# Problem link: http://projecteuler.net/index.php?section=problems&id=35
# use dictionary and prime generator
from myMath import genPrime
def getDigits(n):
L = []
while n != 0:
L.append(n % 10)
n /= 10
return L
n = 1000000
L = genPrime(n);
D = {}
for prime in L:
D[prime] = True
res = 0
for prime in L:
ok = True
digits = getDigits(prime)
num = len(digits)
for i in range(0, num):
value = 0
for j in range(i, i - num, -1):
value = value * 10 + digits[j]
if not D.has_key(value):
ok = False
break
if ok:
res += 1
# Problem link: http://projecteuler.net/index.php?section=problems&id=50
from myMath import genPrime
n = 1000000
primeList = genPrime(n)
D = {}
for prime in primeList:
D[prime] = True
num = len(primeList)
summ = [0] * num
for i in range(0, num):
summ[i] = primeList[i]
if i != 0:
summ[i] += summ[i - 1]
resCnt = 0
resValue = 0
for i in range(0, num - resCnt):
if primeList[i] * resCnt > n:
break
for j in range(i + resCnt, num):
if i == 0:
value = summ[j]
else:
value = summ[j] - summ[i - 1]
if value >= n:
break
cnt = j - i + 1
if D.has_key(value) and cnt > resCnt:
resCnt = cnt
resValue = value
# Problem link: http://projecteuler.net/index.php?section=problems&id=10
from myMath import genPrime
primes = genPrime(2000000)
summ = 0
for k in primes:
summ += k
print summ
if isPrime(num):
return num
else:
return 0
for k in range(n, 0, -1):
if not used[k]:
digits[kth] = k
used[k] = True
res = dfs(kth + 1, n, used, digits)
if res != 0:
return res
used[k] = False
return 0
def findPandigitalPrime(n):
used = [False] * (n + 1)
digits = [0] * n
return dfs(0, n, used, digits)
m = 40000
primes = genPrime(m)
n = 9
res = 0
while True:
res = findPandigitalPrime(n)
if res != 0:
break
n -= 1
print res
# Problem link: http://projecteuler.net/index.php?section=problems&id=37
from myMath import genPrime
n = 1000000
primes = genPrime(n)
D = {}
for prime in primes:
D[prime] = True
res = 0
for prime in primes:
if prime < 10:
continue
ok = True
mod = 10
while True:
if mod > prime:
break
if not D.has_key(prime % mod) or not D.has_key(prime / mod):
ok = False
break
mod *= 10
if ok:
res += prime
print res
# Problem link: http://projecteuler.net/index.php?section=problems&id=12
from myMath import genPrime
prime = genPrime(10000)
def divisorNumber(n):
res = 1
for p in prime:
if p * p > n:
break
k = 0
while n % p == 0:
k = k + 1
n = n / p
res = res * (k + 1)
if n != 1:
res = res * 2
return res
res = 0
n = 1
while True:
res = res + n
n = n + 1
if divisorNumber(res) >= 500:
break
print res