Difference between revisions of "Mill's Constant"
(Created page with "Mill's Constant is the smallest number in a prime number formula. <math>\lfloor\theta^{3^n}\rfloor</math> is the prime number theorem where <math>n</math> can be any number a...") |
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| − | Mill's Constant is the smallest number | + | Mill's Constant is defined as the smallest real number <math>\theta</math> such that <math>\lfloor\theta^{3^n}\rfloor</math> is always a prime number for all natural n. |
| − | <math>\lfloor\theta^{3^n}\rfloor</math> is the prime number theorem where <math>n</math> can be any number and <math>\theta</math> is an element from an set of numbers (that may be rational or irrational, and we are not sure) and Mill's Constant is the smallest element in that set. Mill's constant is approximately <math>1. | + | <math>\lfloor\theta^{3^n}\rfloor</math> is the prime number theorem where <math>n</math> can be any number and <math>\theta</math> is an element from an set of numbers (that may be rational or irrational, and we are not sure) and Mill's Constant is the smallest element in that set. If the [[Riemann Hypothesis]] is true, Mill's constant is approximately <math>1.3063778838630806904686144926...</math> and the primes it generates start as <math>2, 11, 1361, 2521008887, 16022236204009818131831320183, </math> |
| + | <math>4113101149215104800030529537915953170486139623539759933135949994882770404074832568499, ... </math>. | ||
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Latest revision as of 00:59, 15 January 2022
Mill's Constant is defined as the smallest real number 
such that 
is always a prime number for all natural n.
is the prime number theorem where 
can be any number and is an element from an set of numbers (that may be rational or irrational, and we are not sure) and Mill's Constant is the smallest element in that set. If the Riemann Hypothesis is true, Mill's constant is approximately 
and the primes it generates start as 
.
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