75 lines
3.2 KiB
Python
75 lines
3.2 KiB
Python
|
#!/usr/bin/env python3
|
||
|
|
"""Prime Node Analyzer - wave sieve vs Eratosthenes, coprime sieve, irreducibility.
|
||
|
|
The wave sieve captures 97.8% of all primes (misses only 2).
|
||
|
|
With coprime wavelengths, ALL primes survive.
|
||
|
|
Usage: python prime_node_analyzer.py
|
||
|
|
"""
|
||
|
|
import sys,math
|
||
|
|
from collections import defaultdict
|
||
|
|
try:
|
||
|
|
import numpy as np; HAS_NP=True
|
||
|
|
except: HAS_NP=False
|
||
|
|
GRID=1024;K_WL=128;G_WL=8;K_AMP=0.03;G_AMP=0.008
|
||
|
|
def sieve(n):
|
||
|
|
if n<2:return []
|
||
|
|
ip=[True]*(n+1);ip[0]=ip[1]=False
|
||
|
|
for i in range(2,int(math.sqrt(n))+1):
|
||
|
|
if ip[i]:
|
||
|
|
for j in range(i*i,n+1,i):ip[j]=False
|
||
|
|
return [i for i in range(2,n+1) if ip[i]]
|
||
|
|
def isp(n):
|
||
|
|
if n<2:return False
|
||
|
|
if n<4:return True
|
||
|
|
if n%2==0 or n%3==0:return False
|
||
|
|
i=5
|
||
|
|
while i*i<=n:
|
||
|
|
if n%i==0 or n%(i+2)==0:return False
|
||
|
|
i+=6
|
||
|
|
return True
|
||
|
|
def sup1d(n,kwl=K_WL,gwl=G_WL,ka=K_AMP,ga=G_AMP):
|
||
|
|
k1=2*math.pi/kwl;k2=2*math.pi/gwl
|
||
|
|
return [ka*math.cos(k1*x)+ga*math.cos(k2*x) for x in range(n)]
|
||
|
|
def maxima1d(v,tf=0.5):
|
||
|
|
mx=max(v);mn=min(v);th=mn+(mx-mn)*tf
|
||
|
|
return [{'p':i,'v':v[i]} for i in range(1,len(v)-1) if v[i]>v[i-1] and v[i]>v[i+1] and v[i]>th]
|
||
|
|
def csieve(n,k1,k2):
|
||
|
|
return [i for i in range(2,n+1) if math.gcd(i,k1)==1 and math.gcd(i,k2)==1]
|
||
|
|
def wsieve(n,wls):
|
||
|
|
s=list(range(2,n+1))
|
||
|
|
for wl in wls:
|
||
|
|
s=[x for x in s if x%wl!=0]
|
||
|
|
for f in range(2,wl):
|
||
|
|
if wl%f==0:s=[x for x in s if x%f!=0]
|
||
|
|
return s
|
||
|
|
def main():
|
||
|
|
print('='*70+'\n PRIME NODE ANALYZER\n Testing: do irreducible lattice nodes map to primes?\n'+'='*70)
|
||
|
|
N=512;v=sup1d(N);mx=maxima1d(v);pos=[m['p'] for m in mx]
|
||
|
|
print(f'\n--- 1D Superposition ({N} positions) ---')
|
||
|
|
print(f'Khra wl={K_WL}, Gixx wl={G_WL}')
|
||
|
|
print(f'Maxima: {len(mx)}, positions: {pos[:20]}')
|
||
|
|
pp=[p for p in pos if isp(p)]
|
||
|
|
ap=sieve(N)
|
||
|
|
print(f'Prime maxima: {len(pp)}/{len(mx)} ({100*len(pp)/max(1,len(mx)):.1f}%)')
|
||
|
|
print(f'\n--- Wave Sieve vs Eratosthenes (n=200) ---')
|
||
|
|
ap2=set(sieve(200));ws=set(wsieve(200,[K_WL,G_WL]))
|
||
|
|
both=ap2&ws
|
||
|
|
print(f'Primes: {len(ap2)}, Wave survivors: {len(ws)}')
|
||
|
|
print(f'Overlap: {len(both)} ({100*len(both)/max(1,len(ap2)):.1f}% of primes captured)')
|
||
|
|
print(f'Precision: {100*len(both)/max(1,len(ws)):.1f}% of survivors are prime')
|
||
|
|
print(f'Missed primes: {sorted(ap2-ws)}')
|
||
|
|
print(f'\n--- Coprime Sieve ---')
|
||
|
|
cs=set(csieve(200,K_WL,G_WL));co=ap2&cs
|
||
|
|
print(f'Coprime to both {K_WL} and {G_WL}: {len(cs)} positions')
|
||
|
|
print(f'Primes captured: {len(co)}/{len(ap2)}')
|
||
|
|
print(f'Missed: {sorted(ap2-cs)}')
|
||
|
|
print(f'All odd primes captured: {all(p in cs for p in ap2 if p>2)}')
|
||
|
|
print(f'\n--- Coprime wavelength comparison ---')
|
||
|
|
for w1,w2 in [(127,8),(128,9),(127,9),(131,7),(K_WL,G_WL)]:
|
||
|
|
cp=csieve(100,w1,w2);p100=set(sieve(100));cap=p100&set(cp)
|
||
|
|
print(f' WL={w1:>3},{w2}: gcd={math.gcd(w1,w2):>3} survivors={len(cp):>3} primes={len(cap):>2}/{len(p100)} precision={100*len(cap)/max(1,len(cp)):.1f}%')
|
||
|
|
print(f'\n--- CONCLUSION ---')
|
||
|
|
print(f'Both wavelengths are powers of 2, so prime 2 is structural.')
|
||
|
|
print(f'All {len(co)} odd primes <= 200 survive the coprime sieve.')
|
||
|
|
print(f'With coprime wavelengths (e.g. 128,9) precision rises to 71.9%.')
|
||
|
|
if __name__=='__main__':main()
|