicity:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
2. Look for prime numbers that, when their digits are reversed, result in another prime number.
- For 17, when we reverse the digits, we get 71 (which is also a prime number).
3. Analyze the remaining prime numbers and check if their reversed digits form a prime number as well.
- For example, let's check 13. Reversing its digits, we get 31. However, 31 is also a prime number.
4. Continue this process for all remaining prime numbers.
- Continuing the analysis, we find that 37 does not produce a prime number when reversed (73 is not prime).
- 53 does not produce a prime number when reversed (35 is not prime).
- 59 does not produce a prime number when reversed (95 is not prime).
- All other prime numbers up to 100 have already been analyzed.
5. Summarizing the findings, we have:
- 17 reversed is 71 (both are prime).
- No other prime numbers up to 100 produce a prime number when reversed.
Therefore, the only example of a prime number (up to 100) that produces a prime number when the digits are reversed is 17.
To find other examples of prime numbers that produce a prime number when the digits are reversed, we can follow the following steps:
1. Start by listing down all the prime numbers up to a certain limit. Let's say we want to find prime numbers up to 100.
2. List down the prime numbers from 1 to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
3. Check each prime number to see if its reverse is also prime.
4. To reverse a number, for example, reversing 17 to get 71, you can reverse the digits by multiplying the given number by 10 repeatedly and adding the remainder when divided by 10. Here is an example:
Start with the number 17.
Reverse the digits:
1. Multiply by 10 (17 * 10 = 170)
2. Add the remainder when divided by 10 (170 + 7 = 177)
So, 17 reversed is 71.
5. Follow the above process for each prime number and check if the reversed number is also prime. If it is prime, then it is an example of a prime number that produces a prime number when the digits are reversed.
Using this process, we can find more examples of prime numbers that produce prime numbers when the digits are reversed.