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Which of the following are two consecutive prime numbers that differ by 2?
- a)Co-primes
- b)Twin primes
- c)Composite numbers
- d)Both (a) and (b)
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Which of the following are two consecutive prime numbers that differ b...
- Three pairs of prime numbers whose difference is 2 are (5, 7), (11, 13) and (17, 19).
- A pair of prime numbers whose difference is 2 are called twin primes.
- The alternative names given to twin primes are prime twin or prime pair.
Most Upvoted Answer
Which of the following are two consecutive prime numbers that differ b...
Explanation:
Two consecutive prime numbers that differ by 2 are called twin primes. Twin primes are pairs of primes that have a difference of 2 between them. For example, (3, 5), (11, 13), and (17, 19) are twin prime pairs.
Prime Numbers:
Prime numbers are numbers that are greater than 1 and have no divisors other than 1 and themselves. For example, 2, 3, 5, 7, 11, 13, 17, 19, 23, and so on, are prime numbers.
Co-Primes:
Co-primes are numbers that have only 1 as their common divisor. In other words, co-prime numbers have a greatest common divisor (GCD) of 1. For example, (4, 7), (15, 28), and (9, 16) are pairs of co-prime numbers.
Composite Numbers:
Composite numbers are numbers that have more than two factors. In other words, composite numbers have divisors other than 1 and themselves. For example, 4, 6, 8, 9, 10, and 12 are composite numbers.
Answer:
The correct answer is option B, twin primes. Twin primes are the only ones among the given options that satisfy the condition of being two consecutive prime numbers that differ by 2. Co-primes and composite numbers do not necessarily have a difference of 2 between them.
The concept of twin primes is an interesting topic in number theory and has been studied extensively by mathematicians. Twin primes have been a subject of research for many years, and despite efforts, there is still no complete understanding of their distribution and properties.
Two consecutive prime numbers that differ by 2 are called twin primes. Twin primes are pairs of primes that have a difference of 2 between them. For example, (3, 5), (11, 13), and (17, 19) are twin prime pairs.
Prime Numbers:
Prime numbers are numbers that are greater than 1 and have no divisors other than 1 and themselves. For example, 2, 3, 5, 7, 11, 13, 17, 19, 23, and so on, are prime numbers.
Co-Primes:
Co-primes are numbers that have only 1 as their common divisor. In other words, co-prime numbers have a greatest common divisor (GCD) of 1. For example, (4, 7), (15, 28), and (9, 16) are pairs of co-prime numbers.
Composite Numbers:
Composite numbers are numbers that have more than two factors. In other words, composite numbers have divisors other than 1 and themselves. For example, 4, 6, 8, 9, 10, and 12 are composite numbers.
Answer:
The correct answer is option B, twin primes. Twin primes are the only ones among the given options that satisfy the condition of being two consecutive prime numbers that differ by 2. Co-primes and composite numbers do not necessarily have a difference of 2 between them.
The concept of twin primes is an interesting topic in number theory and has been studied extensively by mathematicians. Twin primes have been a subject of research for many years, and despite efforts, there is still no complete understanding of their distribution and properties.
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Which of the following are two consecutive prime numbers that differ by 2?a)Co-primesb)Twin primesc)Composite numbersd)Both(a) and (b)Correct answer is option 'B'. Can you explain this answer?
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