Answer
Verified
330.3k+ views
Hint: First of all check if both the numbers are prime or not. If yes, then check if the difference between the numbers is 2 or not. If both conditions satisfy, then only two numbers are twin prime.
Complete step-by-step answer:
Here, we have to find which of the following pairs twin primes are: (19, 21), (29, 31), (39, 41), (49, 51).
Before proceeding with this question, we must know what twin prime numbers are. Two numbers are twin prime to each other when they both are prime and have a difference of 2 between them. For example, (5, 7) and (11, 13), etc. are twin prime numbers. Also, a prime number is a number that is divisible by 1 and itself only. For example, 2, 7, 17, etc. are prime numbers.
Now, we will check which of the pairs in options are twin prime.
(a) (19, 21)
In the above pair, 19 is a prime number, and the difference between 19 and 21 is 2, but 21 is not a prime number as it has factors like 3, 7, etc. So, we get that the pair (19, 21) is not a twin prime.
(b) (29, 31)
In the above pair, both 29 and 31 are prime numbers and the difference between 29 and 31 is 2. So, we get that the pair (29, 31) is twin prime.
(c) (39, 41)
In the above pair, 41 is a prime number but 39 is not a prime number as it has factors like 3, 13, etc. So we get that the pair (39, 41) is not a twin prime.
(d) (49, 51)
In the above pair, neither 49 nor 51 is a prime number because 49 has factors like 7, etc. and 51 has factors like 17, 3, etc. So, we get that the pair (49, 51) is not a twin prime.
So, we get only one pair that is twin prime and that pair is (29, 31).
Hence, option (b) is the right answer.
Note: Students must note that 2 is the smallest prime number and is the only even prime number. All other prime numbers are odd. Students often make this mistake of considering many odd numbers as prime. For example, many students consider 237, 147, 51, 91, etc. as prime by just looking at them, but they are not prime numbers. So, care must be taken while selecting numbers as prime or not.
Complete step-by-step answer:
Here, we have to find which of the following pairs twin primes are: (19, 21), (29, 31), (39, 41), (49, 51).
Before proceeding with this question, we must know what twin prime numbers are. Two numbers are twin prime to each other when they both are prime and have a difference of 2 between them. For example, (5, 7) and (11, 13), etc. are twin prime numbers. Also, a prime number is a number that is divisible by 1 and itself only. For example, 2, 7, 17, etc. are prime numbers.
Now, we will check which of the pairs in options are twin prime.
(a) (19, 21)
In the above pair, 19 is a prime number, and the difference between 19 and 21 is 2, but 21 is not a prime number as it has factors like 3, 7, etc. So, we get that the pair (19, 21) is not a twin prime.
(b) (29, 31)
In the above pair, both 29 and 31 are prime numbers and the difference between 29 and 31 is 2. So, we get that the pair (29, 31) is twin prime.
(c) (39, 41)
In the above pair, 41 is a prime number but 39 is not a prime number as it has factors like 3, 13, etc. So we get that the pair (39, 41) is not a twin prime.
(d) (49, 51)
In the above pair, neither 49 nor 51 is a prime number because 49 has factors like 7, etc. and 51 has factors like 17, 3, etc. So, we get that the pair (49, 51) is not a twin prime.
So, we get only one pair that is twin prime and that pair is (29, 31).
Hence, option (b) is the right answer.
Note: Students must note that 2 is the smallest prime number and is the only even prime number. All other prime numbers are odd. Students often make this mistake of considering many odd numbers as prime. For example, many students consider 237, 147, 51, 91, etc. as prime by just looking at them, but they are not prime numbers. So, care must be taken while selecting numbers as prime or not.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
What is BLO What is the full form of BLO class 8 social science CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Fill the blanks with proper collective nouns 1 A of class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE