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import math
def get_poly_coeffs(a, n):
n += 1
coeffs = []
for j in range(n):
coeffs.append(math.factorial(n - 1) // (math.factorial(j) * math.factorial(n - 1 - j)))
for i in range(len(coeffs)):
coeffs[i] = coeffs[i] * (a ** i)
return coeffs
def euler_func(value, power=1):
if power == 1:
return value - 1
else:
return value ** power - value ** (power - 1)
def get_order(n, r):
pwr = n
cnt = 1
while pwr % r != 1:
pwr *= n
cnt += 1
return cnt
def check_power(a, n):
powered_a = a
b = 1
while powered_a <= n:
if powered_a == n:
return True, b
powered_a *= a
b += 1
return False, 0
def check_prime(e):
for i in range(2, int(math.sqrt(e))):
if e % i == 0:
return False
return True
def get_all_divisors_brute(n):
for i in range(1, int(n / 2) + 1):
if n % i == 0:
yield i
yield n
def get_only_prime_divisors(inp):
g = 1
prime_divisors = []
while g != inp:
for i in get_all_divisors_brute(inp):
if check_prime(i) and inp % i == 0 and i != 1:
inp = inp / i
prime_divisors.append(int(i))
break
return prime_divisors
def get_euler(r):
p_d = get_only_prime_divisors(r)
euler_func_mult = []
for el_1 in p_d:
el_pw = 0
for el_2 in p_d:
if el_1 == el_2:
el_pw += 1
euler_func_mult.append((el_1, el_pw))
tmp = []
for euler_mult in set(euler_func_mult):
tmp.append(euler_func(*euler_mult))
euler_func_mult = tmp
phi_value = 1
for elem in euler_func_mult:
phi_value *= elem
return phi_value
def check_polinom(a, n):
coeffs = get_poly_coeffs(a, n)
coeffs.remove(coeffs[0])
coeffs[-1] -= a
if not(coeffs[-1]):
coeffs.remove(coeffs[-1])
for cf in coeffs:
if cf % n:
return False
return True
def find_smallest_order(n):
r = 1
while True:
r += 1
if math.gcd(r, n) != 1:
continue
o_r = get_order(n, r)
if o_r > (math.log2(n)) ** 2:
return r
def aks_test(n):
r = find_smallest_order(n)
phi_r = get_euler(r)
border = math.floor(math.sqrt(phi_r) * math.log2(n))
for a in range(2, border):
is_powered, b = check_power(a, n)
if is_powered and b > 1:
return False
if 1 < math.gcd(a, n) < n and a <= r:
return False
if n <= r:
return True
if not check_polinom(a, n):
return False
return True
if __name__ == "__main__":
print("Введите число n:")
n = int(input())
result = aks_test(n)
if result:
print(f"Число {n} является простым")
else:
print(f"Число не является простым")
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