mersenneforum.org Ulam spirale, envolved to
 Register FAQ Search Today's Posts Mark Forums Read

 2022-06-12, 16:27 #1 RomanM   Jun 2021 3×17 Posts Ulam spirale, envolved to Hi. Plot code was taken from here https://community.wolfram.com/groups/-/m/t/1543056 Code: mgonLayer[q_, m_] := Ceiling[1/2 (1 + Sqrt[-8 + m + 8 q]/Sqrt[m])] - 1 maround[q_, m_] := q - (1 + m/2 ((mgonLayer[q, m] - 1) (mgonLayer[q, m]))) mpoint[q_, m_] := (mgonLayer[q, m] AngleVector[(2 \[Pi])/m (#1 - 1)] + #2 2 Sin[\[Pi]/m] AngleVector[2 \[Pi]/m (#1 - 1) + \[Pi]/2 + \[Pi]/m]) & @@ Quiet[QuotientRemainder[maround[q, m], mgonLayer[q, m]]] ListPlot[mpoint[#, M] & /@ (Prime[#] & /@ Range[10000]), Axes -> False, AspectRatio -> Automatic] For classic spirale, M = 4; Lets make a little changes in the plot code: Code: ListPlot[mpoint[#, M] & /@ (Prime[#*#] & /@ Range[20000]), Axes -> False, AspectRatio -> Automatic] M = 403 Sharingan https://www.mersenneforum.org/attach...1&d=1655050840 M = 503 Rinnegan https://www.mersenneforum.org/attach...1&d=1655051029 Attached Thumbnails     Last fiddled with by RomanM on 2022-06-12 at 16:33 Reason: Range[20000] for obtaine the same pictures
 2022-06-18, 19:57 #2 RomanM   Jun 2021 3×17 Posts Hello. Code: ListPlot[mpoint[#, 4] & /@ ((Prime[2*#] - 2*Prime[#]) & /@ Range[15000]), Axes -> True, AspectRatio -> Automatic] what do you think, is it possible to have a prime related function instead of Code:  Prime[2*#] - 2*Prime[#] that gives a symmetry? Attached Thumbnails
2022-06-23, 12:20   #3
RomanM

Jun 2021

3316 Posts

Quote:
 Originally Posted by RomanM *** that gives a symmetry?
some symmery
Code:
ListPlot[mpoint[#, 4] & /@ ((Prime[#]/EulerPhi[#]) & /@ Range[15000]),
Axes -> True, AspectRatio -> Automatic]
on the graph is connection Euler Phi(n) and n-prime number, and it's not impossible to fast compute the n-prime number for given (full factored) n.
Attached Thumbnails

All times are UTC. The time now is 21:37.

Tue Aug 16 21:37:42 UTC 2022 up 40 days, 16:25, 1 user, load averages: 1.08, 1.16, 1.16