Science Forums 2

[Don Blazys]

"Tweaking" the original equation, I was able to garner a substantial improvement in the accuracy of the prime generating constant:

2.566543832171388844467529...

The second root (zero) of the equation:

(((e^(e^(((((((((e^(pi))*((2*3*4-1)*((2+3+4)^2-2)+1/x))^(-1)+1)^(-1)*e^(x+2*3*5-1))^(-1)+1)*sin(x^(1/2)))^(-1)-1)^(-1)-(pi)^2)^(-1)))/2-1)^(-1)/2-1)^(-1)/x-1)=0

is:

2.566543832171388844467529401576979616943754028928 2...

which is accurate to 25 decimal places and generates the primes:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 and 59,

in order of magnitude.

I am now convinced that given enough time, we could continue to "tweak" this (and many similar equations) so as to generate as many primes, in order of magnitude, as we so desire.

Although an exact result may very well be impossible, I have decided that this is a very unique endeavor, (and a lot of fun,) so from time to time, I will continue to post improvements in accuracy. After all, this thread is called the "Holy Grail Of Mathematics"....and you just never know...someone might even spot an interesting pattern!

I'm going on vacation now, and won't be near a computer for a week or so.

I wish you all a very merry Christmas and a happy Hypographical New Year.

God bless you!

Don.