Prime-Generating Formula

2016-04-01, post № 114

mathematics, #generating, #prime formula, #primes

(April Fools’!) I came up with this interesting prime-generating formula. It uses the constant 𝜉 and generates the primes in order!

The constant’s approximation.

$\xi = 1.603502629914017832315523632362646507807932231768273436867961017532625344\dots$

The formula $p_n$ calculates the 𝑛-th prime.

$p_n=\lfloor{10^{2\cdot n}\cdot\sqrt{\xi^3}}\rfloor-\lfloor{10^{2\cdot(n-1)}\cdot\sqrt{\xi^3}}\rfloor\cdot 10^2$

The first few values for $p_n$ when starting with 𝑛 = 𝟢 are as follows.

$p_{0\text{ to }7}=\{2,3,5,7,11,13,17,19\}$