def test_generate():
assert nextprime(-4) == 2
assert nextprime(2) == 3
assert nextprime(5) == 7
assert nextprime(12) == 13
assert nextprime(90) == 97
assert nextprime(10**40) == (10**40 + 121)
pytest.raises(ValueError, lambda: prevprime(2))
assert prevprime(3) == 2
assert prevprime(7) == 5
assert prevprime(13) == 11
assert prevprime(97) == 89
assert prevprime(10**40) == (10**40 - 17)
assert list(primerange(3001110000000, 799999999)) == []
assert list(primerange(2, 7)) == [2, 3, 5]
assert list(primerange(2, 10)) == [2, 3, 5, 7]
assert list(primerange(
1050, 1100)) == [1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097]
s = Sieve()
for i in range(30, 2350, 376):
for j in range(2, 5096, 1139):
A = list(s.primerange(i, i + j))
B = list(primerange(i, i + j))
assert A == B
s = Sieve()
assert s[10] == 29
assert nextprime(2, 2) == 5
pytest.raises(ValueError, lambda: totient(0))
pytest.raises(ValueError, lambda: primorial(0))
assert mr(1, [2]) is False
def func(i):
return (i**2 + 1) % 51
assert next(cycle_length(func, 4)) == (6, 2)
assert list(cycle_length(func, 4, values=True)) == \
[17, 35, 2, 5, 26, 14, 44, 50, 2, 5, 26, 14]
assert next(cycle_length(func, 4, nmax=5)) == (5, None)
assert list(cycle_length(func, 4, nmax=5, values=True)) == \
[17, 35, 2, 5, 26]
assert list(cycle_length(lambda i: 0, 0, nmax=0)) == [(1, 0)]
def test_generate():
assert nextprime(-4) == 2
assert nextprime(2) == 3
assert nextprime(5) == 7
assert nextprime(12) == 13
assert nextprime(90) == 97
assert nextprime(10**40) == (10**40 + 121)
pytest.raises(ValueError, lambda: prevprime(2))
assert prevprime(3) == 2
assert prevprime(7) == 5
assert prevprime(13) == 11
assert prevprime(97) == 89
assert prevprime(10**40) == (10**40 - 17)
assert list(primerange(3001110000000, 799999999)) == []
assert list(primerange(2, 7)) == [2, 3, 5]
assert list(primerange(2, 10)) == [2, 3, 5, 7]
assert list(primerange(1050, 1100)) == [1051, 1061,
1063, 1069, 1087, 1091, 1093, 1097]
s = Sieve()
for i in range(30, 2350, 376):
for j in range(2, 5096, 1139):
A = list(s.primerange(i, i + j))
B = list(primerange(i, i + j))
assert A == B
s = Sieve()
assert s[10] == 29
assert nextprime(2, 2) == 5
pytest.raises(ValueError, lambda: totient(0))
pytest.raises(ValueError, lambda: primorial(0))
assert mr(1, [2]) is False
def func(i):
return (i**2 + 1) % 51
assert next(cycle_length(func, 4)) == (6, 2)
assert list(cycle_length(func, 4, values=True)) == \
[17, 35, 2, 5, 26, 14, 44, 50, 2, 5, 26, 14]
assert next(cycle_length(func, 4, nmax=5)) == (5, None)
assert list(cycle_length(func, 4, nmax=5, values=True)) == \
[17, 35, 2, 5, 26]
assert list(cycle_length(lambda i: 0, 0, nmax=0)) == [(1, 0)]