Goldbach's comet follows x^(0.8) ?

goldbach-comet.py

from matplotlib import pyplot as plt
import numpy as np
import pandas as pd
from sympy import sieve

def prime_doubles(upper):
    result = [0] * (2 * upper + 1)
    sieve.extend(upper)
    max_prime_index, _ = sieve.search(upper)
    for i in range(1, max_prime_index+1):
        for j in range(i, max_prime_index+1):
            result[sieve[i] + sieve[j]] += 1
    return result
  
UPPER = 100000
doubles = prime_doubles(UPPER)
x = range(6, UPPER, 2)
df = pd.DataFrame([doubles[i] for i in x], x, ["patterns by 2 primes"])

df.plot(linestyle='None',marker='o',markersize=0.1)
a = 0.8
b = np.array([ 0.058, 0.079, 0.118, 0.162, 0.19,  0.23])
x = np.linspace(0,UPPER,10000)
# x = np.logspace(1,5,10000)
for i in range(6):
    y = b[i]*np.power(x, a)
    plt.plot(x, y)
# plt.yscale('log')
# plt.xscale('log')