/vatsanspiral

An open approach towards understanding Primes

Primary LanguageGo

#Vatsan spiral

TL;DR

https://github.com/nrshrivatsan/vatsanspiral/tree/master/js#tldr

https://youtu.be/h-_yl3vPf6w

Resulting Patterns

  • Below is a table with observations
  • Prime Numbers in first column
  • Prime Gaps Second column has the difference between the prime number in current row and the next row
  • Prime Gap Diff Third column has the difference between the Prime Gaps ALWAYS 16
  • Fourth column referes to the Wolfram Alpfa analysis of the series of prime-gaps (elegant expressions representing them)

Linear Prime Sequences of Vatsan Spiral

Prime Number Prime Gaps (PG) Primal-Gap Diff Wolfram link for Prime Gap Diff
7079 482 16 http://www.wolframalpha.com/input/?i=482+498+514+530+546+562+578+594
7561 498 16
8059 514 16
8573 530 16
9103 546 16
9649 562 16
10211 578 16
10789 594
11383
3929 346 16 http://www.wolframalpha.com/input/?i=346+330+314
3583 330 16
3253 314
2939
5821 422 16 http://www.wolframalpha.com/input/?i=422+406+390+374
5399 406 16
4993 390 16
4603 374
4229
7933 510 16 http://www.wolframalpha.com/input/?i=510+526+542+558
8443 526 16
8969 542 16
9511 558
10069

Diagonal Prime Sequences of Vatsan Spiral

Prime Number Prime Gaps (PG) Primal-Gap Diff Wolfram Alpha link
9007 544 **16** http://www.wolframalpha.com/input/?i=544+560+576+592+608+624+640+656+672
9551 560 **16**
10111 576 **16**
10687 592 **16**
11279 608 **16**
11887 624 **16**
12511 640 **16**
13151 656 **16**
13807 672
14479
3391 336 **16** http://www.wolframalpha.com/input/?i=336+352+368+384+400+416+432
3727 352 **16**
4079 368 **16**
4447 384 **16**
4831 400 **16**
5231 416 **16**
5647 432
6079

Significance

  • From above patterns Diagonal and Linear, one could make sense that the Prime-gaps are interleaved by 16.
  • Once a system of equations could be drafted to characterize the Prime Numbers and the Prime-gaps, elegant equations to predict prime numbers.
  • May be in a remote way Reimann's hypothesis could be addressed

Motivation

==============

Prime numbers are 'Prime'. They piqued my interest.

Prime number generation is non-trivial. Sieves are a good help.

My favorite : Ulam Sprial [http://en.wikipedia.org/wiki/Ulam_spiral]

Ulam Spiral

My contribution : Vatsan Spiral [http://thinkination.blogspot.com/2013/07/vatsan-spiral.html]

Vatsan Spiral

Vatsan Spiral QR

A pixel-ated version of Vatsan spiral! Look deep to view patterns in primes!

Vatsan Spiral QR 255

This repo in Git is about creating a simple approach towards understanding primes in a better way.

Request

All readers are requested to view the code, provide valuable comments either in my blog or here in git.

I will try my best to add as many features as possible.