"""
Prime generating integers
https://projecteuler.net/problem=357
"""
from eulerlib import Crible
crible = Crible(100000000)
def diviseurs(n):
d = 1
while d * d <= n:
q, r = divmod(n, d)
if r == 0:
if not crible.est_premier(d + q):
return False
d += 1
return True
assert diviseurs(30)
sum = 1 # pour n=1
for n in range(2, 100000000, 2):
if diviseurs(n):
sum += n
print(n)
print(sum)
"""
Totient permutation
https://projecteuler.net/problem=70
"""
from eulerlib import Crible
crible = Crible(10000000)
phi = crible.EulerPhi()
def est_permutation(a, b):
chiffres = [0] * 10
while a != 0:
a, r = divmod(a, 10)
chiffres[r] += 1
while b != 0:
b, r = divmod(b, 10)
chiffres[r] -= 1
return all(c == 0 for c in chiffres)
rmin, nmin = 10, 0
for n in range(2, 10000000):
p = phi[n]
r = n / p
if r < rmin:
if est_permutation(n, p):
rmin, nmin = r, n
print(nmin)
The number 3797 has an interesting property. Being prime itself, it is possible to continuously
remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly
we can work from right to left: 3797, 379, 37, and 3.
Find the sum of the only eleven primes that are both truncatable from left to right and right to
left.
NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
https://projecteuler.net/problem=37
"""
from eulerlib import Crible
crible = Crible(1000000)
nb = 0
somme = 0
for p in crible.liste():
if p < 10:
continue
ko = False
gauche = p
droite = 0
i = 0
while gauche >= 10 and not ko:
"""
Quadratic primes
https://projecteuler.net/problem=27
"""
from eulerlib import Crible
crible = Crible(1000)
premiers = crible.liste()
premiers.extend([-i for i in premiers])
solution = 0
n_max, a_max, b_max = 0, 0, 0
for b in premiers:
for a in range(-999, 1000):
for n in range(0, 1000):
p = n * n + a * n + b
if not crible.est_premier(p):
if n > n_max:
# print("nouveau max", n, a, b)
n_max, a_max, b_max = n, a, b
break
print(a_max * b_max)
print("n²{:+d}n{:+d} ⇒ {} premiers".format(a_max, b_max, n_max))
The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330,
is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the
4-digit numbers are permutations of one another.
There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting
this property, but there is one other 4-digit increasing sequence.
What 12-digit number do you form by concatenating the three terms in this sequence?
https://projecteuler.net/problem=49
"""
from eulerlib import Crible
crible = Crible(10000)
premiers = crible.liste()
premiers = [i for i in premiers if i >= 1000]
nb = len(premiers)
for i in range(nb - 2):
p1 = premiers[i]
# exclut la solution de l'énoncé
if p1 == 1487:
continue
for j in range(i + 1, nb - 1):
p2 = premiers[j]
p3 = p2 + (p2 - p1)
""" Summation of primes The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. https://projecteuler.net/problem=10 """ from eulerlib import Crible MAX = 2000000 # solution avec crible crible = Crible(MAX) print(sum(crible.liste()))
"""
from eulerlib import Crible
def rotation(n):
nombres = []
chiffres = 0
q = n
while q != 0:
q //= 10
chiffres += 1
decalage = 10**(chiffres - 1)
for _ in range(chiffres):
n, r = divmod(n, 10)
n += r * decalage
nombres.append(n)
return nombres
crible = Crible(1000000)
resultat = 0
for i in crible.liste():
if all([crible.est_premier(j) for j in rotation(i)]):
resultat += 1
print(resultat)