def is_truncatable_prime(p):
if p < 10:
return False
p_str = str(p)
for i in range(1, len(p_str)):
left = int(p_str[:i])
right = int(p_str[i:])
if not math_ext.is_prime(left) or not math_ext.is_prime(right):
return False
return True
def prime_decompose(x):
if x == 1 or math_ext.is_prime(x):
return [x]
factors = []
for p in primes():
if p > x:
break
if x % p == 0:
q = 1
while x % p == 0:
x = int(x / p)
q *= p
factors.append(q)
if math_ext.is_prime(x):
factors.append(x)
break
return sorted(factors)
def has_number_of_primes(numbers, prime_count):
threashold = len(numbers) - prime_count
for n in numbers:
if not math_ext.is_prime(n):
threashold -= 1
if threashold < 0:
return False
return True
def solve():
max_elem = {"a": 1, "b": 41, "len": 40}
for b in range(0, 1001):
if abs(b) <= max_elem["len"] or not math_ext.is_prime(b):
continue
for a in range(-1000, 1001):
if get_prime_length(a, b) > max_elem["len"]:
max_elem = {"a": a, "b": b, "len": get_prime_length(a, b)}
return max_elem["a"] * max_elem["b"]
def solve():
corners, primes = [], []
for n in math_ext.corners():
corners.append(n)
if math_ext.is_prime(n, k=50):
primes.append(n)
if (len(corners) - 1) % 4 == 0 and len(corners) > 2:
if len(primes) / len(corners) < 0.1:
return math.floor((len(corners) + 2) / 4) * 2 + 1
def is_goldbach(n):
for i in range(1, n + 1):
j = n - 2 * (i**2)
print("{} = {} + 2 * {} ^ 2".format(n, j, i))
if j < 0:
return False
if j == 1 or math_ext.is_prime(j):
return True
return False
def get_max_consecutive_prime_sum(threashold):
primes = list(slice_seq(math_ext.primes(), 0, threashold))
start, end = 0, 1
for i in range(len(primes)):
for j in range(i + end - start, len(primes)):
p = sum(primes[i:j])
if p >= threashold:
break
if math_ext.is_prime(p):
start, end = i, j
return sum(primes[start:end])
def is_circular_prime(x):
return all([math_ext.is_prime(y) for y in get_circular_numbers(x)])
def composite_numbers():
return filter(lambda n: not math_ext.is_prime(n), itertools.count(4))
def is_prime_pair(p1, p2):
p3 = int(str(p1) + str(p2))
p4 = int(str(p2) + str(p1))
return math_ext.is_prime(p3) and math_ext.is_prime(p4)
def test_is_prime():
assert not math_ext.is_prime(-1)
assert not math_ext.is_prime(0)
assert not math_ext.is_prime(1)
assert math_ext.is_prime(2)
assert math_ext.is_prime(3)
assert not math_ext.is_prime(4)
assert math_ext.is_prime(5)
assert not math_ext.is_prime(6)
assert math_ext.is_prime(7)
assert not math_ext.is_prime(8)
assert not math_ext.is_prime(9)
assert not math_ext.is_prime(10)
pseudo_primes = [
341, 561, 645, 1105, 1387, 1729, 1905, 2047, 2465, 2701, 2821, 3277,
4033, 4369, 4371, 4681, 5461, 6601, 7957, 8321, 8481, 8911
]
assert all([not math_ext.is_prime(n, k=50) for n in pseudo_primes])