def smallest_multiple(n):
primes = get_primes(n);
result = 1
for i in primes:
temp = i
while temp <= n:
result *= i
temp *= i
return result
def smallest_multiple(n):
primes = get_primes(n)
result = 1
for i in primes:
temp = i
while temp <= n:
result *= i
temp *= i
return result
def find_solution(n, start=1):
primes = get_primes(10**n)
prime_set = set(primes)
for i in primes:
if i <= start:
continue
for j in range(1, int(10**(n - 1) * 9 / 2)):
if i + j > 10 ** n or i + 2 * j > 10 ** n or i + j not in prime_set or i + 2 * j not in prime_set or \
origin_sequence(i) != origin_sequence(i + j) or origin_sequence(i) != origin_sequence(i + 2 * j):
continue
return str(i) + str(i + j) + str(i + 2 * j)
return 0
def find_solution(n, start=1):
primes = get_primes(10 ** n)
prime_set = set(primes)
for i in primes:
if i <= start:
continue
for j in range(1, int(10 ** (n - 1) * 9 / 2)):
if i + j > 10 ** n or i + 2 * j > 10 ** n or i + j not in prime_set or i + 2 * j not in prime_set or \
origin_sequence(i) != origin_sequence(i + j) or origin_sequence(i) != origin_sequence(i + 2 * j):
continue
return str(i) + str(i + j) + str(i + 2 * j)
return 0
flag = False
break
if flag:
present.append(primes[i])
result = _solution(primes, i + 1, present, k)
if result:
return result
present.pop()
def solution(primes, k):
for i in range(0, len(primes)):
present = [primes[i]]
result = _solution(primes, i + 1, present, k)
if result:
return result
present.pop()
if __name__ == "__main__":
n = 10000
primes = get_primes(n)
assert solution(primes, 4) == [3, 7, 109, 673]
result = solution(primes, 5)
print(result, sum(result))
from common import is_pandigital, get_primes
if __name__ == "__main__":
"""8位和9位的数能被3整除，所以直接找从7位的开始找, 7位的直接从7开头的开始找"""
n = 10**6 * 8
PRIMES = set(get_primes(n))
while True:
if n in PRIMES and is_pandigital(n, 7):
break
n -= 1
print(n)
from common import get_primes
n = 10 ** 5
COINS = get_primes(n)
summation = {}
def prime_summation(n):
return _prime_summation(n, n)
def _prime_summation(n, maximum):
key = '{}-{}'.format(n, maximum)
if key in summation:
return summation[key]
if n < 0:
return 0
if n == 0:
return 1
value = sum(_prime_summation(n - i, i) for i in COINS if i <= maximum)
summation[key] = value
return value
if __name__ == "__main__":
assert prime_summation(10) == 5
for i in range(1, n):
if prime_summation(i) >= 5000:
print(i)
break
#coding:utf-8 ''' Created on 2016年1月3日 @author: robinjia @email: [email protected] ''' from common import get_primes if __name__ == "__main__": print(sum(get_primes(2000000)))
from common import prime_factor, get_primes
PRIMES = set(get_primes(10 ** 8))
def find_smallest(t):
i = 1
while True:
if i in PRIMES:
i += 1
continue
flag = True
for j in range(0, t):
if i + j in PRIMES or len(prime_factor(i + j)) != t:
flag = False
break
if flag:
return i
i += 1
if __name__ == "__main__":
assert find_smallest(2) == 14
assert find_smallest(3) == 644
print(find_smallest(4))
from common import get_primes
MAXIMUM = 1000000
PRIMES = set(get_primes(MAXIMUM))
def is_circular_prime(n):
for i in range(0, len(str(n))):
if int(str(n)[i:n] + str(n)[0:i]) not in PRIMES:
return False
return True
if __name__ == "__main__":
assert is_circular_prime(719) == True
n = 1000000
print(len([i for i in range(1, n) if is_circular_prime(i)]))
from common import get_primes
PRIMES = set(get_primes(10000000))
def quadratic_prime(a, b):
i = 0
while True:
s = i**2 + a * i + b
if s not in PRIMES:
return i
i += 1
if __name__ == "__main__":
n = 1000
a = 0
b = 0
maximum = 0
for i in range(-n + 1, n):
for j in range(-n, n + 1):
print(i, j)
temp = quadratic_prime(i, j)
if temp > maximum:
maximum = temp
a = i
b = j
print(a, b, a * b)
from common import get_primes
PRIMES = set(get_primes(10000000))
def quadratic_prime(a, b):
i = 0
while True:
s = i ** 2 + a * i + b
if s not in PRIMES:
return i
i += 1
if __name__ == "__main__":
n = 1000
a = 0
b = 0
maximum = 0
for i in range(-n + 1, n):
for j in range(-n, n + 1):
print(i, j)
temp = quadratic_prime(i, j)
if temp > maximum:
maximum = temp
a = i
b = j
print(a, b, a * b)
from common import get_primes
n = 10**7
primes = set(get_primes(n))
def truncatable_prime(n):
n = str(n)
for i in range(1, len(n)):
if int(n[0:i]) not in primes:
return False
if int(n[-i:]) not in primes:
return False
return int(n) in primes
if __name__ == "__main__":
assert truncatable_prime(3797) == True
s = [i for i in range(10, n) if truncatable_prime(i)]
print(s, sum(s))
from common import get_primes
MAXIMUM = 1000000
PRIMES = set(get_primes(MAXIMUM))
def is_circular_prime(n):
for i in range(0, len(str(n))):
if int(str(n)[i:n] + str(n)[0:i]) not in PRIMES:
return False
return True
if __name__ == "__main__":
assert is_circular_prime(719) == True
n = 1000000
print(len([i for i in range(1, n) if is_circular_prime(i)]))
from common import get_primes
if __name__ == "__main__":
n = 1000000
primes = get_primes(n)
p = 1
for i in primes:
if p * i > n:
break
p = p * i
print(p)
from common import is_pandigital, get_primes
if __name__ == "__main__":
"""8位和9位的数能被3整除，所以直接找从7位的开始找, 7位的直接从7开头的开始找"""
n = 10 ** 6 * 8
PRIMES = set(get_primes(n))
while True:
if n in PRIMES and is_pandigital(n, 7):
break
n -= 1
print(n)