def screen_by_t(a_base, B, t, equal_list):
clearfile(f"lib/{B}/{t}/t_signs_{t}_{B}.txt")
### Посчет времени работы
start_time = time.time()
###
screening_list = []
for item in equal_list: # item - простые числа с одинаковой сигнатурой
if len(item.primes) >= t - 1 and item.primes[0] > a_base[-1]:
# берем больше, так как позже будем проверять по группам p1*p2*...*p(t-1)^2<B
combine = combinations(item.primes, t - 1) # в порядке возрастания
for prms in combine:
prod = np.prod(prms) * prms[-1]
if prod < B:
screening_list.append(Signature(item.sign, prms))
###
total_time = "--- %s seconds ---\n" % (time.time() - start_time)
###
### Запись в файл
for j in range(len(screening_list)):
s = f"{j} {screening_list[j].sign} {screening_list[j].primes}\n"
writefile(f"lib/{B}/{t}/t_signs_{t}_{B}.txt", s)
writefile(f"lib/{B}/{t}/t_signs_{t}_{B}.txt", total_time)
return screening_list
def t_2(a_base, B, primes_list):
clearfile(f"res/jae/2/{a_base}/spsp_{B}.txt")
spsp = []
### Посчет времени работы
start_time = time.time()
###
i = 1
for p in primes_list:
if p < int(root(B, 2)):
if p > a_base[-1]:
lmd_p = Lambda_p(a_base, p)
lmd = numth.lcm(lmd_p, 2)
for k in range(int(1 + (p - 1) / lmd),
int((B - p) / (p * lmd)) + 1, 1):
q = 1 + k * lmd
if p * q <= B: # and p * q > B // 100:
if numth.is_prime(q) and q > p:
if q + 1 == 2 * p:
if check_signs(a_base, [p, q]) and psp_2(
a_base, [p, q]):
item = Signature(Sign(a_base, p), [p, q])
s = f"{i} {np.prod(item.primes)} {item.primes} {item.sign}\n"
writefile(
f"res/jae/2/{a_base}/spsp_{B}.txt", s)
i += 1
spsp.append(item)
else:
continue
else:
P = p * (1 + k * lmd)
if psp(a_base, P) and check_signs(
a_base, [p, q]):
item = Signature(Sign(a_base, p), [p, q])
s = f"{i} {np.prod(item.primes)} {item.primes} {item.sign}\n"
writefile(
f"res/jae/2/{a_base}/spsp_{B}.txt", s)
i += 1
spsp.append(item)
# else:
# break
###
total_time = "--- %s seconds ---\n" % (time.time() - start_time)
###
writefile(f"res/jae/2/{a_base}/spsp_{B}.txt", total_time)
return spsp
def t_more_3(a_base, B, t, primes_list):
clearfile(f"res/jae/{t}/{a_base}/spsp_{B}.txt")
spsp = []
### Посчет времени работы
start_time = time.time()
###
i = 1
equal_list = parsefile(f"lib/equal/{a_base}/equal_signs.txt")
for item in equal_list: # item - простые числа с одинаковой сигнатурой
if len(item.primes) >= t - 1 and item.primes[0] > a_base[-1]:
# берем больше, так как позже будем проверять по группам p1*p2*...*p(t-1)^2<B
combine = combinations(item.primes, t - 1) # в порядке возрастания
for prms in combine:
prod = np.prod(prms)
if prod * prms[-1] < B:
a = a_base[0]
mu = Lambda_list([a], prms)
if gcd(mu, prod) > 1:
continue
else:
import gmpy2
c = gmpy2.powmod(prod, -1, mu)
for pt in primes_list:
if pt > prms[
-1] and pt <= B / prod and pt % mu == c:
if psp(a_base, pt * prod) and check_signs(
a_base, [pt, prms[-1]]):
item = Signature(Sign(a_base, pt),
prms + [pt])
s = f"{i} {np.prod(item.primes)} {item.primes} {item.sign}\n"
writefile(
f"res/jae/{t}/{a_base}/spsp_{B}.txt",
s)
i += 1
spsp.append(item)
else:
break # к другому item'у т.к. combine упорядочен вертикально и горизонтально
###
total_time = "--- %s seconds ---\n" % (time.time() - start_time)
###
writefile(f"res/jae/{t}/{a_base}/spsp_{B}.txt", total_time)
return spsp
def find_equal_signs(a_base, primes_list):
clearfile(f"lib/equal/{a_base}/equal_signs.txt")
clearfile(f"lib/equal/{a_base}/total_time.txt")
### Посчет времени работы
start_time = time.time()
###
signs_list = [
] # так как нельзя вернуть словарь с ключом-списком, заводим список сигнатур
primes_dict = {} # ключами являются индексы в списке сигнатур
for prime in primes_list[len(a_base):]:
print("finding equal ... %s" % (prime))
sign = Sign(a_base, prime)
if sign in signs_list:
primes_dict[signs_list.index(sign)].append(prime)
else:
signs_list.append(sign)
primes_dict[signs_list.index(sign)] = [prime]
###
total_time = "--- %s seconds ---\n" % (time.time() - start_time)
###
### Преобразование по классу
equal_list = []
for j in range(len(signs_list)):
temp = Signature(signs_list[j], primes_dict[j])
equal_list.append(temp)
###Запись в файл
tot_s = total_time
writefile(f"lib/equal/{a_base}/total_time.txt", tot_s)
s = ""
for j in range(len(signs_list)):
s += f"{j} {equal_list[j].sign} {equal_list[j].primes}\n"
writefile(f"lib/equal/{a_base}/equal_signs.txt", s)
return equal_list
def step_t_4(a_base, B):
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)
return np.array(spsp)
def step_t_3(a_base, B):
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)
return np.array(spsp)
def step_t_2(a_base, B, primes_list):
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)
return np.array(spsp)