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A Formula That Generates The Entire Sequence Of Prime Numbers In Order Of
Magnitude Using Only The Constants (Pi) And e .
By: Don Blazys
The second root (“zero”) of the equation:
((sin( x ^ (1 / 2)))^ (−1) − 1)^ (−1) /(( Pi)^ 2 + (ln(ln(2 * ((2 * ( x ^ (−1) + 1))^ (−1) + 1))))^ (−1)) − 1 = 0
is approximately: ( 2.566,543,832,171,388,844,467,529…).
Note that the whole number part is the first prime 2, and that:
((2.566,543,832,171,388,844,467,529...) / 2 − 1)^ (−1)
is approximately: ( 3.530,176,989,721,365,539,402,422…),
where the whole number part is the second prime 3, and that:
((3.530,176,989,721,365,539,402,422...) / 3 − 1)^ (−1)
is approximately: (5.658,487,746,849,688,216,649,061…),
where the whole number part is the third prime 5, and that:
((5.658,487,746,849,688,216,649,061...) / 5 − 1)^ (−1)
is approximately: (7.593,155,717,658,844,724,384,335…),
where the whole number part is the fourth prime 7, and so on.
In short, we divide the approximate number by its whole number part, subtract one, and
take the reciprocal of the result to get the next approximate number where the whole
number part is the next prime!
The initial “prime generating constant”: (2.566,543,832,171,388,844,467,529…)
can also be defined as the second “intersection” at x = (2047.518,568,428...) of the
expressions:
(( Pi) − sin^ (−1)(( x ^ (−1) + 1)^ (−1)))^2
and
((e^ (e^ (( x − ( Pi )^ 2)^ (−1))) / 2 − 1)^ (−1) / 2 − 1)^ (−1).
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Whereas Eulers famous equation: e^ (( Pi )(−1)^ (1 / 2)) = (−1) shows a deep and
mysterious connection between the numbers: (Pi ) , e and (-1), the above formula reveals
an even deeper and more mysterious connection between: (Pi ) , e and the entire
sequence of prime numbers!
In fact, this formula has such an astonishing network of surprising relationships that the
possibility for further questions and discoveries is probably endless.
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