Question 17 of 36beginner🔧 ApplyShort Answer2 marks

Twin primes are pairs of primes having a difference of 2. For example, 3 and 5 are twin primes. So are 17 and 19. Find the other twin primes between 1 and 100.

Correct Answer

Definition: Twin primes are pairs of primes having a difference of 2.

Step 1: List all primes 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

Step 2: Identify pairs with difference 2.

Step 3: (3, 5): 5 − 3 = 2 ✓

Step 4: (5, 7): 7 − 5 = 2 ✓

Step 5: (11, 13): 13 − 11 = 2 ✓

Step 6: (17, 19): 19 − 17 = 2 ✓

Step 7: (29, 31): 31 − 29 = 2 ✓

Step 8: (41, 43): 43 − 41 = 2 ✓

Step 9: (59, 61): 61 − 59 = 2 ✓

Step 10: (71, 73): 73 − 71 = 2 ✓

Answer: The twin primes between 1 and 100 are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73).

Exercise: Figure it Out (Section 3) | Q: 8 | (Page Page 8)
For More Understanding

Explanation

Twin primes are pairs of primes that differ by 2. Looking at the list of primes 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. Pairs with difference 2: (3,5), (5,7), (11,13), (17,19), (29,31), (41,43), (59,61), (71,73).

Solution Steps

  1. Step 1: List all primes up to 100.

  2. Step 2: Identify pairs with difference 2.

  3. Step 3: (3,5): 5-3=2 ✓

  4. Step 4: (5,7): 7-5=2 ✓

  5. Step 5: (11,13): 13-11=2 ✓

  6. Step 6: (17,19): 19-17=2 ✓

  7. Step 7: (29,31): 31-29=2 ✓

  8. Step 8: (41,43): 43-41=2 ✓

  9. Step 9: (59,61): 61-59=2 ✓

  10. Step 10: (71,73): 73-71=2 ✓

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