def is_prime_proof(self, n):
string_n = str(n)
string_test = str(n)
if n % 2 == 0 or n % 5 == 0:
for i in [1, 3, 7, 9]:
string_test = string_test[:-1] + str(i)
if primes.is_prime_opti(int(string_test)):
return False
return True
else:
for i in range(1, 10):
if i == string_n[0]:
continue
string_test = string_test[:0] + str(i) + string_test[1:]
if primes.is_prime_opti(int(string_test)):
return False
for i in range(1, len(string_n)):
string_test = str(n)
for j in range(0, 10):
if j == string_n[i]:
continue
string_test = string_test[:i] + str(j) + string_test[i +
1:]
if primes.is_prime_opti(int(string_test)):
return False
return True
def get(self):
k = 10**14
for i in range(1, self.limit + 1):
while not primes.is_prime_opti(
k): # it uses Miller6rabin algorithm to test primality
k += 1
self.res = (self.res + self.fibonacci_mod(k)) % self.mod
k += 1
def main():
start = time.perf_counter()
resultat = 0
for i in range(0, 50000000):
if primes.is_prime_opti((2*(i**2))-1):
resultat += 1
print(resultat)
print('temps d execution', time.perf_counter() - start, 'sec')
def main():
start = time.perf_counter()
resultat = 0
for i in range(0, 50000000):
if primes.is_prime_opti((2 * (i**2)) - 1):
resultat += 1
print(resultat)
print('temps d\'exécution', time.perf_counter() - start, 'sec')
def get_list_prime_candidates(self):
for d in sympy.divisors(self.factorial):
p = d + 1
if primes.is_prime_opti(p):
n = self.factorial // d
exp = 0
while n % p == 0:
n = n // p
exp += 1
self.list_prime_candidates.append((p, exp))
self.list_prime_candidates.sort()
def main():
start = time.perf_counter()
lim = 150000000
i = 10
somme = 0
while i <= lim:
s = i**2
if primes.is_prime_opti(s + 1) and primes.is_prime_opti(s + 3) and primes.is_prime_opti(s + 7) and \
primes.is_prime_opti(s + 9) and primes.is_prime_opti(s + 13) and primes.is_prime_opti(s + 27) and not \
primes.is_prime_opti(s + 11) and not primes.is_prime_opti(s + 17) and not primes.is_prime_opti(s + 21) \
and not primes.is_prime_opti(s + 23):
somme += i
i += 10
print(somme)
print('temps d\'exécution', time.perf_counter() - start, 'sec')
def main():
start = time.perf_counter()
lim = 150000000
i = 10
somme = 0
while i <= lim:
s = i ** 2
if primes.is_prime_opti(s + 1) and primes.is_prime_opti(s + 3) and primes.is_prime_opti(s + 7) and \
primes.is_prime_opti(s + 9) and primes.is_prime_opti(s + 13) and primes.is_prime_opti(s + 27) and not \
primes.is_prime_opti(s + 11) and not primes.is_prime_opti(s + 17) and not primes.is_prime_opti(s + 21) \
and not primes.is_prime_opti(s + 23):
somme += i
i += 10
print(somme)
print('temps d execution', time.perf_counter() - start, 'sec')
def main():
start = time.perf_counter()
n = 1
p = n**2 + (n + 1)**2
compteur = 0
while p < 5 * 10**15:
if primes.is_prime_opti(p):
compteur += 1
n += 1
p = n**2 + (n + 1)**2
print(compteur)
print('temps d\'exécution', time.perf_counter() - start, 'sec')
def main():
start = time.perf_counter()
ht = gen_trunc_harshad()
somme = 0
for u in ht:
if is_strong(u):
for k in [1, 3, 7, 9]:
temp1 = u*10+k
if primes.is_prime_opti(temp1):
somme += temp1
print(somme)
print('temps d execution', time.perf_counter() - start, 'sec')
def main():
start = time.perf_counter()
n = 1
p = n ** 2 + (n + 1) ** 2
compteur = 0
while p < 5 * 10 ** 15:
if primes.is_prime_opti(p):
compteur += 1
n += 1
p = n ** 2 + (n + 1) ** 2
print(compteur)
print("temps d execution", time.perf_counter() - start, "sec")
def main():
start = time.perf_counter()
ht = gen_trunc_harshad()
somme = 0
for u in ht:
if is_strong(u):
for k in [1, 3, 7, 9]:
temp1 = u*10+k
if primes.is_prime_opti(temp1):
somme += temp1
print(somme)
print('temps d\'exécution', time.perf_counter() - start, 'sec')
def main():
start = time.perf_counter()
compteur = 2
r = 0
while compteur < 2000:
r += 1
if primes.is_prime_opti(6*r+7) and primes.is_prime_opti(12*r+17) and primes.is_prime_opti(6*r+5):
compteur += 1
if primes.is_prime_opti(12*r+5) and primes.is_prime_opti(6*r+5) and primes.is_prime_opti(6*r+11):
compteur += 1
if compteur == 2001:
print(3*r**2+3*r+2)
elif primes.is_prime_opti(6*r+7) and primes.is_prime_opti(12*r+17) and primes.is_prime_opti(6*r+5):
print(3*r**2+3*r+2)
else:
print(3*r**2+9*r+7)
print('temps d execution', time.perf_counter() - start, 'sec')
def solve(m):
count = 1
for i in range(2, 10**7):
l = 1
n = 308 * i
b = sympy.divisors(n)
for j in b:
if primes.is_prime_opti(j + 1):
l *= j + 1
if l > 20010:
break
if l == 20010:
count += 1
if count == m:
return n
def solve(m):
count = 1
for i in range(2, 10**7):
l = 1
n = 308*i
b = sympy.divisors(n)
for j in b:
if primes.is_prime_opti(j+1):
l *= j+1
if l > 20010:
break
if l == 20010:
count += 1
if count == m:
return n
def init_list_candidates(self):
candidate = self.d-1
while candidate < self.n: # determines the primes such that d divides them
if primes.is_prime_opti(candidate):
self.list_primes_candidates.append((candidate, candidate, 1))
candidate += self.d
for p in self.list_primes:
candidate = p**2
exponent = 2
while candidate < self.n:
sigma = (candidate*p - 1)//(p - 1)
if sigma % self.d == 0:
self.list_primes_candidates.append((p**exponent, p, exponent))
candidate *= p
exponent += 1
self.list_primes_candidates = sorted(self.list_primes_candidates)
def main():
start = time.perf_counter()
compteur = 2
r = 0
while compteur < 2000:
r += 1
if primes.is_prime_opti(6 * r + 7) and primes.is_prime_opti(
12 * r + 17) and primes.is_prime_opti(6 * r + 5):
compteur += 1
if primes.is_prime_opti(12 * r + 5) and primes.is_prime_opti(
6 * r + 5) and primes.is_prime_opti(6 * r + 11):
compteur += 1
if compteur == 2001:
print(3 * r**2 + 3 * r + 2)
elif primes.is_prime_opti(6 * r + 7) and primes.is_prime_opti(
12 * r + 17) and primes.is_prime_opti(6 * r + 5):
print(3 * r**2 + 3 * r + 2)
else:
print(3 * r**2 + 9 * r + 7)
print('temps d\'exécution', time.perf_counter() - start, 'sec')
def s(self, n, d):
lim = n-1
i = lim
somme = 0
digits_available = self.digits.replace(str(d), '')
while not somme:
s_rep = ''
for j in range(i):
s_rep += str(d)
for j in itertools.combinations_with_replacement(digits_available, n-i):
js = self.format_perm(j)
number = js + s_rep
for k in set(itertools.permutations(number)):
ks = self.format_perm(k)
if ks[0] != '0' and primes.is_prime_opti(int(ks)):
somme += int(ks)
i -= 1
return somme
def s(self, n, d):
lim = n - 1
i = lim
somme = 0
digits_available = self.digits.replace(str(d), '')
while not somme:
s_rep = ''
for j in range(i):
s_rep += str(d)
for j in itertools.combinations_with_replacement(
digits_available, n - i):
js = self.format_perm(j)
number = js + s_rep
for k in set(itertools.permutations(number)):
ks = self.format_perm(k)
if ks[0] != '0' and primes.is_prime_opti(int(ks)):
somme += int(ks)
i -= 1
return somme
def is_strong(n):
return primes.is_prime_opti(n//sum_digits(n))
def get_res(self):
for i in range(2 * 10**9, 2 * 10**9 + 2000 + 1):
if primes.is_prime_opti(i):
print(i)
self.mod = i
self.res += self.S()
def main():
start = time.perf_counter()
p1 = primes.primes(500000)
p2 = []
for i in range(len(p1)):
if str(p1[i]).count('0') == 3 or str(p1[i]).count('1') == 3 or str(p1[i]).count('2') == 3:
p2.append(p1[i])
for j in range(len(p2)):
s = str(p2[j])
if s.count('0') == 3:
if s.rindex('0') != len(s):
a = s.replace('0', '1')
b = s.replace('0', '2')
c = s.replace('0', '3')
d = s.replace('0', '4')
e = s.replace('0', '5')
f = s.replace('0', '6')
g = s.replace('0', '7')
h = s.replace('0', '8')
i = s.replace('0', '9')
compt = 0
for k in [a, b, c, d, e, f, g, h, i]:
if primes.is_prime_opti(int(k)):
compt += 1
if compt == 7:
print(s)
break
if s.count('1') == 3:
if s.rindex('1') != len(s):
b = s.replace('1', '2')
c = s.replace('1', '3')
d = s.replace('1', '4')
e = s.replace('1', '5')
f = s.replace('1', '6')
g = s.replace('1', '7')
h = s.replace('1', '8')
i = s.replace('1', '9')
compt = 0
for k in [b, c, d, e, f, g, h, i]:
if primes.is_prime_opti(int(k)):
compt += 1
if compt == 7:
print(s)
break
if s.count('2') == 3:
if s.rindex('2') != len(s):
c = s.replace('2', '3')
d = s.replace('2', '4')
e = s.replace('2', '5')
f = s.replace('2', '6')
g = s.replace('2', '7')
h = s.replace('2', '8')
i = s.replace('2', '9')
compt = 0
for k in [c, d, e, f, g, h, i]:
if primes.is_prime_opti(int(k)):
compt += 1
if compt == 7:
print(s)
break
print('temps d\'exécution', time.perf_counter() - start, 'sec')
def test(one, two):
if primes.is_prime_opti(int(str(one)+str(two))) and primes.is_prime(int(str(two)+str(one))):
return True
return False
def fun_fortunate(n):
p = n + 3
while not primes.is_prime_opti(p):
p += 2
return p - n
def test(one, two):
if primes.is_prime_opti(int(str(one) + str(two))) and primes.is_prime(
int(str(two) + str(one))):
return True
return False
def is_strong(n):
return primes.is_prime_opti(n//sum_digits(n))
def fun_fortunate(n):
p = n + 3
while not primes.is_prime_opti(p):
p += 2
return p - n
def get_largest(self):
for i in self.candidates:
if primes.is_prime_opti(int(i)):
return i
def is_prime(self, n):
if n < 10**9:
return n in self.primes_table
else:
return primes.is_prime_opti(n)
def main():
start = time.perf_counter()
p1 = primes.primes(500000)
p2 = []
for i in range(len(p1)):
if str(p1[i]).count('0') == 3 or str(p1[i]).count('1') == 3 or str(p1[i]).count('2') == 3:
p2.append(p1[i])
for j in range(len(p2)):
s = str(p2[j])
if s.count('0') == 3:
if s.rindex('0') != len(s):
a = s.replace('0', '1')
b = s.replace('0', '2')
c = s.replace('0', '3')
d = s.replace('0', '4')
e = s.replace('0', '5')
f = s.replace('0', '6')
g = s.replace('0', '7')
h = s.replace('0', '8')
i = s.replace('0', '9')
compt = 0
for k in [a, b, c, d, e, f, g, h, i]:
if primes.is_prime_opti(int(k)):
compt += 1
if compt == 7:
print(s)
break
if s.count('1') == 3:
if s.rindex('1') != len(s):
b = s.replace('1', '2')
c = s.replace('1', '3')
d = s.replace('1', '4')
e = s.replace('1', '5')
f = s.replace('1', '6')
g = s.replace('1', '7')
h = s.replace('1', '8')
i = s.replace('1', '9')
compt = 0
for k in [b, c, d, e, f, g, h, i]:
if primes.is_prime_opti(int(k)):
compt += 1
if compt == 7:
print(s)
break
if s.count('2') == 3:
if s.rindex('2') != len(s):
c = s.replace('2', '3')
d = s.replace('2', '4')
e = s.replace('2', '5')
f = s.replace('2', '6')
g = s.replace('2', '7')
h = s.replace('2', '8')
i = s.replace('2', '9')
compt = 0
for k in [c, d, e, f, g, h, i]:
if primes.is_prime_opti(int(k)):
compt += 1
if compt == 7:
print(s)
break
print('temps d execution', time.perf_counter() - start, 'sec')
def get_largest(self):
for i in self.candidates:
if primes.is_prime_opti(int(i)):
return i
