Recent content by Marchal

Quote: That really looks like a made-up rule specifically for this example. Yes it is limited to small numbers, as the product of all primes up to the square root grows faster than the number, but a general rule cannot have any exceptions, otherwise it is not a general rule. Reply: Right, I was...

Hello mfb In the interval (0<n<2x3x5x7x11x13) there are exactly 1650 numbers with the properties: (1) they are relative primes with regard to the prime numbers (2, 3, 5, 7, 11, 13), Quote: I doubt that statement. Why would it be -2 in the factors? Why would that statement depend on 176 at...

Thanks for commenting, mfb! I try to correct/improve this thread as follows:Take as an example m=176, which admits 11 as a divisor, but none of the primes 3, 5, 7, 13. Then the expression r=(3-2)x(5-2)x(7-2)x(11-1)x(13-2)=1650 means that In the interval (0<n<2x3x5x7x11x13) there are exactly...

An example:For m= 176 (132<176<172 one finds r=(3-2)x(5-2)x(7-2)x(11-1)x(13-2)=1650 relative primes (0<v<2x3x5x7x11x13), forming 825 asymmetric pairs, among them four partitions into prime numbers:19+157, 37+139, 67+109, 73+103, 79+97.

Here I am again! For correct formula & deduction, see APPENDIX attached.

Thanks, Greg. I fully agree. Besides, I suspect my deduction to be substantially erronous. I'll need some time to clarify the matter. Until then Marchal

Please ignore my last message. Here comes page3-improved version.

I still worked on page 3. Here it comes with corrections.

Did I miss uploading the file Goldbach3?

Dear CBGreathouse Thanks for reviewing my text with so much attention!. In standard notation I should write n\neq0 (modp) (equation 2a) q\neq0 (modp) and q\neqn (modp) (equation 2.2.1) I changed the equivalence...

Here is a revised version of my article.

Thank you indeed, CRGreathouse, for signalling this error. Using Merten's Theorem, I find, that g_alt must be divided by 2*exp(-gamma)=1,122918967..., with gamma=0,577215664901... being Euler-Mascheroni's constant. Then, g_alt will be asymptotically equivalent to g_HL I'm now working...

Intuitive reasoning has led me to develop a simple approximation, which contains factors different from those used in well knoen formulas. Numerically, "my" formula delivers results, which are almost as accurate, as Hardy-Littlewood`s with the Shah-Wilson correction. Thanks in advance for any...