Dr. SMRH Moosavi has claimed that he had derived a general formula for finding the $ n$ -th prime number. More details can be found here at PrimeNumbersFormula.com and a brief discussion here at Math.SE titled  “Formula for the nth prime number: discovered?”

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General Formula
Prime Numbers Formula For $ k$ -th prime numberGeneral Formula
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  3. You might try the Lambert Prime Number formula (see above web site). Much simpler, and produces
    all the primes and nothing but the primes. Summary treatise, “Lambert Prime Number Formula” now available on Amazon.com, Barnes & Noble, and many other book dealers. Hope to publish all 8 treatises in a single volume within the year, covering the determination of the percentage of primes to infinity (e), how to determine the limits of vast consecutive composite numbers series and how often they repeat, the generation and use of prime number templates, the subject of split primorials, and a relatively easy way to determine whether or not a titanic number is prime after generating it with the Lambert formula when bypassing all the preliminaries. #PrimeNumberGuy

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