 mersenneforum.org Where is the weakness of this reasoning?
 Register FAQ Search Today's Posts Mark Forums Read 2020-08-23, 10:50 #1 Charles Kusniec   Aug 2020 Brasil 1000002 Posts Where is the weakness of this reasoning? Let’s be any two positive and/or negative Odd Primes P1 and P2. Because both are Odd Primes, there will always exist an Integer reference r equidistant from them such as: P1=r+d P2=r-d being |d| the equal distance from the reference r to the both Odd Primes. For P1=P2, d=0. Then, P1+P2=2r r=(P1+P2)/2. And, P1-P2=2d d=(P1-P2)/2. If r=Odd, then d=Even and vice-versa. OK. Now, the Semiprime formed with the two Primes above is P1P2=(r+d)(r-d) So, P1P2=r^2-d^2. Consequently, if any Odd number can be expressed as a difference of two Squares, and if any Odd difference between two Squares can be expressed as an Odd Semiprime number, then there will always exist 2 Primes P1 and P2 such as P1+P2=2r for any r. For P1=P2, the Semiprime is a Prime squared. And absolute value of d do not need necessarily be less than r.   2020-08-23, 12:42 #2 Viliam Furik   "Viliam Furík" Jul 2018 Martin, Slovakia 2·373 Posts I have noticed, that if you set the r = 2, you can't find a pair of primes that would satisfy, because at the beginning you said the primes have to be odd. But I think that's OK, you are only one case short to infinity But I think the weakness is that you assume that EVERY number 2d can be expressed as a difference of two primes. As far as Google tells me, it has not been proven yet. Also, I am not sure about this part (...if any Odd difference between two Squares can be expressed as an Odd Semiprime number,...). If you manage to prove both my doubts, I am fairly certain you prove the Goldbach conjecture.   2020-08-23, 12:50   #3
kruoli

"Oliver"
Sep 2017
Porta Westfalica, DE

23·3·5·7 Posts Quote:
 Originally Posted by Viliam Furik I have noticed, that if you set the r = 2, you can't find a pair of primes that would satisfy, because at the beginning you said the primes have to be odd. But I think that's OK, you are only one case short to infinity That's only when you only allow positive primes. Otherwise, let P1=-3, P2=7, then P1+P2=4=2*2=2r with your r=2.    2020-08-24, 09:24   #4
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

53·79 Posts Quote:
 Originally Posted by Charles Kusniec Where is the weakness of this reasoning?
There is no weakness of the reasoning. The reasoning is sound.

What does it prove?

(if you answer "Goldbach" then you still have to show us how you express 105 as a semiprime)

(edit: ignore the other two guys above )

Last fiddled with by LaurV on 2020-08-24 at 09:34   2020-08-24, 09:40   #5
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

53×79 Posts Quote:
 Originally Posted by Viliam Furik But I think the weakness is that you assume that EVERY number 2d can be expressed as a difference of two primes. As far as Google tells me, it has not been proven yet.
He never said that, which would be equivalent with G. He said difference of squares, which is true, every odd number is a difference of squares, because all squares can be obtained as partial sums of the 1+3+5+7+...., but the second part, about every odd being a semiprime... well.... I still can't write 105 as a semiprime, with all my efforts... maybe he teaches us how to do it.   2020-08-24, 12:11   #6
Dr Sardonicus

Feb 2017
Nowhere

2×2,687 Posts (my emphasis)
Quote:
 Originally Posted by Charles Kusniec if any Odd number can be expressed as a difference of two Squares, and if any Odd difference between two Squares can be expressed as an Odd Semiprime number, then there will always exist 2 Primes P1 and P2 such as P1+P2=2r for any r. For P1=P2, the Semiprime is a Prime squared. And absolute value of d do not need necessarily be less than r.
That is what may be called "too big an if."   2020-08-24, 18:17   #7
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

25×3×101 Posts Quote:
 Originally Posted by Charles Kusniec if any Odd number can be expressed as a difference of two Squares
Of course it can! 2n + 1 = (n+1)2 - n2  Thread Tools Show Printable Version Email this Page Similar Threads Thread Thread Starter Forum Replies Last Post jwaltos Probability & Probabilistic Number Theory 20 2019-10-12 03:03

All times are UTC. The time now is 08:28.

Thu Jan 27 08:28:54 UTC 2022 up 188 days, 2:57, 1 user, load averages: 1.41, 1.47, 1.44