On The Elementary and Numerical Approach to k-tuple Conjecture

In 1922 Hardy and Littlewood proposed a conjecture on the asymptotic density of admissible prime k-tuples. Here we have used a sieve method and shown an elementary process to calculate the approximate number of admissible prime k-tuples and compared with Hardy-Littlewood conjecture and real values. Then we have combined our elementary formula with the results obtained from numerical data of real values and generated a new formula which gives almost same results as Hardy-Littlewood conjecture. We have also proposed an easy form of this conjecture which gives us a new perspective to think about it.