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Let $E$ over $\mathbb{Q}$ be a non-CM elliptic curve. A well known conjecture of Koblitz gives an asymptotic for the number of primes $p$ for which $|E(F_p)|$ is prime. However the constant that was suggested by Koblitz assumes independence in the distribution modulo different primes. A corrected constant was suggested and justified by Zywina in 2009. In this talk, we would like to provide another approach towards obtaining and understanding this constant.