Question

Define these:--

1).Twin Primes:-

2). Co-Primes:-

3). Prime Triplet:-

4).Perfect Numbers:-


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Answer 1

$\huge \tt \green {twin \: primes}$

Twin primes are pairs of primes which differ by two.

(This name was coined by Stäckel in 1916.) The first twin primes are {3,5}, {5,7}, {11,13,} and {17,19}.

It has been conjectured that there are infinitely many twin primes (see the twin prime conjecture for further information).

$\huge \tt \green{co - prime}$

Two numbers are coprime if their highest common factor (or greatest common divisor if you must) is 1.

You can have the set of positive integers which are coprime to a given number: for example those coprime to 12 are 1,5,7,11,13,17,19,23,25, and so on.

$\huge \tt \green{prime - triplet}$

Prime Triplet is a set of three prime numbers of the form (p, p+2, p+6) or (p, p+4, p+6).

This is the closest possible grouping of three prime numbers, since one of every three sequential odd numbers is a multiple of three, and hence not prime (except for 3 itself) except (2, 3, 5) and (3, 5, 7) .

$\huge \tt \green{perfect \: no.}$

Perfect number, a positive integer that is equal to the sum of its proper divisors.

The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128.

Answer 2

pair of prime numbers whose difference is 2, is called twin prime whereas two numbers having only 1 as a common factor is called co-prime numbers. And Prime triplet is a set of three prime numbers in which the smallest and largest of the three differ by 6. In particular, the sets must have the form (p, p + 2, p + 6) or (p, p + 4, p + 6).

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