User:Chrisdecorte

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Chris De Corte is a freelance consultant living in Aalst (Belgium) and is among others also a mathematical hobbyist.

Chris is interested in unsolved problems

Chris found that the equality between the Riemann zèta function and the Euler product does not seem to hold (for s<=1). This is explained here.

Chris independently developed his own sieve: the "Sine Sieve" which has some resemblance with the Sieve of Eratosthenes and which is explained here.

Chris independently derived 2 new formulas to determine if a given number n is prime or not:



and:



Using these formulas, he can prove twice Goldbach's Conjecture & Twin prime Conjecture.

This is done by replacing n with 2n=p+q (p and q being 2 primes) and working out the sinus terms.

One of the 2 primes primes that compose the Goldbach requirement needs to be a solution to the following equation:



Other Prime testing formula's he developed are (for those who can't see the beauty of the sine function):


and:


This last formula is true for primes but is also true for some non-primes as 4, 9, 15, ...

Chris also developed multiple prime counting formula:

His probabilistic prime counting formula is his final one and can be represented as follows:



where can be very closely approximated as:



The origin of this formula can be found here and it will take a long time before someone will improve the accurateness of this formula. A video about this formula can be found here.

His previous formula had also very good accuracy:

Others are:


This formula seems to be better than the pure version of the Logarithmic Integral x/lnx up to approximately 1E+10 (except for a short range between 2 and 9000).

Therefore, he would like to propose the following improved formula:



Other works:

Chris found a very close approximation to the angle trisection problem

He also found an approximation to the squaring of the circle and made some interesting but unanswered comments.

Category:Mathematicians Category:Unsolved problems in mathematics Category:Prime numbers Category:Primality tests‎ Category:Theorems about prime numbers

I calculated the approximation of some famous constants as a fractal.