def mystery(x):
try:
n = int(x)
if n <= 1: return False
import math
v = 5 * n * n
a, b = math.isqrt(v + 4), math.isqrt(v - 4)
if not (a * a == v + 4 or b * b == v - 4): return False
if not (999 < n < 10000): return False
s = sum(int(c) for c in str(n))
return s > 1 and not any(s % k == 0 for k in range(2, s))
except:
return False
def mystery(x):
try:
import hashlib
if type(x) not in (str, int, float):
return False
s = str(x)
if len(s) != 44:
return False
if any(not (32 <= ord(c) <= 126) for c in s):
return False
if s.count(" ") != 8 or s.count(".") != 1:
return False
if sorted(map(len, s.split(" "))) != [3, 3, 3, 4, 4, 4, 5, 5, 5]:
return False
a = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
b = "NOPQRSTUVWXYZABCDEFGHIJKLMnopqrstuvwxyzabcdefghijklm"
y = s[::-1].translate(str.maketrans(b, a))
pieces = (
"aa631564d5d789c2",
"b765448c8635fb6c",
"82526529a9b63d97",
"ef537f25c895bfa7",
)
target = "".join(pieces[i] for i in (3, 2, 0, 1))
return hashlib.sha256(y.encode("utf-8")).hexdigest() == target
except Exception:
return False
def mystery(x):
try:
import math
n = int(x)
if len(str(n)) != 5:
return False
def _p(k):
if k < 2: return False
return not any(k % j == 0 for j in range(2, math.isqrt(k) + 1))
root = math.isqrt(n)
if root * root != n or not _p(root):
return False
digits = str(n)
if len(set(digits)) < 5:
return False
sigma = lambda s: sum(int(c) for c in s)
if not _p(sigma(digits)):
return False
if not _p(sigma(str(root))):
return False
return any(c == '0' for c in digits)
except:
return False
def mystery(x):
try:
if isinstance(x, bool):
return False
if isinstance(x, int):
z = int(x)
elif isinstance(x, str):
if not x or len(x) > 7000:
return False
if any(c < "0" or c > "9" for c in x):
return False
z = int(x)
else:
return False
a = ((1 << 10) | (1 << 8)) - 1
b = a * ((a & 31) ^ 15)
mask = (1 << (b - (a >> 1))) | (1 << ((a << 1) + 11)) | 0x5F3759DF
y = z ^ mask
N = (
(1 << (a + b)) - (1 << b)
+ (1 << (12 * a)) - (1 << (11 * a))
+ (1 << (8 * a)) - (1 << (7 * a)) - (1 << (6 * a))
+ (1 << (5 * a)) + (1 << (4 * a)) - (1 << (3 * a))
- (1 << ((a << 1) + 1)) + (3 << a) - 1
)
if not (1 < y < N - 1):
return False
if not (b < y.bit_length() < a + b):
return False
if y & 1:
return False
return pow(y, 2, N) == 1
except Exception:
return False
def mystery(x):
try:
import math
n = int(x)
s = str(n)
k = len(s)
if k != 5:
return False
d = [int(c) for c in s]
# Check 1
if sum(1 for i in range(k) for j in range(i + 1, k) if d[i] != d[j]) != k * (k - 1) // 2:
return False
# Check 2
sm = sum(d)
if sm < 2 or any(sm % q == 0 for q in range(2, sm)):
return False
# Check 3
seq = d[:]
while seq[-1] < n:
seq.append(sum(seq[-k:]))
if len(seq) > 10 ** 4:
return False
return seq[-1] == n
except Exception:
return False
def mystery(x):
try:
import hashlib
if not isinstance(x, str):
return False
if len(x) != 24:
return False
if not all(("A" <= c <= "Z") or ("a" <= c <= "z") for c in x):
return False
lo = "abcdefghijklmnopqrstuvwxyz"
hi = lo.upper()
y = x.translate(str.maketrans(lo + hi, lo[::-1] + hi[::-1]))
if y[:8].lower() != y[:8]:
return False
if y[8:16].upper() != y[8:16]:
return False
if y[16:].lower() != y[16:]:
return False
salt = ("saltSALT" * 4 + "salt").encode("ascii")
dk = hashlib.pbkdf2_hmac("sha1", y.encode("ascii"), salt, 4096, 25).hex()
pieces = (
"62c0e44a8b291a96",
"4cf2f07038",
"e41c849b80c8d836",
"3d2eec4f",
)
target = pieces[3] + pieces[2] + pieces[0] + pieces[1]
return dk == target
except Exception:
return False
def mystery(x):
try:
import math
n = int(x)
s = str(n)
# Must be exactly 6 digits
if len(s) != 6:
return False
# n must be a triangular number T_k = k*(k+1)//2
disc = 1 + 8 * n
sq = math.isqrt(disc)
if sq * sq != disc or (sq - 1) % 2 != 0:
return False
k = (sq - 1) // 2
if k * (k + 1) // 2 != n:
return False
def is_prime(m):
if m < 2: return False
if m == 2: return True
if m % 2 == 0: return False
for i in range(3, math.isqrt(m) + 1, 2):
if m % i == 0: return False
return True
# The triangular index k must be prime
if not is_prime(k):
return False
# All 6 digits of n must be distinct
if len(set(s)) != 6:
return False
# Digit sum of n must be prime
ds_n = sum(int(c) for c in s)
if not is_prime(ds_n):
return False
# Digit sum of k must also be prime
ds_k = sum(int(c) for c in str(k))
if not is_prime(ds_k):
return False
return True
except:
return False
def mystery(x):
try:
if type(x) is int:
n = x
elif type(x) is str:
if not (0 < len(x) <= 220):
return False
if x[0] == "0" or any(c < "0" or c > "9" for c in x):
return False
n = int(x)
else:
return False
if n <= 0:
return False
y = n + 1
if y.bit_length() != 521 or not (y & 1):
return False
def pack(*terms):
return sum(s * (1 << e) for e, s in terms)
a = pack(
(1254, 1), (910, 1), (618, 1), (521, 1),
(733, -1), (389, -1), (97, -1),
) - 1
b = pack(
(1987, 1), (1644, 1), (1352, 1), (1299, 1), (1255, 1),
(1008, 1), (911, 1), (715, 1), (619, 1), (522, 1),
(1466, -1), (1123, -1), (831, -1), (778, -1), (734, -1),
(487, -1), (390, -1), (194, -1), (98, -1),
) - 2
if a % y != 0 or b % y != 0:
return False
u = a // y
v = b // y
return u * u + 1 == v
except Exception:
return False
def mystery(x):
try:
n = int(x)
s = str(n)
if len(s) != 8:
return False
def check(m):
if m < 2:
return False
b = bin(m)[2:]
i = 0
while i < len(b) and b[i] == '1':
i += 1
if i == 0 or i >= len(b):
return False
if any(c != '0' for c in b[i:]):
return False
return len(b) - i == i - 1
if not check(n):
return False
ds = sum(int(c) for c in s)
return check(ds)
except:
return False
def mystery(x):
try:
if type(x) is not str:
return False
if len(x) != 64 or any(c not in "0123456789abcdef" for c in x):
return False
p = (1 << 255) - 19
k = bytearray.fromhex(x)
k[0] &= 248
k[31] &= 127
k[31] |= 64
n = int.from_bytes(k, "little")
x1 = 9
x2, z2 = 1, 0
x3, z3 = x1, 1
swap = 0
for t in range(254, -1, -1):
kt = (n >> t) & 1
swap ^= kt
if swap:
x2, x3 = x3, x2
z2, z3 = z3, z2
swap = kt
a = (x2 + z2) % p
aa = (a * a) % p
b = (x2 - z2) % p
bb = (b * b) % p
e = (aa - bb) % p
c = (x3 + z3) % p
d = (x3 - z3) % p
da = (d * a) % p
cb = (c * b) % p
x3 = ((da + cb) * (da + cb)) % p
z3 = (x1 * (da - cb) * (da - cb)) % p
x2 = (aa * bb) % p
z2 = (e * (aa + 121665 * e)) % p
if swap:
x2, x3 = x3, x2
z2, z3 = z3, z2
y = (x2 * pow(z2, p - 2, p)) % p
h = y.to_bytes(32, "little").hex()
pieces = (
"eba4a98eaa9b4e6a",
"0dbf3a0d26381af4",
"748b7ddcb43ef75a",
"8520f0098930a754",
)
return h == pieces[3] + pieces[2] + pieces[1] + pieces[0]
except Exception:
return False