def nines(d):
primes = []
for exp in range(10):
powers = [x for x in range(10)]
powers.remove(exp)
base_digits = sum([d * 10**i for i in powers])
for i in range(10):
if exp == 9 and i == 0: continue
candidate = base_digits + i * 10**exp
if isPrime(candidate):
primes.append(candidate)
return primes
def eights(d):
primes = []
replacement_exponents = [x for x in combinations(range(10), 2)]
for (a, b) in replacement_exponents:
powers = [x for x in range(10)]
powers.remove(a)
powers.remove(b)
base_digits = sum([d * 10**i for i in powers])
for i in range(10):
for j in range(10):
if b == 9 and j == 0: continue
candidate = base_digits + i * 10**a + j * 10**b
if isPrime(candidate):
primes.append(candidate)
return primes
def sum_digits(n):
r = 0
while n:
r, n = r + n % 10, n / 10
return r
s = 0
#prime_lookup = defaultdict(bool)
xList = [1, 2, 4, 6, 8]
iterCount = 0
while iterCount < 12:
newList = []
for n in xList:
for i in range(10):
x = n * 10 + i
if x % sum_digits(x) == 0: newList.append(x)
for n in newList:
for i in [1, 3, 7, 9]:
x = n * 10 + i
if int(str(n)[0]) != 1 and isPrime(
n / sum_digits(n)) and isPrime(x):
s += x
print x
xList = newList[:]
iterCount += 1
from numtheory import isPrime
import time
t = time.clock()
a, b, c = {}, {}, {}
a[0], b[0] = 2, 19
hits = [1, 2, 19]
n = 1
while len(hits) < 2000:
a[n] = 6 * n + a[n - 1]
if isPrime(6 * (n) + 5) and isPrime(6 * (n) + 7) and isPrime(12 *
(n) + 17):
hits.append(a[n])
b[n] = 6 * (n + 2) + b[n - 1]
if isPrime(6 * (n) + 11) and isPrime(6 * (n) + 17) and isPrime(12 *
(n) + 17):
hits.append(b[n])
n += 1
print hits[-1]
print time.clock() - t, "seconds"
for (a, b) in replacement_exponents:
powers = [x for x in range(10)]
powers.remove(a)
powers.remove(b)
base_digits = sum([d * 10**i for i in powers])
for i in range(10):
for j in range(10):
if b == 9 and j == 0: continue
candidate = base_digits + i * 10**a + j * 10**b
if isPrime(candidate):
primes.append(candidate)
return primes
s = 0
for i in range(1, 10):
for j in [1, 3, 7, 9]:
candidate = i * 10**9 + j
if isPrime(candidate):
s += candidate
for d in range(1, 10):
nine_list = nines(d)
print nine_list
s += sum(nine_list)
if len(nine_list) == 0:
s += sum(eights(d))
print s