what are twin prime numbers ?

Question

what are twin prime numbers ?

can you please provide me an example

thanks

is it same as co-prime ? ex: 5,6 are co-prime as they dont have any common factor except 1 ...does twin prime ==co-prime ?

Answer 1

Twin primes are prime numbers that differ by 2, such as (5,7), or (11,13), or (41,43), etc. See wikipedia.

Answer 2

A twin prime is a prime number that differs from another prime number by two. Except for the pair (2, 3), this is the smallest possible difference between two primes. Some examples of twin prime pairs are (5, 7), (11, 13), and (821, 823). Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin.

The question of whether there exist infinitely many twin primes has been one of the great open questions in number theory for many years. This is the content of the twin prime conjecture. A strong form of the twin prime conjecture, the Hardy-Littlewood conjecture, postulates a distribution law for twin primes akin to the prime number theorem.

Using his celebrated sieve method, Viggo Brun shows that the number of twin primes less than x is << x/(log x)2. This result implies that the sum of the reciprocals of all twin primes converges (see Brun's constant and Brun's theorem). This is in stark contrast to the sum of the reciprocals of all primes, which diverges. He also shows that every even number can be represented in infinitely many ways as a difference of two numbers both having at most 9 prime factors. Chen Jingrun's well known theorem states that for any m even, there are infinitely many primes that differ by m from a number having at most two prime factors. (Before Brun attacked the twin prime problem, Jean Merlin (1876-1914) had also attempted to solve this problem using the sieve method. He was killed in World War I.)

Every twin prime pair greater than 3 is of the form (6n − 1, 6n + 1) for some natural number n, and with the exception of n = 1, n must end in 0, 2, 3, 5, 7, or 8.

It has been proven that the pair m, m + 2 is a twin prime if and only if

4((m-1)! + 1) \equiv -m \pmod {m(m+2)}

If m−4 or m+6 is also prime then the 3 primes are called a prime triplet.

Answer 3

A twin prime is a prime number that differs from another prime number by two. Except for the pair (2, 3), this is the smallest possible difference between two primes. Some examples of twin prime pairs are (5, 7), (11, 13), and (821, 823). Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin.
No, it's not the same as co-prime cos (as your example stated) 6 is NOT a prime number.

Answer 4

Twin primes are two primes that are only two units apart, like 3 and 5, or 5 and 7, or 29 and 31.

So, no, being twin primes is not the same as being co-prime.

Answer 5

this is a twin best purely with the two 179 or 183. yet 183 is conveniently seen to be divisible with the aid of three. (a style is divisible with the aid of three if the sum of its digits is divisible with the aid of three. The sum of the digits of 183 is 12, this is divisible with the aid of three.) certainly, 183 = 3*sixty one. subsequently 179 ought to be best. you may independently be advantageous that 179 is best utilising any common primality try. in case you want to apply a common sieve, bear in mind you purely ought to verify whether it has aspects decrease than its sq. root. So merely verify whether 179 has aspects decrease than or equivalent to fourteen.