#%matplotlib inlineThe autoreload extension is already loaded. To reload it, use:
%reload_ext autoreload
README file and the index of documentation.
pip install nbdev_sieveFor now, only the sieve(N: int) generator can be called
## Helper functions
def primes(N: int = 10):
"get list of primes"
return [p for p in sieve(N)]
print (primes(17))[2, 3, 5, 7, 11, 13, 17]
| n | π(n) |
|---|---|
| 0 | |
| 4 | |
| 25 | |
| 168 | |
| 1,229 | |
| 9,592 | |
| 78,498 | |
| 664,579 | |
| 5,761,455 | |
| 50,847,534 | |
| 455,052,511 |
def prime_count(om: int = 8):
"#primes < 10^om"
return {n: len(primes(n)) for o in range(om) if(n:=10**o)}
π = prime_count()
π{1: 0,
10: 4,
100: 25,
1000: 168,
10000: 1229,
100000: 9592,
1000000: 78498,
10000000: 664579}
import matplotlib.pyplot as pltfig, ax = plt.subplots()
ax.scatter([math.log10(n) for n in π], [c/n for n, c in π.items()])
plt.xlabel("Order of Magnitude (10^n)")
plt.ylabel("Fraction of primes")
plt.show()
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