A Twin Prime number is a prime number which differs from other prime number by two. eg (5,7), (11,13), (17,19), (29,31), (41,43), (59,61)........ Prove that number between twin primes is divisible by 6.
Solution 1:
all prime numbers are of the form 6x+1 or 6x-1
so to be twin primes they should be 6x-1 and 6x+1 for some x
so the number netween them is 6x which is divided by 6
Solution 2:
For a number to be divisible by 6
- Must be divisible by both 2 and 3
Since it is between 2 primes, it is even and hence divisible by 2. Since every third number is divisible by three and the two adjacent ones of this number are prime, this number must also be divisible by three. Hence every numer between twin primes (except (3, 5)) is divisible by 6.
Solution 1:
all prime numbers are of the form 6x+1 or 6x-1
so to be twin primes they should be 6x-1 and 6x+1 for some x
so the number netween them is 6x which is divided by 6
Solution 2:
For a number to be divisible by 6
- Must be divisible by both 2 and 3
Since it is between 2 primes, it is even and hence divisible by 2. Since every third number is divisible by three and the two adjacent ones of this number are prime, this number must also be divisible by three. Hence every numer between twin primes (except (3, 5)) is divisible by 6.
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