def primePermute(num):
permute=[int(''.join(i)) for i in list(permutations(str(num)))]
answer=[]
for i in permute:
if i not in answer and isprime(i) and i>1000:
answer.append(i)
return sorted(answer)
def checkFamily(fixedRoot, insertions, digits):
family = []
insert = 0
for i in range(len(insertions)):
if insertions[i] == 1:
insert += 10**i
fixedRoot += 9 * 10**i * int(fixedRoot / (10**i))
for n in range(10):
family.append(fixedRoot + insert * n)
familyPrimes = [i for i in family if isprime(i) and i > 10**(digits - 1)]
if len(familyPrimes) >= 8:
return min(familyPrimes)
return 0
def largestPandigitPrime():
primes = []
for n in range(9, 0, -1):
pandigits = list(permutations([i for i in range(1, n + 1)]))
pandigits = [
int(''.join([str(j) for j in pandigits[i]]))
for i in range(len(pandigits))
]
for p in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]:
pandigits = [i for i in pandigits if i % p != 0]
pandigits.sort(reverse=True)
for i in range(len(pandigits)):
if isprime(pandigits[i]):
return pandigits[i]
return 0
def Problem_35():
def number_rotator(number):
number = deque(number)
number.rotate(-1)
return(''.join(number))
list_of_normal_primes, circular_primes = list_substractor(sieveErato(1000000), sieveErato(10)), {2,3,5,7}
for normal_prime in list_of_normal_primes:
check_num, circular_prime_checker = str(normal_prime), 0
for x in range(len(check_num)-1):
check_num = number_rotator(check_num)
if isprime(int(check_num)):
circular_prime_checker += 1
continue
break
if circular_prime_checker == len(str(normal_prime))-1:
circular_primes.add(normal_prime)
print(len(circular_primes))
from itertools import permutations
from myFunctions import isprime
def primePermute(num):
permute=[int(''.join(i)) for i in list(permutations(str(num)))]
answer=[]
for i in permute:
if i not in answer and isprime(i) and i>1000:
answer.append(i)
return sorted(answer)
def threeChain(listNums):
for i in range(len(listNums)):
for j in range(i+1,len(listNums)):
if (2*listNums[j]-listNums[i]) in listNums:
print str(listNums[i])+str(listNums[j])+str(2*listNums[j]-listNums[i])
return True
return False
candidates=[]
for a in range(10):
for b in range(10):
for c in range(10):
for d in range(1,min(a,b,c)+1):
num=d*1000+c*100+b*10+a
if isprime(num):
if threeChain(primePermute(num)):
candidates.append(num)
# Doesn't return in the exact form, but the answer's there.
def p(A, B):
if isprime(int(str(A) + str(B))) and isprime(int(str(B) + str(A))):
return True
return False
# No need to check lower right corners.
from myFunctions import isprime
primes = 3
layers = 2
while 1.0 * primes / (4 * layers - 3) > .1:
if isprime((2 * layers - 1)**2 + (2 * layers)):
primes += 1
if isprime((2 * layers - 1)**2 + 2 * (2 * layers)):
primes += 1
if isprime((2 * layers - 1)**2 + 3 * (2 * layers)):
primes += 1
layers += 1
print 2 * layers - 1
from myFunctions import primes, isprime
prime = primes(10000)
sum = 0
maxLength = 0
while sum <= 10**6:
sum += prime[maxLength]
maxLength += 1
found = False
for runLength in range(maxLength - 1, 0, -1):
for i in range(maxLength - runLength):
sum = 0
for j in range(i, i + runLength):
sum += prime[j]
if isprime(sum):
print sum
found = True
break
if found:
break