one of the most important branches of mathematics is Number Theory, which can be considered as a never-ending theory. For whenever it solves some problems in an area, there arise some other problems in some other restricted sense in that area.
There are some very sophisticated and interesting conjectural formulae or problems in Number Theory, which are still eluding solution. One of them is the Prime Number system. For example, certain areas of the Goldbach conjecture, twin prime conjecture, perfect number conjecture, mersenne prime conjecture etc. are yet to be solved.The eighteenth century mathematician C F Goldbach conjectured about 264 years back, that every even number ‘n’ larger than 2, can be expressed as a sum of two primes. The other two conjectures of the primes are twin prime conjectures and mersenne prime conjectures. Dr Kalita has formulated a theorem on the existence of consecutive primes > 13 connected with Goldbach conjecture.As proof of the Goldbach conjecture that every even number ‘n’ larger than 2, can be expressed as a sum of two primes, Dr Kalita states, “We follow the proof of the conjecture in opposite way, that is, if we can show that every sum of two primes >13 can be expressed as an even number, this will follow the proof of the Goldbach conjecture.” He proposed two cases for the purpose and in the first case, he says, some even numbers can be expressed as a sum of two equal primes and in the case of the second, every sum of two primes > 13 can be expressed as an even number.