Miller-Rabin method is the most prevalently used primality test. However, this method mistakenly reports a Carmichael number or semi-prime number as prime (strong lier) although they are composite numbers. To eradicate this problem, it selects k number of m, whose value satisfies the following : m=[2,n-1], (m,n)=1. The Miller-Rabin method determines that a given number is prime, given that after the computation of $n-1=2^sd$, $0{leq}r{leq}s-1$, the outcome satisfies $m^d{equiv}1$(mod n) or $m^{2^rd}{equiv}-1$(mod n). This paper proposes a step-by-step primality testing algorithm that restricts m=2, hence achieving 98.8% probability. The proposed method, as a first step, rejects composite numbers that do not satisfy the equation, $n=6k{pm}1$, $n_1{ eq}5$. Next, it determines prime by computing $2^{2^{s-1}d}{equiv}{eta}_{s-1}$(mod n) and $2^d{equiv}{eta}_0$(mod n). In the third step, it tests ${eta}_r{equiv}-1$ in the range of $1{leq}r{leq}s-2$ for ${eta}_0$ > 1. In the case of ${eta}_0$ = 1, it retests m=3,5,7,11,13,17 sequentially. When applied to n=[101,1000], the proposed algorithm determined 96.55% of prime in the initial stage. The remaining 3% was performed for ${eta}_0$ >1 and 0.55% for ${eta}_0$ = 1.