The Riemann zeta function states all non-trivial zeros have a real part equal to ( ½ ) . When you think about it, this statement is rather profound . In our real world mathematics a zero is either a placeholder in a number ( 301 ) or has a value of zero ( 0 ) . Riemann didn't say so but as soon as these zeros ( 0 ) crossed the line ( y = ½ ) that zero had a value of ( ½ ) . Riemann went on to extend the original equation into the imaginary plane and that meant that zero ( 0 ) had a value of ( ½ + it ) on the line ( y = ½ + it ) where.”i” is imaginary and “t” is real . Riemann's unspoken thought suggests that there is undiscovered mathematics .
When you think about this statement zero can have a value of :
- zero ( 0 )
- ( ½ + it )
Riemann took the original equation into the complex plane which is represented by “i” . Since zero is a single digit, the undiscovered mathematics seems to indicate that if the digits in a number are added they can be placed on a line that has a single value. Since Riemann took the original equation into the complex plane, this means that zero ( 0 ) can have a single value that is part real and part imaginary . For instance if the digits in the number ( 47 ) are added ( 4 + 7 = 11 ) and ( 1 + 1= 2 ) , then ( 47 ) is on the line ( y = 2 ) . ( 47 ) can also be on the line ( y = 11 ) because ( 4 + 7 = 11 ) . Zero ( 0 ) doesn't have a “real” digit so it can't be on a line that has a “real” meaning ( y = 0 ) . Zero ( 0 ) in the numerical system seems to be equivalent to “i” in the symbolic mathematical system, except that zero can have any value whereas “i” is limited to √ - 1 . The Riemann Hypothesis has something to do with primes . A prime is a number that can only be divided evenly by itself and one ( 1 ) . A prime number has the digits ( 1, 3, 7, 9 ) in column ( 0 ) which is the far right column . The single digit primes are ( 1, 2, 3, 5, 7 ) . Primes with more than one digit are on the lines ( 1, 2, 4, 5, 7, 8 ) . The number of primes are infinite . The ordinary numbers that aren't primes are also infinite .That being said, Riemann developed a formula for the number of primes less than a number . The “number” was defined as the sum of the zeros ( 0 ) in the zeta function. Riemann had taken the original equation into the complex plane which meant that the value of the zero ( 0 ) was now ( ½ + it ) on the line ( y = ½ + it ) . The formula said that the magnitude of the oscillations of the primes around their expected position is controlled by the real parts of the zeta function . If the zeros are on the line ( y = ½ + it ) , their value is ( ½ + it ) which means ( it ) has to have a “real” value. If ( it ) is real you add up the numbers obtaining a real number . Lastly , the error term in the prime number theorem is closely related to the position of the zeros . When you think about the statement “ the “number” was defined as the sum of the zeros ( 0 ) on the zeta function “ it really doesn't matter because the number of primes are always less than any other number. The first prime numbers are ( 1, 2, 3 ) . Their positions are ( 1, 2, 3 ) . The error term in the prime number theorem is closely related to the position of the zeros . If you multiply the primes ( 1, 2, 3 ) by 100% you get the prime's positions ( 1, 2, 3 ) . If you multiply the primes ( 1, 2, 3 ) by 10% you obtain ( .1, .2, .3 ) for the position of the primes . You dropped one ( 1 ) zero and your calculation was out. Therefore the error term in the prime number theorem is closely related to the position of the zeros. The single digit primes are ( 1, 2, 3, 5, 7 ) . Prime number 5 is in the fourth ( 4th ) position . If you multiply prime 5 by .8 you get 4 . The number ( .8 ) is obtained by adding using the zeta function . Prime number 7 is in the fifth position ( 5th ) . If you multiply 7 X .714285714 you get 5. This term is obtained by adding the zeta function . If you add zeros to .714285714 or put zeros somewhere within .714285714 ( for instance .7140285714 ) you will soon see that the error term in the prime number theorem is closely related to the position of the zeros .