# Prime numbers and Goldbach’s conjecture visualization.

isn’t it?The German mathematician G.

F.

B.

Riemann (1826–1866) observed that the distribution of prime numbers is very closely related to the behavior of the Riemann Zeta function.

Being one of the millennial questions, it has its application in various fields and could unravel many hidden mysteries.

Mathematicians observed that prime numbers were capable of deriving patterns in the number system out of which Goldbach’s conjectures are ones that are really capable of tantalizing anyone towards math.

Goldbach’s conjecture of even numbers: The Goldbach conjecture asserts that every even integer greater than 4 is the sum of two primes.

The conjecture has been tested up to 400,000,000,000,000.

Although every even number has one or more possible ways of writing it as the sum of two primes.

2+2=43+3=63+5=83+7=105+5=10.

13+37=5019+31=5043+7=5047+3=50.

As simple as it seems to be, its proof had always been haunting some of the very intelligent beings under the sun, 250 years for now and still remained a question.

Till date, nobody has found a larger prime number that cannot be formed using two prime numbers.

This pattern can be represented using an arrow like structure.

The ends represent the prime numbers meeting at their respective sums.

Interestingly, as the even number increases the no.

of ways it can be formed through prime combinations increases.

The plot between the even numbers and the no.

of ways it can be formed using 2 primes is called Goldbach’s comet.

Visualization of Goldbach’s comet using matplotlib-pythonFrom the scatter plot we can notice that the no.

of prime combinations increases as the number increases but there’s no proof (yet) that this pattern could hold true or false.

Many brains that put efforts to prove this would result in being clueless from the beginning itself.

But there’s always hope because since we were able to prove the Goldbach’s conjecture of odd numbers, we could be able to prove this too.

YESS!!.The Goldbach’s weak conjecture or the conjecture of odd numbers was proven by Harald Helfgott in the year 2013.

Goldbach’s conjecture of odd numbers: It asserts that every odd number greater than 7 can be expressed as the sum of three primes.

1+3+5=91+3+7=111+5+7=135+5+7=175+7+7=19.

Fermat’s room is one of the most liked Spanish thriller movies about four mathematicians where the core plot deals with the proof of Goldbach’s conjecture.

In my opinion, its a must watch if you are a math maniac or a puzzle lover.

Sounds interesting?.Then grab a pen and paper and start trying.

because a solution worth a million dollars is worth a try.

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