Answer :
To determine the twin prime pairs up to 100, we need to identify pairs of prime numbers such that the second number in the pair is exactly two more than the first, and both numbers themselves are prime.
Here are the steps involved:
1. Identify Prime Numbers: First, list all prime numbers up to 100. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
2. Check for Twin Primes: Next, check each prime number and see if adding 2 to it yields another prime number. If it does, they form a twin prime pair.
Let's go through the process:
### Prime Numbers up 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
### Checking for Twin Primes:
Now we will check each prime number and see if there is another prime exactly two units larger:
1. 3 and 5: Both are primes and differ by 2. So, `(3, 5)` is a twin prime pair.
2. 5 and 7: Both are primes and differ by 2. So, `(5, 7)` is a twin prime pair.
3. 11 and 13: Both are primes and differ by 2. So, `(11, 13)` is a twin prime pair.
4. 17 and 19: Both are primes and differ by 2. So, `(17, 19)` is a twin prime pair.
5. 29 and 31: Both are primes and differ by 2. So, `(29, 31)` is a twin prime pair.
6. 41 and 43: Both are primes and differ by 2. So, `(41, 43)` is a twin prime pair.
7. 59 and 61: Both are primes and differ by 2. So, `(59, 61)` is a twin prime pair.
8. 71 and 73: Both are primes and differ by 2. So, `(71, 73)` is a twin prime pair.
Therefore, the twin prime pairs up to 100 are:
[tex]\[ (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73) \][/tex]
Here are the steps involved:
1. Identify Prime Numbers: First, list all prime numbers up to 100. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
2. Check for Twin Primes: Next, check each prime number and see if adding 2 to it yields another prime number. If it does, they form a twin prime pair.
Let's go through the process:
### Prime Numbers up 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
### Checking for Twin Primes:
Now we will check each prime number and see if there is another prime exactly two units larger:
1. 3 and 5: Both are primes and differ by 2. So, `(3, 5)` is a twin prime pair.
2. 5 and 7: Both are primes and differ by 2. So, `(5, 7)` is a twin prime pair.
3. 11 and 13: Both are primes and differ by 2. So, `(11, 13)` is a twin prime pair.
4. 17 and 19: Both are primes and differ by 2. So, `(17, 19)` is a twin prime pair.
5. 29 and 31: Both are primes and differ by 2. So, `(29, 31)` is a twin prime pair.
6. 41 and 43: Both are primes and differ by 2. So, `(41, 43)` is a twin prime pair.
7. 59 and 61: Both are primes and differ by 2. So, `(59, 61)` is a twin prime pair.
8. 71 and 73: Both are primes and differ by 2. So, `(71, 73)` is a twin prime pair.
Therefore, the twin prime pairs up to 100 are:
[tex]\[ (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73) \][/tex]