The prime numbers 31 and 41 differ by 10,
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Two other examples of prime numbers differing by 10 are the pair (61, 71) and the pair (101, 111).
To find other examples of prime numbers differing by 10, we can start by adding or subtracting 10 to the given prime numbers.
1. Add 10 to 31: 31 + 10 = 41 (Already given example)
2. Subtract 10 from 31: 31 - 10 = 21, but 21 is not a prime number.
3. Add 10 to 41: 41 + 10 = 51, but 51 is not a prime number.
4. Subtract 10 from 41: 41 - 10 = 31 (Already given example)
Therefore, the only two prime numbers that differ by 10 are 31 and 41.
To find other examples of prime numbers that differ by 10, we can start by identifying the given prime numbers: 31 and 41.
To systematically find prime numbers differing by 10, we can follow these steps:
1. Start with the first prime number after 41 (which is 43), and check if it differs by 10 from any previous prime numbers.
2. To check if a number is prime, divide it by all prime numbers less than its square root. If it is not divisible by any of the prime numbers, then it is a prime number itself.
3. Repeat this process for subsequent prime numbers until you find other examples differing by 10.
Let's go step by step to find more prime numbers that differ by 10:
1. The next prime number after 41 is 43. Let's check if it differs by 10 from any previous prime numbers: 43 - 10 = 33 (not prime), 43 + 10 = 53 (prime). So, 43 differs by 10 from 53.
2. The following prime number is 47. Let's check if it differs by 10 from any previous prime numbers: 47 - 10 = 37 (prime), 47 + 10 = 57 (not prime). So, 47 differs by 10 from 37.
3. The next prime number is 53. We have already checked it when examining 43, so we don't need to repeat the steps.
4. The subsequent prime number is 59. Let's check if it differs by 10 from any previous prime numbers: 59 - 10 = 49 (not prime), 59 + 10 = 69 (not prime).
Therefore, the prime numbers that differ by 10 are: 31-41, 43-53, and 47-37.