def test_prime_count(self):
self.assertEqual(pyprimes.prime_count(PRIMES[-1]), len(PRIMES))
# Table of values from http://oeis.org/A000720
# plus one extra 0 to adjust for Python's 0-based indexing.
expected = [
0, 0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8,
8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12,
12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16,
16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19,
20, 20, 21, 21, 21, 21, 21, 21]
for i, count in enumerate(expected):
self.assertEqual(pyprimes.prime_count(i), count)
def test_prime_count(self):
self.assertEqual(pyprimes.prime_count(PRIMES[-1]), len(PRIMES))
# Table of values from http://oeis.org/A000720
# plus one extra 0 to adjust for Python's 0-based indexing.
expected = [
0, 0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8,
8, 9, 9, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12,
12, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16,
16, 16, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 21,
21, 21, 21, 21, 21
]
for i, count in enumerate(expected):
self.assertEqual(pyprimes.prime_count(i), count)
def test_bertelsen(self):
# http://mathworld.wolfram.com/BertelsensNumber.html
result = pyprimes.prime_count(10**9)
self.assertNotEqual(
result, 50847478,
"prime_count returns the erronous Bertelsen's Number")
self.assertEqual(result, 50847534)
def test_prime_count_tens(self):
# Test prime_count function with powers of ten.
# Values come from:
# http://mathworld.wolfram.com/PrimeCountingFunction.html
# http://oeis.org/A006880
expected = [0, 4, 25, 168, 1229, 9592, 78498]
for i, count in enumerate(expected):
self.assertEqual(pyprimes.prime_count(10**i), count)
def test_prime_count_tens(self):
# Test prime_count function with powers of ten.
# Values come from:
# http://mathworld.wolfram.com/PrimeCountingFunction.html
# http://oeis.org/A006880
expected = [0, 4, 25, 168, 1229, 9592, 78498]
for i, count in enumerate(expected):
self.assertEqual(pyprimes.prime_count(10**i), count)
def test_prime_count_tens_big(self):
# See also PyPrimesTest.test_prime_count_tens.
self.assertEqual(pyprimes.prime_count(10**7), 664579)
self.assertEqual(pyprimes.prime_count(10**8), 5761455)
def test_bertelsen(self):
# http://mathworld.wolfram.com/BertelsensNumber.html
result = pyprimes.prime_count(10**9)
self.assertNotEqual(result, 50847478,
"prime_count returns the erronous Bertelsen's Number")
self.assertEqual(result, 50847534)
def test_prime_count_tens_big(self):
# See also PyPrimesTest.test_prime_count_tens.
self.assertEqual(pyprimes.prime_count(10**7), 664579)
self.assertEqual(pyprimes.prime_count(10**8), 5761455)
import pyprimes
import itertools
import math
import time
start = time.time()
numList = []
below = 5000000
cUpper = math.ceil(below**(4**-1))
primeList = list(pyprimes.primes(2, math.ceil(math.sqrt(50000000))))
cList = primeList[:pyprimes.prime_count(cUpper - 1)]
for i in range(len(cList) - 1, -1, -1):
csquare = cList[i]**4
bUpper = math.ceil((below - csquare)**(3**-1))
bList = primeList[:pyprimes.prime_count(bUpper - 1)]
for j in range(len(bList) - 1, -1, -1):
bsquare = bList[j]**3
aUpper = math.ceil(math.sqrt(below - csquare - bsquare))
aList = primeList[:pyprimes.prime_count(aUpper - 1)]
for k in range(len(aList) - 1, -1, -1):
result = (aList[k]**2 + bsquare + csquare)
if result not in numList:
numList.append(result)
print(len(numList))