def probleme49(L):
r = set(str(L[0]))
for i in L:
if not r == set(str(i)): return False
if not mt.is_prime(i): return False
r = set(str(i))
return True
def testquadratic(a, b, affi=False):
n = 0
while True:
r = (n**2) + (a * n) + b
#print(r)
if r < 0: return n, r
elif not mt.is_prime(r):
return n, r
if affi: print(r)
n += 1
def num_prime(n):
z = 1 / (10**n)
a = 1
m = 0, 0
while True:
r = 2
L = []
while True:
s = a**(2**r)
if not mt.is_prime(floor(s)): break
L.append(floor(s))
r += 1
if m[0] < r - 2: m = r - 2, a, L
a += z
a = round(a, n)
if a >= 2: return m
def minimal(base):
minimal = []
for i in mt.minimal(mt.primegenfast(), base, limit=base**3):
minimal.append(i)
familytest = []
last_digits = minimal_last_digits(base)
digits = minimal_digits(base)
for x in digits[1:]:
for z in last_digits:
Y = [
dig for dig in digits if not any(
is_subsequence(
num,
str_base(x, base) + str_base(dig, base) +
str_base(z, base), base) for num in minimal)
]
if Y:
familytest.append(Family(x, Y, z, base=base))
familytest = list(filter(lambda x: x.contain_prime(), familytest))
i = 0
while familytest:
new = []
for family in familytest:
new += family.lemma19()
familytest = new[:]
new = []
for family in familytest:
w = family(0, True)
if subword_in_minimal(w, minimal, base): pass
elif mt.is_prime(w):
minimal.append(w)
else:
new += family.lemma21(minimal, 1)
familytest = new[:]
new = []
#print(familytest)
for family in familytest:
new += family.lemma23(minimal)
familytest = new[:]
familytest = list(filter(lambda x: x.contain_prime(), familytest))
if i % 10 == 0: print(familytest)
i += 1
return minimal
def contain_prime(self):
if self.is_num(): return mt.is_prime(self(0, True))
return not (1 < mt.gcd(*self(1, True), self(0, True)) < self(0, True))