All the twin prime numbers can be expressed in the form of (6n-1, 6n+1) except the pair (3,5). The next pair of twin prime numbers can be found because they can be expressed in the form of (6n-1, 6n+1). The first set of twin prime numbers are (3,5). To find the first few pairs of twin primes we have to look at the prime numbers that occur first. So, it is the only prime number that occurs in two prime twins. It has a negative gap of 2 with 3 and a positive gap of 2 with 7. 5 is the only prime number that has both positive and negative prime gaps.Hence, they cannot be considered as twin primes. For example, the prime numbers (2,3) have no composite number between them. Any two prime numbers that do not have a composite number between them cannot be considered as twin prime.The sum of every twin prime number except (3,5) can be expressed in the form of 12n.Every twin prime number except (3,5) can be expressed in one given form.Some of the properties depicted by the twin prime numbers are given below: Numbers that belong to these categories depict some common properties. These numbers have something common between them. We discussed that twin primes are prime numbers that have a difference of two between them.
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