Unsolved problems in Maths : Working on the Goldbach Conjectures

[Afghanistan2010]

Asalam alykum warahmatullahi wabaraktuh,

all praise due to Allah the most high,and there is no God except God and Muhammad (pbuh) is his messenger and beloved,may Allah be pleased with his companions and his offspring and may Allah have mercy upon us all the believers and may Allah sent guidance to the nonbelievers,



dear readers,i do not know who of you have knowledge with unsolved mathematical problems,but i love to use my time to solve problems in math even i do not have much knowledge,except in some areas of maths (like vectors and others),i have been working on this problem and it is just crazy,

so here you go :

Goldbach a german mathematician assumed that adding two prime numbers together is always dividable by 2,but all prime number > 2 (greater than 2),

this is easy to define this by a formula like :

a + b/2 while a and b are both prime number > 2.

but what if we include 2 and try to explain it by formula,is way difficult and maybe will remain unsolved.

if anyone is interested in a small programm written by me in java for the second problem,and if you have knowledge of java you can expand it and maybe find a problem oneday for this problem.

[Al Hanif]

Wa Alaykum Salam Wa Rahmatullahi Wa Barakatuhu,



Goldbach's Conjecture states that :

Every even integer greater than 2 can be written as the sum of two primes.


It is equivalent to say that : (I think you missed the parenthesis)

Any integer greater than 1 is the arithmetic mean of two primes.


Do you mean that you created a programm to test the small values of integers ?

[Afghanistan2010]

yes indeed,thank you for the add,the worst problem i and maths has faced is the prime number 2.

I love to enjoy my time with maths,how beautiful,they are there but we do not know them,verily Allah has already created them and established them and our job is to find it and be astonished and amazed at it.

[RevolutionThroughReason]

To solve goldbach's conjecture you have to develop a proof structure which which can be applied to all cases You dont necessarily need a formula; but a rigorous verification that it will work from 2..n integers.

Here are some suggestions

1.) Try induction; it is actually one of my favorite proof methods,strong induction would be best because if you can show infinitely sequential cases match previous cases that is always good.

2.) look at other prime number theorems ;there are a few theorems which relate moduli to prime numbers namely Euler's Theorem, which is a special case of Fermat's Little Theorem.

There's a chance you could develop a formulaic relationship from these theorems.

One technique you could apply is with Fermat's Little Theorem the fact that P^(q-1) + q^(p) is congruent to 1 mod pq


but you have to start learning some stuff about modular arithmetic which I don't think you have.

[Afghanistan2010]

Thank you
i had some littel experiences with modulars,they were especially brought to light by Taniyama-Shimura and Andrew Wiles regarding the elliptical curves,and also regarding the final proof for Fermat's Last Theorem.

[RevolutionThroughReason]

Well all higher level analytic number theory depends on modular arithmetic . It is nothing new to the field. When you're dealing with integers you need mod or else you get fractions, when make it no longer Number Theory but Real Number Analysis.


Andrew Wiles is a Number Theorist so it makes sense. His proof using elliptical curves was very interesting but long; if you ever see the whole thing it's like a small book.

[Afghanistan2010]

Well all higher level analytic number theory depends on modular arithmetic . It is nothing new to the field. When you're dealing with integers you need mod or else you get fractions, when make it no longer Number Theory but Real Number Analysis.


Andrew Wiles is a Number Theorist so it makes sense. His proof using elliptical curves was very interesting but long; if you ever see the whole thing it's like a small book.

I will try myself to educate myself further in number theory inshaAllah.


I was attached to that book "Fermat's Last Theorem",and some parts of the release of Andrew were mentioned but yet not all,i felt in love with the maths of euler.

[RevolutionThroughReason]

euler is good, what chaps my hide though is many of the things attributed to Euler and Fermat were actually discovered or developed by Ibn Haytham and the like.

What I am doing right now is like an interface between Number Theory and Differential Geometry/Calabi Yau Manifolds

[Afghanistan2010]

My general problem is,i have love for many different subjects,but i can't stick to them all in higher level,i must decide if i want to remain in chemistry or switch either in areas of medicine or engeenering/maths.

[RevolutionThroughReason]

My real passions are Physics, Math and AstronomyCosmology; these three subjects compliment each other. Of course other subjects are interesting, but more as extensions of these three.

[Afghanistan2010]

Mine are Astronomy,Chemistry (in regards of human) and Robotics.

[RevolutionThroughReason]

chemistry in regards to humans, as opposed to what?