write defination, examples, symbols of prime, co-prime, composite, twin prime & perfect number....
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Answer:
Two prime numbers are called twin primes if there is present only one composite number between them. Or we can also say two prime numbers whose difference is two are called twin primes. For example, (3,5) are twin primes, since the difference between the two numbers 5 – 3 = 2. The alternative names, given to twin primes are prime twin or prime pair. Also, learn prime numbers here.
The set of prime numbers, though not having fixed or regular structure within it, should be symbolized as N either in Boldface or Blackboard
♦Prime number♦
Prime numbers are the positive integers having only two factors, 1 and the integer itself.
example
factors of 6 are 1,2,3 and 6, which are four factors in total
♦Co - prime ♦
A Co-prime number is a set of numbers or integers which have only 1 as their common factor i.e. their highest common factor (HCF)
Example
21 and 22
For 21 and 22:
The factors of 21 are 1, 3, 7, and 21.
The factors of 22 are 1, 2, 11, and 22.
Here 21 and 22 have only one common factor that is 1. Hence, their HCF is 1 and are co-prime.
♦ Composite♦
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself.
example
4, 6, 8, 9 and 10 are the first few composite numbers.
♦Twin number♦
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair.
Example
3 and 5
♦ Perfect Number♦
In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself.
Example
6 has divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number.