Formula For Primes

P(n) = n² + n + 41

$0\; =\; wz\; +\; h\; +\; j\; -\; q$

$0\; =\; (gk\; +\; 2g\; +\; k\; +\; 1)(h\; +\; j)\; +\; h\; -\; z$

$0\; =\; (16k\; +\; 1)^3(k\; +\; 2)(n\; +\; 1)^2\; +\; 1\; -\; f^2$

$0\; =\; 2n\; +\; p\; +\; q\; +\; z\; -\; e$

$0\; =\; e^3(e\; +\; 2)(a\; +\; 1)^2\; +\; 1\; -\; o^2$

$0\; =\; (a^2\; -\; 1)y^2\; +\; 1\; -\; x^2$

$0\; =\; 16r^2y^4(a^2\; -\; 1)\; +\; 1\; -\; u^2$

$0\; =\; n\; +\; l\; +\; v\; -\; y$

$0\; =\; (a^2\; -\; 1)l^2\; +\; 1\; -\; m^2$

$0\; =\; ai\; +\; k\; +\; 1\; -\; l\; -\; i$

$0\; =\; ((a\; +\; u^2(u^2\; -\; a))^2\; -\; 1)(n\; +\; 4dy)^2\; +\; 1\; -\; (x\; +\; cu)^2$

$0\; =\; p\; +\; l(a\; -\; n\; -\; 1)\; +\; b(2an\; +\; 2a\; -\; n^2\; -\; 2n\; -\; 2)\; -\; m$

$0\; =\; q\; +\; y(a\; -\; p\; -\; 1)\; +\; s(2ap\; +\; 2p\; -\; p^2\; -\; 2p\; -\; 2)\; -\; x$

$0\; =\; z\; +\; pl(a\; -\; p)\; +\; t(2ap\; -\; p^2\; -\; 1)\; -\; pm$

$f(n)\; =\; 2\; +\; (2(n!)\; \backslash operatorname\{mod\}\; (n+1))$

$\backslash pi(m)\; =\; \backslash sum\_\{j=2\}^m\; \backslash frac$

$\backslash pi(m)\; =\; \backslash sum\_\{j=2\}^m\; \backslash left\backslash lfloor\; \{(j-1)!\; +\; 1\; \backslash over\; j\}\; -\; \backslash left\backslash lfloor\{(j-1)!\; \backslash over\; j\}\backslash right\backslash rfloor\; \backslash right\backslash rfloor$

$p\_n\; =\; 1\; +\; \backslash sum\_\{m=1\}^\{2^n\}\; \backslash left\backslash lfloor\; \backslash left\backslash lfloor\; \{\; n\; \backslash over\; 1\; +\; \backslash pi(m)\; \}\; \backslash right\backslash rfloor^\{1\; \backslash over\; n\}\; \backslash right\backslash rfloor$

$\backslash pi(k)\; =\; k\; -\; 1\; +\; \backslash sum\_\{j=2\}^k\; \backslash left\backslash lfloor\; \{2\; \backslash over\; j\}\; \backslash left(1\; +\; \backslash sum\_\{s=1\}^\{\backslash left\backslash lfloor\backslash sqrt\{j\}\backslash right\backslash rfloor\}\; \backslash left(\backslash left\backslash lfloor\{\; j-1\; \backslash over\; s\}\backslash right\backslash rfloor\; -\; \backslash left\backslash lfloor\{j\; \backslash over\; s\}\backslash right\backslash rfloor\backslash right)\; \backslash right)\backslash right\backslash rfloor$

$p\_n\; =\; 1\; +\; \backslash sum\_\{k=1\}^\{2(\backslash lfloor\; n\; \backslash ln(n)\backslash rfloor+1)\}\; \backslash left(1\; -\; \backslash left\backslash lfloor\{\backslash pi(k)\; \backslash over\; n\}\; \backslash right\backslash rfloor\backslash right)$

External links

• Prime-Generating Polynomial

• Mill's Constant

• FRACTRAN

• Formula for Primes, Twinprimes, Number of Primes, and Number of Twinprimes page 2 page 3 page 4 Erratum

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