I have some fascination about prime numbers. Why i dont know. Here goes some observed trend... I hope its consistent enough.
Take a pair of prime numbers such that the difference between them is 2. Now the number between these two prime numbers is always divisible by 6.
The reasoning being......
Facts: There is only one even prime number i.e. 2
1. Such two prime numbers are always odd. And the number in between has to be divisible by 2
2.Lets consider that x and (x+2) are the prime numbers. Now, there are no three consecutive numbers i.e. x, (x+1) and (x+2) out of which none is divisible by 3.
Hence x+1 has to be divisible by 3.
3. Continuing point 2, another observation is: If x is a prime number where x >=5, then (x+1) or (x-1) is divisible by six. For instance, 19 is prime and 18 is divisible by 6. 29 is prime and 30 is divisible by 6.
Take a pair of prime numbers such that the difference between them is 2. Now the number between these two prime numbers is always divisible by 6.
The reasoning being......
Facts: There is only one even prime number i.e. 2
1. Such two prime numbers are always odd. And the number in between has to be divisible by 2
2.Lets consider that x and (x+2) are the prime numbers. Now, there are no three consecutive numbers i.e. x, (x+1) and (x+2) out of which none is divisible by 3.
Hence x+1 has to be divisible by 3.
3. Continuing point 2, another observation is: If x is a prime number where x >=5, then (x+1) or (x-1) is divisible by six. For instance, 19 is prime and 18 is divisible by 6. 29 is prime and 30 is divisible by 6.
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