theodorenghiem

23 hours ago, Sensei said:

I have no idea what is your entire "discovery" about, but I have advice concerning programming.

You wrote that "0.97% failed due to the limitation of great number processing of my programming language (C and Java) ".

Advice is: you can use "long long" for 64 bit signed and "unsigned long long" for 64 bit unsigned integers. They will greatly enhance your integer range. You will be able to find primes from 2 to 2^64-1.

 

Thanks for your feedback.

My second attempt to consolidate 3 rules into one whole number = prime + fibonacci1 + fibonacci2 has  been verified with 10,000,000 without failure. Please view my txt file in the link

This is the upgrading of my first research with the same subject, which can be found in

https://www.linkedin.com/pulse/relationships-between-prime-number-fibonacci-thinh-nghiem/?lipi=urn%3Ali%3Apage%3Ad_flagship3_profile_view_base_post_details%3BCuXz0krLTjSmIWUuweQOBg%3D%3D

My conclusion in the first article has been optimized as below:

A whole number, odd or even, can be analyzed as the sum of a prime number and two Fibonacci numbers. Here we have some examples

52362 = 52127 (prime) + 2 (Fibonacci 1) + 233 (Fibonacci 2)

52381 = 51769 (prime) + 2 (Fibonacci 1) + 610 (Fibonacci 2)

Also, this time I verified with range [5 - 10,000,000 (ten millions)]. It’s lucky that no failing case as the first time. That means all positive integer number from 5 to 10,000,000 match my rule above.

To view my result, first of all, readers can go to this location

https://drive.google.com/drive/u/0/folders/1y5nPwNbIGo2puNTT1b03f2LAd0nEUJvi

Then download file test.txt to local machine and open it with Notepad++.

Here the first column is the prime number, the second column is the first Fibonacci number, the third column is the second Fibonacci number. And the last one is the whole number to be calculated.

I also put my new research in LinkedIn with the link:

https://www.linkedin.com/pulse/relationships-between-prime-number-fibonacci-part-3-thinh-nghiem/

Please put your feedback there so that I can keep track and answer.

Welcome all of you

Regards,

Thinh Nghiem from Vietnam

Originally, I also had the same thinking like yours by considering it as coincident. However I replaced PI with other irrational number, such as Euler number or golden ratio, and replicated all above testing. This time these values above could not be found with up to 5 or 6 digits like the result with PI.

So I declare that this is PI's secret that needs to be investigated more

Dear all,

I explored the value of PI up to 10 million digits with the following link

http://pi.karmona.com/

From here I realized that it included many scientific constants. Below are some examples (See the string in BOLD)

· 85236194426736533892035293381796879434588513096544808259521653348853314258590660527010020998130498690661069867723414515021618033218172517802616380355080061151485165018703481386496623229835504747481403

Where

1.618033 ~ golden ratio to be used in design, painting, and architecture etc.

(Source: http://mathworld.wolfram.com)

· 96685196391413997448756843434713683467684405191628302400411300444463543904105050551088502982716308576980991021240051192505245400533996852921477011645488697170458489815728942231323809045241271828309703

Where

2.71828 ~ Euler’s number

(Source: http://mathworld.wolfram.com)

· 42418316129787393244798498349610314002739639418622623492139400688701330038857369897639683856722411572475207203447744724370976474297127526070665511577919477138667408363547467649387788800049461595697608

Where

6.67408 ~ constant of gravitation

(Source: http://physics.nist.gov)

· 0516553790686627333799585115625784322988273723198987571415957811196358330059408730681216028764962867

Where 8.987 ~ Coulomb constant in electrostatic

(Source: http://scienceworld.wolfram.com/physics)

· 9386128894440412613786249523444947505596522332025294451178219959213450685005376828854182268925755038

Where 8.85418 ~ electric constant (Or Vacuum permittivity)

(Source: http://physics.nist.gov)

· 6818843187021953946745788068387330450266993482047409308509529400887069518186325483548249662607066502

Where 6.626070 ~ Planck constant

(Source: http://physics.nist.gov)

· 1908021458055350953241324036224334117794355382888601011516021766306897099412973119095150917160058845

Where 1.6021766 ~ elementary charge (Charge of electron)

(Source: http://physics.nist.gov)

· 4422845118273209748513571044742385749109383133850655948526797212711896813103833449229778166368094302

Where 9.109383 ~ electron mass

(Source: http://physics.nist.gov)

· 9589217885429733331100886707221516688335762492009010311009976090980665252668644423844360766963859177

Where 9.80665 ~ acceleration of gravity

(Source: http://physics.nist.gov)

· 6267712886022140859278535537337471953589903987579336102194906780894369912982198261645474805859604149

Where 6.02214085 ~ Avogadro constant

(Source: http://physics.nist.gov)

· 7195452860809748682548745244590362604731380648393797344681866249700721554710601935002386483893437562

Where 1.380648 ~ Boltzmann constant

(Source: http://physics.nist.gov)

· 5292492422161329574504065382201672623986186616485814342988831519203159057960073366305926447801768242

Where 1.67262 ~ Proton mass

(Source: http://physics.nist.gov)

And maybe there are more cases. I wonder this interesting finding is only accidental, or there is any implicit rule here.

Any feedback or discussion can be sent to theodorenghiem@yahoo.co.nz

It’s nice if you can share my article in social media for more opinions

Thinh Nghiem

Dears,

Recently when learning programming language, I accidentally found out an interesting relationship between prime number and Fibonacci number.

That is, a positive integer number can be analyzed as either

- the sum of a prime number and a Fibonacci number

For example

16 = 11 (prime) + 5 (Fibonnaci)

61 = 59 (prime) + 2 (Fibonacci)

- or a prime number minus a Fibonacci number

For example

59 = 61 (prime) – 2 (Fibonacci)

83 = 227 (prime) – 144 (Fibonacci)

I have tried with the first 1,000 positive integer number from 1 to 1,000 MANUALLY and ensured that all of them matched with one of the two above rules.

I shared my analyzing here in the excel file with 1,000 positive integer number from 1 to 1,000 with the link

https://drive.google.com/file/d/0BzAetX6K_uyAUXZHQTd5V3ZIa2c/view?usp=sharing

The majority of them belong to the first case are formatted with normal writing. I set the minority cases (the second one where result equals to prime minus Fibonacci) with red and bold format.

So prime number and Fibonacci number are in actual not completely independent with each other.

It is perfect if anyone can prove this rule in general case, or explain its reason. I do not think that this is only an accidental effect.

You can discuss here or email me at email deleted

Regards,

Thinh Nghiem