Look ma, I've solved the Prime Numbers! ;.)

Hum. I either broke the matrix or I've stumbled across nature's secret morse code.

 

In any case this looks very interesting I must say. Again what we see here is the outcome of my playing with the Ulam Prime Number Spiral concept. In my variation I have arranged the prime numbers up to 1000000 in a fermat spiral using an angle increase of 2.41379035550925 (henceforth called the "Klingemann Constant" ;-))

 

As usual I probably did not do my homework properly and others have come across this pattern before. Only neither on Wikipedia nor on Mathworld Wolfram I could find any traces of it. Also google image search did not turn up anything except the usual ones. If you know of any prior sightings please leave a link in the comments.

 

My next step will be to try to find the formulas for those rays, since if my totally unscientific hunch holds true that any prime number must lie on one of those rays one could devise a simple test for primality.

 

[UPDATE 19:30]

Holy Crap, something is at work here... Now guess what this is:

41

2441

12041

13241

15641

18041

20441

32441

33641

34841

40841

45641

50441

57641

60041

66041

70841

[...]

792041

800441

801641

805241

811241

814841

823241

830441

832841

841241

844841

853241

855641

856841

860441

867641

868841

872441

873641

876041

883241

884441

890441

892841

895241

903641

908441

915641

916841

918041

920441

924041

925241

931241

932441

937241

942041

948041

949241

951641

957641

961241

962441

966041

969641

978041

982841

992441

 

These are all prime numbers that lie on a single ray of this diagram.

  • Mario Klingemann 6y

    Another ray:

    7,3607,6007,7207,12007,14407,15607,19207,20407,22807,24007,26407,28807,34807,36007,39607,43207,46807,49207,51607,52807,55207,63607,78007,80407,88807,90007,93607,98407,99607,105607,108007,112807,127207,129607,130807,135607,138007,140407,145207,146407,147607,152407,153607,154807,156007,157207,158407,160807,162007,166807,172807,174007,178807,180007,186007,188407,190807,192007,199207,200407,204007,206407,208807,214807,217207,219607,220807,222007,223207,231607,234007,236407,237607,240007,241207,248407,249607,250807,254407,262807,264007,265207,272407,276007,279607,283207,284407,288007,292807,297607,300007,304807,312007,313207,314407,318007,322807,331207,338407,345607,349207,354007,360007,362407,367207,373207,375607,376807,379207,381607,382807,398407,405607,406807,412807,416407,421207,422407,426007,432007,433207,434407,441607,442807,444007,448807,451207,456007,458407,459607,463207,469207,471607,475207,476407,481207,482407,488407,492007,494407,502807,507607,510007,517207,523207,525607,534007,535207,536407,543607,544807,548407,549607,553207,558007,561607,565207,567607,568807,578407,580807,583207,589207,590407,595207,601207,603607,609607,615607,619207,624007,634807,648007,656407,657607,658807,662407,668407,669607,673207,675607,676807,679207,681607,684007,692407,693607,702007,708007,712807,718807,720007,721207,723607,724807,726007,729607,748807,751207,760807,762007,766807,769207,771607,787207,793207,794407,800407,801607,804007,807607,811207,819607,822007,826807,828007,834007,835207,838807,841207,842407,843607,850807,854407,855607,864007,870007,874807,879607,885607,886807,897607,900007,901207,903607,906007,910807,912007,920407,922807,933607,936007,937207,948007,954007,958807,963607,978007,979207,984007,987607,997207

    Rule: last two digits are 07 and the rest of the number if 07 is chopped off is divisible by 12
  • Mario Klingemann 6y

    11,2411,6011,7211,12011,14411,16811,19211,20411,21611,22811,27611,30011,32411,36011,46811,49211,50411,54011,61211,63611,64811,67211,74411,75611,81611,82811,84011,88811,90011,94811,98411,99611,100811,108011,109211,111611,115211,116411,120011,126011,128411,130811,136811,140411,142811,150011,153611,156011,157211,162011,163211,165611,175211,181211,183611,187211,190811,199211,201611,205211,206411,210011,212411,213611,214811,220811,222011,223211,225611,231611,232811,235211,240011,246011,259211,260411,266411,267611,268811,271211,272411,274811,276011,280811,282011,283211,285611,301211,302411,306011,308411,313211,319211,321611,324011,332411,338411,340811,348011,349211,350411,355211,357611,358811,361211,363611,368411,373211,376811,378011,386411,393611,394811,397211,405611,406811,408011,410411,411611,418811,424811,426011,428411,430811,434411,436811,447611,450011,459611,465611,468011,470411,478811,481211,483611,487211,493211,495611,499211,504011,508811,511211,517211,518411,519611,524411,531611,532811,537611,543611,550811,552011,553211,556811,559211,560411,571211,579611,582011,584411,586811,588011,591611,600011,602411,604811,608411,612011,621611,627611,628811,642011,644411,645611,652811,654011,655211,667211,669611,670811,675611,680411,682811,697211,700811,702011,703211,708011,709211,716411,722411,727211,730811,734411,738011,746411,747611,753611,754811,756011,758411,766811,781211,789611,801611,802811,817211,822011,825611,826811,828011,829211,830411,837611,852011,853211,856811,862811,864011,865211,872411,876011,878411,885611,888011,889211,894011,895211,901211,904811,906011,907211,909611,915611,918011,920411,921611,926411,930011,934811,939611,949211,952811,954011,955211,957611,966011,974411,978011,979211,986411,993611,994811,996011,998411,999611
  • Mario Klingemann 6y

    13,1213,3613,4813,7213,9613,18013,19213,21613,28813,30013,32413,33613,36013,40813,42013,45613,51613,52813,54013,55213,60013,67213,74413,82813,85213,86413,87613,88813,92413,96013,97213,102013,105613,108013,114013,126013,128413,133213,135613,136813,141613,144013,145213,147613,151213,160813,164413,168013,170413,176413,178813,181213,186013,189613,192013,194413,198013,204013,205213,206413,211213,213613,219613,225613,226813,228013,229213,231613,242413,243613,244813,250813,252013,254413,255613,256813,259213,260413,264013,267613,268813,273613,277213,278413,279613,284413,285613,286813,289213,294013,297613,303613,304813,315613,328813,331213,337213,338413,339613,352813,357613,361213,366013,370813,372013,373213,382813,386413,387613,388813,394813,399613,410413,411613,414013,415213,416413,418813,427213,441613,456013,457213,460813,462013,463213,464413,470413,478813,480013,482413,487213,489613,492013,494413,495613,496813,498013,500413,505213,511213,520813,523213,524413,528013,529213,531613,534013,544813,550813,559213,562813,564013,566413,570013,574813,576013,579613,580813,582013,583213,586813,589213,597613,603613,607213,609613,613213,614413,620413,622813,625213,633613,642013,643213,650413,660013,666013,681613,688813,692413,698413,705613,716413,718813,721213,724813,726013,729613,746413,752413,760813,765613,766813,768013,783613,786013,788413,794413,796813,805213,807613,810013,813613,818413,822013,824413,825613,828013,830413,834013,835213,836413,838813,841213,843613,847213,852013,856813,859213,860413,861613,864013,865213,870013,874813,876013,877213,878413,880813,883213,898813,901213,902413,903613,906013,907213,909613,915613,922813,928813,931213,932413,933613,939613,940813,942013,943213,949213,952813,962413,966013,970813,973213,985213,990013,994813,999613
  • Mario Klingemann 6y

    17,1217,2417,3617,4817,13217,21617,22817,26417,27617,28817,33617,36017,37217,42017,44417,46817,48017,50417,52817,55217,56417,60017,62417,63617,64817,67217,75617,78017,84017,88817,90017,96017,103217,104417,117617,120017,127217,130817,134417,135617,140417,146417,147617,148817,152417,157217,159617,160817,162017,165617,169217,171617,174017,176417,178817,182417,187217,188417,189617,196817,198017,202817,211217,214817,218417,223217,226817,229217,240017,246017,252017,255617,260417,266417,268817,271217,272417,273617,274817,277217,280817,297617,298817,300017,302417,303617,315617,316817,320417,321617,325217,330017,331217,332417,337217,339617,344417,348017,352817,354017,361217,380417,384017,391217,394817,397217,398417,399617,406817,409217,411617,414017,416417,417617,423617,424817,438017,439217,442817,446417,447617,453617,470417,471617,472817,474017,480017,488417,492017,493217,495617,496817,500417,501617,504017,506417,508817,516017,517217,518417,522017,538817,541217,543617,546017,548417,554417,556817,558017,559217,564017,566417,572417,574817,582017,584417,598817,606017,609617,610817,614417,615617,621617,627617,630017,634817,636017,643217,649217,651617,657617,658817,661217,668417,675617,680417,684017,686417,697217,698417,699617,702017,703217,708017,709217,711617,722417,723617,728417,735617,736817,739217,742817,748817,751217,753617,759617,762017,766817,770417,774017,777617,781217,786017,787217,790817,799217,800417,801617,804017,819617,831617,835217,842417,848417,853217,854417,860417,861617,865217,866417,867617,868817,873617,876017,879617,882017,883217,884417,891617,892817,896417,907217,908417,910817,913217,925217,928817,932417,940817,942017,944417,955217,960017,962417,970817,972017,974417,976817,978017,980417,984017,986417,991217,992417,993617,994817

    There is indeed a rule: the last two digits are 17 and the remainding number when you chop of the 17 is divisible by 3 and 4
  • David Bollinger 6y

    i wonder if the Klingemann Constant ;) isn't a factor of something else...
    if you examine the pattern of rays around the circle, you'll find repeating groupings of 1,2,2,1..2.. rays. i haven't bothered to count how many times that grouping repeats, but... what would happen if you multiplied your angular constant by the number of groupings? would you be left with a single instance of that 8-ray grouping? (or in general, what happens to those groupings when you multiply your constant by some integer n, say 2, for example?)
  • Prehensile Eye 6y

    try floating this to a number theorist in some university. i'm sure it would be interesting to them. :)
  • Mario Klingemann 6y

    Dave - now that I have cooled down a bit I've finally understood what you mean - yes that pattern stings in the eye, gosh - it might be only 8 angles after all. 160 rays divided by 8 is 20 groups, maybe I can go down to 18° segments.
  • Mario Klingemann 6y

    Yes, there are indeed 20 groups. When I clean up the roundoff errors I get a series of distances that are spaced out approximately 31,21,10,21,11,21,31,11
  • Mario Klingemann 6y

    @drauh - yes at the University they will be as happy about is as the scientists in Douglas Adams' Hitchhikers Guide:

    "Then, one day, a student who had been left to sweep up after a particularly unsuccessful party found himself reasoning in this way: If, he thought to himself, such a machine is a virtual impossibility, it must have finite improbability. So all I have to do in order to make one is to work out how exactly improbable it is, feed that figure into the finite improbability generator, give it a fresh cup of really hot tea... and turn it on!

    He did this and was rather startled when he managed to create the long sought after golden Infinite Improbability generator. He was even more startled when just after he was awarded the Galactic Institute's Prize for Extreme Cleverness he was lynched by a rampaging mob of respectably physicists who had realized that one thing they couldn't stand was a smart-ass."
  • Leander Herzog 6y

    :)
  • Mario Klingemann 6y

    Discussion continues here:
    This is so beautiful, it must be true by Quasimondo
  • Mario Klingemann 6y

    In case you came here first - check this: incubator.quasimondo.com/flash/wheel_of_primes.php
  • Alexandre Hamada Possi 2y

    neat!
  • Anabela Montes 2y

    how did you get the number 2.41379035550925, the increase angle of your nice spiral?
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