Prime Triplet Numbers
A group of three consecutive prime numbers that differ by 2 is called a prime triplet.
For example: (3, 5, 7) is the only prime triplet.
Solved Examples on Prime Triplet Numbers:
1. The prime triplet is
(a) 11, 15, 17; (b) 7, 10, 17; (c) 3, 5, 7; (d) 17, 18, 19
Solution:
(a) 11, 15, 17
Difference between 15 and 11 = 4
Difference between 17 and 15 = 2
(b) 7, 10, 17
Difference between 10 and 7 = 3
Difference between 17 and 10 = 7
(c) 3, 5, 7
Difference between 5 and 3 = 2
Difference between 7 and 5 = 2
(d) 17, 18, 19
Difference between 18 and 17 = 1
Difference between 19 and 18 = 1
Only in (c) we can see that the three consecutive prime numbers (17, 18, 19) are differ by 2.
So, the correct option is (c).
2. Check whether the following is a prime triplet.
(i) 23, 29, 31; (ii) 3, 5, 7.
Solution:
(i) 23, 29, 31
Difference between 29 and 23 = 6
Difference between 31 and 29 = 2
Therefore, the three consecutive prime numbers 23, 29, 31 are not differ by 2.
So, they are not prime triplet.
(ii) 3, 5, 7.
Difference between 5 and 3 = 2
Difference between 7 and 5 = 2
Therefore, the three consecutive prime numbers 3, 5, 7 are differ by 2.
So, they are prime triplet.
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