State True or False.

There are pairs of twin primes between 50 and 100.

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True

False

answer is A.

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Detailed Solution

The given statement is there are pairs of twin primes between 50 and 100.
In the number system, there exists a pair of prime numbers such that the difference between two consecutive prime numbers is exactly 2. Those pairs are said to be twin primes.
There exist two pairs of twin primes between 50 and 100.
These two pairs of twin primes are grouped as and (71, 73) respectively.
We see that 61-59=2, and 73- 71=2.
Also, we find that the prime numbers in the pair (59, 61) appear as consecutive prime numbers in the number line, and also the prime numbers in the pair (71, 73) appear as consecutive prime numbers in the number line.
Thus, the required twin primes between 50 and 100 are (61,59), (71, 73).
Therefore, the given statement is true.
Hence the correct answer is option (1).

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