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:
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):
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:
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:
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:Unsolved problems in mathematics
Category:Theorems about prime numbers
I calculated the approximation of some famous constants as a fractal.