lambda_p = Lambda_p(a_base, p)

# print("a_base %s\nord_base %s\n lambda_p = %s" % (a_base, ord_base, lambda_p))

mu = int((p - 1) / lambda_p)

clearfile(f"lib/free_sqr.txt")

start_time = time.time()

free_sqr = []

for n in range(3, Q11, 2):

print(n)

arr = numth.factorization(n)

power = 1

for i in range(len(arr)):

power *= arr[i][1]

if power == 1:

free_sqr.append(n)

writefile(f"lib/free_sqr.txt", f"{n} ")

total_time = "\n--- %s seconds ---\n" % (time.time() - start_time)

writefile(f"lib/free_sqr.txt", total_time)

clearfile(f"lib/mu/{a_base}/total_time.txt")

### Посчет времени работы

start_time = time.time()

###

primes_dict = {}

for prime in primes[len(a_base):]:

mu = Mu_p(a_base, prime)

print(prime, mu)

# if mu == 1:

# continue

if mu in primes_dict.keys():

primes_dict[mu].append(prime)

else:

primes_dict[mu] = [prime]

###

total_time = "--- %s seconds ---\n" % (time.time() - start_time)

###

tot_s = total_time

writefile(f"lib/mu/{a_base}/total_time.txt", tot_s)

for item in primes_dict:

clearfile(f"lib/mu/{a_base}/mu_{item}.txt")

s = ''.join(str(l) + ' ' + '\n' * (n % 8 == 7) for n, l in enumerate(primes_dict[item]))

writefile(f"lib/mu/{a_base}/mu_{item}.txt", s)

true_list = []

# print(primes)

for i in range(len(primes) - 1):

# print(f"prime i {primes[i]} {primes[i+1]}")

if Sign(a_base, primes[i]) == Sign(a_base, primes[i + 1]):

true_list.append(True)

else:

true_list.append(False)

p3_next_list = []

###Случай подбора

r = powmod(b, -1, lmd)

p = r

if primes[-1] < B_h / b:

bound = primes[-1]

else:

bound = B_h / b

while p < bound:

if numth.is_prime(int(p)):

p3_next_list.append(p)

p += lmd

b = int(np.prod(p_exist))

if check_signs(a_base, p_exist) and b / p_exist[-1] < B / p_exist[-2]:

lmd = Lambda_list(a_base, p_exist)

print(f"lmd {lmd}")

if gcd(b, lmd) == 1:

p_next_list = checking_p(b, lmd, B)

# print(f"p_next_list {p_next_list}")

return sorted(p_next_list)

elif gcd(b, lmd) != 1:

clearfile(f"res/jnd/2/{a_base}/spsp_{B}.txt")

clearfile(f"res/jnd/2/{a_base}/n_list_{B}.txt")

n_list = []

### Посчет времени работы

start_time = time.time()

###

for p1 in primes_list:

p1 = int(p1)

if p1 < int(root(B, 2)):

if p1 > a_base[-1]:

s = ""

if p1 < 10 ** 6:

gcd_23 = int(gcd(2 ** (p1 - 1) - 1, 3 ** (p1 - 1) - 1))

factors = sorted(numth.factorization(gcd_23))

for i in range(len(factors)):

p2 = factors[i][0]

if p2 * p1 <= B: # and p1 * p2 > B // 100:

if p2 > p1: # В дальнейшем для того, чтобы числа в интервалах не повторялись

signss = check_signs(a_base, [p1, p2])

if signss:

item = Signature(Sign(a_base, p1), [p1, p2])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

# else:

# break

elif p1 > 10 ** 8:

lmd_p = Lambda_p(a_base, p1) # lmd_p = p1-1

p2 = 1

while p2 <= p1: # and p1 * p2 > B // 100: # к условию, что p2>p1

p2 += lmd_p

while p2 * p1 <= B: # and p1 * p2 > B // 100:

signss = check_signs(a_base, [p1, p2])

if signss:

item = Signature(Sign(a_base, p1), [p1, p2])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(Signature(item.sign, [p1, p2]))

p2 += lmd_p

else: # между 10**6..10**8

if len(a_base) > 6:

a_base = a_base[:6]

lmd_p = Lambda_p(a_base, p1)

leg1 = []

for a in a_base:

leg1.append(numth.jacobi(a, p1))

if p1 % 4 == 1:

p2_4k3 = readfile("primes/4k+3.txt")

p2_4k1 = readfile("primes/4k+1.txt")

for p2 in p2_4k3:

if p1 * p2 <= B: # and p1 * p2 > B // 100:

if p2 % lmd_p == 1 and p2 > p1:

leg2 = []

for a in a_base:

leg2.append(numth.jacobi(a, p2))

signss = check_signs(a_base, [p1, p2])

if leg1 == leg2 and signss:

item = Signature(Sign(a_base, p1), [p1, p2])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

# else:

# break

for p2 in p2_4k1:

if p1 * p2 <= B: # and p1 * p2 > B // 100:

if p2 % lmd_p == 1 and p2 > p1:

leg2 = []

for a in a_base:

leg2.append(numth.jacobi(a, p2))

signss = check_signs(a_base, [p1, p2])

if np.prod(leg2) == 1 and signss: # если все 1, то произведение 1

item = Signature(Sign(a_base, p1), [p1, p2])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

# else:

# break

elif p1 % 8 == 5:

p2_8k5 = readfile("primes/8k+5.txt")

p2_8k1 = readfile("primes/8k+1.txt")

for p2 in p2_8k5:

if p1 * p2 <= B: # and p1 * p2 > B // 100:

if p2 % lmd_p == 5 and p2 > p1:

leg2 = []

for a in a_base:

leg2.append(numth.jacobi(a, p2))

signss = check_signs(a_base, [p1, p2])

if leg1 == leg2 and signss:

item = Signature(Sign(a_base, p1), [p1, p2])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

# else:

# break

for p2 in p2_8k1:

if p1 * p2 <= B: # and p1 * p2 > B // 100:

if p2 % lmd_p == 1 and p2 > p1:

leg2 = []

for a in a_base:

leg2.append(numth.jacobi(a, p2))

signss = check_signs(a_base, [p1, p2])

if np.prod(leg2) == 1 and signss:

item = Signature(Sign(a_base, p1), [p1, p2])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

# else:

# break

elif p1 % 8 == 1:

sign = Sign([2], p1)[0]

e, f = Val(2, p1 - 1), Val(2, sign)

for p2 in primes:

if p1 * p2 <= B: # and p1 * p2 > B // 100:

if p2 > p1 and e == f:

if p2 % (2 ** (e - 1)) == 2 ** e % (2 ** (e - 1)) and p2 % lmd_p == 1:

leg2 = []

for a in a_base:

leg2.append(numth.jacobi(a, p2))

signss = check_signs(a_base, [p1, p2])

if leg1 == leg2 and signss:

item = Signature(Sign(a_base, p1), [p1, p2])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

elif p2 % 2 ** (e + 1) == 1 and p2 % lmd_p == 1:

leg2 = []

for a in a_base:

leg2.append(numth.jacobi(a, p2))

signss = check_signs(a_base, [p1, p2])

if np.prod(leg2) == 1 and signss:

item = Signature(Sign(a_base, p1), [p1, p2])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

elif p2 > p1 and f < e and p1 * p2 <= B: # and p1 * p2 > B // 100:

signss = check_signs(a_base, [p1, p2])

if p2 % lmd_p == 1 and signss:

item = Signature(Sign(a_base, p1), [p1, p2])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

# else:

# break

writefile(f"res/jnd/2/{a_base}/n_list_{B}.txt", s)

else:

continue

i = 1

spsp = []

ss = ""

for item in n_list:

prod = np.prod(item.primes)

if psp(a_base, prod):

ss += f"{i} {prod} {item.primes} {item.sign}\n"

i += 1

spsp.append(item)

###

total_time = "--- %s seconds ---\n" % (time.time() - start_time)

###

ss += f"{total_time}\n"

writefile(f"res/jnd/2/{a_base}/spsp_{B}.txt", ss)

clearfile(f"res/jnd/3/{a_base}/spsp_{B}.txt")

clearfile(f"res/jnd/3/{a_base}/n_list_{B}.txt")

n_list = []

### Посчет времени работы

start_time = time.time()

###

# equal_2_list = parsefile(f"res/jnd/2/{a_base}/n_list_{B}.txt")

# упорядочены по возрастанию p1, где p1<p2

# if len(equal_2_list) != 0:

# for i in range(len(equal_2_list)):

# p1 = equal_2_list[i].primes[0]

# p2 = equal_2_list[i].primes[1]

# b = int(p1 * p2)

for p1 in primes:

p1 = int(p1)

print(p1)

if p1 <= int(root(B, 3)): # and b * p2 < B:

if p1 > a_base[-1]:

print(p1)

s = ""

if len(a_base) > 6:

a_base = a_base[:6]

leg1 = []

for a in a_base:

leg1.append(numth.jacobi(a, p1))

p2_3k4 = readfile("primes/4k+3.txt")

p2_1k4 = readfile("primes/4k+1.txt")

p2_5k8 = readfile("primes/8k+5.txt")

p2_1k8 = readfile("primes/8k+1.txt")

if p1 % 4 == 3:

print(f"p1 34 {p1}")

for p2 in p2_3k4:

if p2 > p1 and p2 < B and p2 < B: # на всякий случай проверим

print(f"p2 34 {p2}")

leg2 = []

b = int(p1 * p2)

for a in a_base:

leg2.append(numth.jacobi(a, p2))

if leg1 == leg2: # Prop.2 inverse is true

if b < 2 * 10 ** 6: # a trick

gcd_23 = int(gcd(2 ** (b - 1) - 1, 3 ** (b - 1) - 1))

factor_list = numth.factorization(gcd_23)

for i in range(len(factor_list)):

p3 = factor_list[i][0]

if p3 * b <= B: # and p3 * b > B // 100:

if p3 > p2:

print(f"p3 {p3}")

signss = check_signs(a_base, [p1, p3])

if signss:

item = Signature(Sign(a_base, p1), [p1, p2, p3])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

else:

p_exist = np.array([p1, p2])

p3_list = next_p(p_exist, a_base, B) # ищем подходящие p3

if isinstance(p3_list, list) and len(p3_list) != 0:

for p3 in p3_list:

if p3 * b <= B: # and p3 * b > B // 100:

if p3 > p2:

print(f"p3 {p3}")

signss = check_signs(a_base, [p1, p3])

if signss:

item = Signature(Sign(a_base, p1), [p1, p2, p3])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

# else:

# continue # новый item из equal_2_list

# else:

# continue

for p2 in p2_1k4:

print(f"p2 14 to mu {p2}")

if Mu_p(a_base, p2) == 4:

pass # переход к mu=4

elif p1 % 8 == 5:

print(f"p1 58 {p1}")

for p2 in p2_5k8:

if p2 > p1 and p2 < B:

print(f"p2 58 {p2}")

if len(a_base) > 5:

a_base = a_base[:5]

leg2 = []

b = int(p1 * p2)

for a in a_base:

leg2.append(numth.jacobi(a, p2))

if leg1 == leg2:

p_exist = np.array([p1, p2])

p3_list = next_p(p_exist, a_base, B)

print(p3_list, type(p3_list))

if isinstance(p3_list, list) and len(p3_list) != 0:

for p3 in p3_list:

if p3 * b <= B: # and p3 * b > B // 100:

if p3 > p2:

print(f"p3 {p3}")

signss = check_signs(a_base, [p1, p3])

if signss:

item = Signature(Sign(a_base, p1), [p1, p2, p3])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

# else:

# continue

# else:

# continue

for p2 in p2_1k8:

if p2 > p1 and p2 < B:

print(f"p2 18 {p2}")

if p2 % 16 == 9:

print(f"p2 916 {p2}")

leg2 = []

b = int(p1 * p2)

for a in a_base:

leg2.append(numth.jacobi(a, p2))

if np.prod(leg2) == 1 and p2 > p1: # если все 1, то произведение 1

p_exist = np.array([p1, p2])

p3_list = next_p(p_exist, a_base, B)

if isinstance(p3_list, list) and len(p3_list) != 0:

for p3 in p3_list:

if p3 * b <= B: # and p3 * b > B // 100:

if p3 > p2:

print(f"p3 {p3}")

signss = check_signs(a_base, [p1, p3])

if signss:

item = Signature(Sign(a_base, p1), [p1, p2, p3])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

else:

continue

else:

continue

elif p2 % 16 == 1:

print(f"p2 116 to mu {p2}")

if Mu_p(a_base, p2) == 4:

pass # переход к mu=4

for p2 in p2_3k4:

if p2 > p1 and p2 < B: # в тексте этого нет, но на всякий случай проверим

print(f"p2 34 {p2}")

b = int(p1 * p2)

p_exist = np.array([p1, p2])

p3_list = next_p(p_exist, a_base, B)

# print(f"p3 list {p3_list}")

if isinstance(p3_list, list) and len(p3_list) != 0:

for p3 in p3_list:

if p3 * b <= B: # and p3 * b > B // 100:

if p3 > p2:

print(f"p3 {p3}")

signss = check_signs(a_base, [p1, p3])

if signss:

item = Signature(Sign(a_base, p1), [p1, p2, p3])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

# else:

# continue

elif p1 % 8 == 1:

print(f"p1 18 {p1} p2 any {p2}")

e, f = Val(2, p1 - 1), Val(2, Lambda_p(a_base, p1))

if len(a_base) > 5:

a_base = a_base[:5]

for p2 in primes:

if p2 > p1 and p2 < B and e == f:

if p2 % (2 ** (e + 1)) == (1 + 2 ** e) % (2 ** (e + 1)): # !!!! СКОБКИ???

leg2 = []

b = int(p1 * p2)

for a in a_base:

leg2.append(numth.jacobi(a, p2))

if leg1 == leg2:

p_exist = np.array([p1, p2])

p3_list = next_p(p_exist, a_base, B)

if isinstance(p3_list, list) and len(p3_list) != 0:

for p3 in p3_list:

if p3 * b <= B: # and p3 * b > B // 100:

if p3 > p2:

print(f"p3 {p3}")

signss = check_signs(a_base, [p1, p3])

if signss:

item = Signature(Sign(a_base, p1), [p1, p2, p3])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

else:

continue

else:

continue

elif p2 % (2 ** (e + 2)) == 1:

if Mu_p(a_base, p2) == 4:

pass # переход к mu=4

elif p2 % (2 ** (e + 2)) != 1 and p2 % (2 ** (e + 2)) == (1 + 2 ** (e + 1)) % 2 ** (

e + 2): # !!!! СКОБКИ???

leg2 = []

b = int(p1 * p2)

for a in a_base:

leg2.append(numth.jacobi(a, p2))

if np.prod(leg2) == 1:

p_exist = np.array([p1, p2])

p3_list = next_p(p_exist, a_base, B)

if isinstance(p3_list, list) and len(p3_list) != 0:

for p3 in p3_list:

if p3 * b <= B: # and p3 * b > B // 100:

if p3 > p2:

print(f"p3 {p3}")

signss = check_signs(a_base, [p1, p3])

if signss:

item = Signature(Sign(a_base, p1), [p1, p2, p3])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

else:

continue

else:

continue

elif p2 > p1 and p2 < B and f < e:

if p2 % 2 ** f == p1:

if f == e - 1 and Mu_p(a_base, p1) == 2: # это есть условие выше

p_exist = np.array([p1, p2])

p3_list = next_p(p_exist, a_base, B)

b = int(p1 * p2)

if isinstance(p3_list, list) and len(p3_list) != 0:

for p3 in p3_list:

if p3 * b <= B: # and p3 * b > B // 100:

if p3 > p2:

print(f"p3 {p3}")

signss = check_signs(a_base, [p1, p3])

if signss:

item = Signature(Sign(a_base, p1), [p1, p2, p3])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

else:

continue

else:

continue

else:

continue

# p1 is any in primes

mu_4 = readfile(f"lib/mu/{a_base}/mu_4.txt")

for p2 in mu_4:

if p2 > p1 and p2 < B: # если p2 mu=4, то не обязательно чтобы и p1 mu=4

print(f"p2 mu4 {p2}")

p_exist = np.array([p1, p2])

p3_list = next_p(p_exist, a_base, B)

b = int(p1 * p2)

if isinstance(p3_list, list) and len(p3_list) != 0:

for p3 in p3_list:

if p3 * b <= B: # and p3 * b > B // 100:

if p3 > p2:

print(f"p3 {p3}")

signss = check_signs(a_base, [p1, p3])

if signss:

item = Signature(Sign(a_base, p1), [p1, p2, p3])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

# else:

# continue

writefile(f"res/jnd/3/{a_base}/n_list_{B}.txt", s)

else:

continue

else:

break

i = 1

spsp = []

ss = ""

for item in n_list:

prod = np.prod(item.primes)

if psp(a_base, prod):

ss += f"{i} {prod} {item.primes} {item.sign}\n"

i += 1

spsp.append(item)

###

total_time = "--- %s seconds ---\n" % (time.time() - start_time)

###

ss += f"{total_time}\n"

writefile(f"res/jnd/3/{a_base}/spsp_{B}.txt", ss)

clearfile(f"res/jnd/4/{a_base}/spsp_{B}.txt")

clearfile(f"res/jnd/4/{a_base}/n_list_{B}.txt")

n_list = []

### Посчет времени работы

start_time = time.time()

###

equal_3_list = parsefile(f"res/jnd/3/{a_base}/n_list_{B}.txt")

# упорядочены по возрастанию p1, где p1<p2

if len(equal_3_list) != 0:

for i in range(len(equal_3_list)):

p1 = equal_3_list[i].primes[0]

p2 = equal_3_list[i].primes[1]

p3 = equal_3_list[i].primes[2]

b = int(p1 * p2 * p3)

if p1 <= int(root(B, 4)) and b * p3 < B:

s = ""

if p1 % 4 == 3: # Вместо сигнатур вычисляется символ Лежандра

p4_3k4 = readfile("primes/4k+3.txt")

for p4 in p4_3k4:

if p4 * b <= B: # and p4 * b > B // 100:

if p4 > p3:

f"p4 {p4}"

signss = check_signs(a_base, [p1, p4])

if signss:

item = Signature(Sign(a_base, p1), [p1, p2, p3, p4])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

else:

p_exist = np.array([p1, p2, p3])

p4_list = next_p(p_exist, a_base, B)

if isinstance(p4_list, list):

for p4 in p4_list:

if p4 * b <= B: # and p4 * b > B // 100:

if p4 > p3:

f"p4 {p4}"

signss = check_signs(a_base, [p1, p4])

if signss:

item = Signature(Sign(a_base, p1), [p1, p2, p3, p4])

s += f"{item.primes} {signss} {item.sign}\n"

n_list.append(item)

writefile(f"res/jnd/4/{a_base}/n_list_{B}.txt", s)

else:

continue

i = 1

spsp = []

ss = ""

for item in n_list:

prod = np.prod(item.primes)

if psp(a_base, prod):

ss += f"{i} {prod} {item.primes} {item.sign}\n"

i += 1

spsp.append(item)

###

total_time = "--- %s seconds ---\n" % (time.time() - start_time)

###

ss += f"{total_time}\n"

writefile(f"res/jnd/4/{a_base}/spsp_{B}.txt", ss)

if p1 <= int(root(B, 5)):

### Посчет времени работы

start_time = time.time()

###

n_list = []

l = 5

if p1 % 4 == 3:

n_list = [p1]

q_3k4 = readfile("primes/4k+3.txt")

sign_p1 = []

for a in a_base:

sign_p1.append(numth.jacobi(a, p1))

for q in q_3k4:

if q % 24 == p1 % 24:

sign_q = []

for a in a_base:

sign_q.append(numth.jacobi(a, q))

if sign_q == sign_p1:

n_list.append(q)

# else:

# for p in primes:

###

total_time = "--- %s seconds ---\n" % (time.time() - start_time)

###

return np.array(n_list)

else:

print()

# Готовы

for i in range(6, 14, 2):

for j in range(2, 4):

print(i, j)

step_t_2(bases[:j], 10 ** i, primes)

# Не готовы

# for i in range(10, 18, 2):

print()

# Готовы

for i in range(6, 12, 2):

for j in range(2, 4):

print(i, j)

step_t_3(bases[:j], 10 ** i)

# Не готовы

# for i in range(10, 18, 2):

print()

# Готовы

# for i in range(6, 12, 2):

# step_t_2(bases[:base_len], 10 ** i)

# Не готовы

# for i in range(10, 18, 2):