def test_count_primes():
"""Test count_primes function."""
assert primesieve.count_primes(100) == 25
assert primesieve.count_primes(10**6) == 78498
assert primesieve.count_primes(100, 10**6) == 78473
assert primesieve.count_primes(10**10) == 455052511
assert primesieve.count_primes(10**9, 10**10) == 404204977
def test_count_primes(self):
for testcase1 in ((100, 25), (10**6, 78498), (10**10, 455052511)):
self.assertEqual(primesieve.count_primes(testcase1[0]),
testcase1[1])
for testcase2 in (((100, 10**6), 78473), ((10**9, 10**10), 404204977)):
self.assertEqual(
primesieve.count_primes(testcase2[0][0], testcase2[0][1]),
testcase2[1])
def _make_pitch_candidates(
used_primes: typing.Tuple[int, ...] = (3, 5, 7, 11),
max_exponent: int = 2,
max_combinations: int = 2,
) -> typing.Tuple[pitches.JustIntonationPitch, ...]:
elements_per_prime = [[] for _ in used_primes]
for tonality in (True, False):
for nth_prime, prime in enumerate(used_primes):
nth_prime_number = primesieve.count_primes(prime)
for exponent in range(1, max_exponent + 1):
exponents = [0 for _ in range(nth_prime_number)]
exponents[-1] = exponent
if not tonality:
exponents[-1] = -exponents[-1]
pitch = pitches.JustIntonationPitch(exponents)
elements_per_prime[nth_prime].append(pitch)
candidates = [pitches.JustIntonationPitch()]
for combination in itertools.product(*elements_per_prime):
for n_pitches in range(1, max_combinations + 1):
for elements_to_combine in itertools.combinations(
combination, n_pitches):
pitch = functools.reduce(operator.add, elements_to_combine)
if pitch not in candidates:
candidates.append(pitch)
for candidate in candidates:
candidate.normalize()
return tuple(candidates)
#!/usr/bin/python3
# -*- coding: utf-8 -*-
import primesieve
LIMIT = 10**10
R = int(LIMIT**(1/2))
counter = 0
for n in range(1, R+1):
counter += primesieve.count_primes(n, LIMIT//n)
print(LIMIT-counter)
def test_count_primes():
assert primesieve.count_primes(100) == 25
assert primesieve.count_primes(10**6) == 78498
assert primesieve.count_primes(100, 10**6) == 78473
assert primesieve.count_primes(10**10) == 455052511
assert primesieve.count_primes(10**9, 10**10) == 404204977
def test_count_primes():
assert primesieve.count_primes(100) == 25
assert primesieve.count_primes(10**6) == 78498
assert primesieve.count_primes(100, 10**6) == 78473
self.primePoint = 1
self.currentFactorialTop = 1
def sOfP(self, p):
for i in range(self.currentFactorialTop + 1, p - 4):
self.primePoint *= i
self.currentFactorialTop = i
retVal = 0
tempFactorial = self.currentFactorialTop
for i in range(1,6):
retVal += tempFactorial
tempFactorial *= (p - 5 + i)
return retVal % p
print(primesieve.count_primes(10**8))
iterator = primesieve.Iterator()
prime = iterator.next_prime()
prime = iterator.next_prime()
prime = iterator.next_prime()
count = 0
topPoint = 10 ** 8
s = solver()
while prime < topPoint:
temp = s.sOfP(prime)
count += temp
#print (str(prime) + ': ' + str(temp) + ', ' + str(count) + '; ' + str(s.currentFactorialTop) + '! = ' + str(s.primePoint))
prime = iterator.next_prime()