def main():
global primeList
n = 10000
primeList = getPrimeList(n)
i = 2
while f(i, i-1) <= 5000:
i += 1
if i > primeList[-1]:
n *= 10
primeList = getPrimeList(n)
print i
def find(n, minimal, index):
p = getPrimeList(n)
length = len(p)
for a in range(index, length):
if minimal and p[a] > minimal/5:
return True, minimal, a
for b in range(a+1, length):
if not isConcatenatePrime(p[a], p[b]):
continue
for c in range(b+1, length):
if (not isConcatenatePrime(p[a], p[c])
or not isConcatenatePrime(p[b], p[c])):
continue
for d in range(c+1, length):
if (not isConcatenatePrime(p[a], p[d])
or not isConcatenatePrime(p[b], p[d])
or not isConcatenatePrime(p[c], p[d])):
continue
for e in range(d+1, length):
if (not isConcatenatePrime(p[a], p[e])
or not isConcatenatePrime(p[b], p[e])
or not isConcatenatePrime(p[c], p[e])
or not isConcatenatePrime(p[d], p[e])):
continue
if minimal and (p[a] + p[b] + p[c] + p[d] + p[e] >
minimal):
minimal = p[a] + p[b] + p[c] + p[d] + p[e]
break
return False, minimal, length
def main():
N = 50000000
primelist = getPrimeList(N ** 0.5)
square = []
cube = []
fourthpower = []
for p in primelist:
a = p*p
if a >= N:
break
square.append(a)
if a*p <= N:
cube.append(a*p)
if a*p*p <= N:
fourthpower.append(a*p*p)
count = []
for c in fourthpower:
for b in cube:
if c+b >= N:
break
for a in square:
if c+b+a >= N:
break
count.append(c+b+a)
print len(set(count))
def getPhi(n):
primelist = getPrimeList(n)
res = [i for i in range(2, n+1)]
for i in range(len(primelist)):
l = primelist[i]
m = l
while l <= n:
res[l-2] *= (m-1)
res[l-2] /= m
l += m
return res
def f(n):
primeList = getPrimeList(n)
subPrimeList = []
length = 1
tmpList = []
for i in primeList:
if len(str(i)) == length:
tmpList.append(i)
else:
length += 1
subPrimeList.append(tmpList)
tmpList = [i]
else:
subPrimeList.append(tmpList)
for subIndex in range(len(subPrimeList)):
primeList = subPrimeList[subIndex]
while len(primeList) >= 8:
i = primeList[0]
primeList.remove(i)
strNum = str(i)
for j in range(3):
stro = str(j)
tmpList = strNum.split(stro)
length = len(tmpList)
if length == 1:
continue
for ii in range(2**(length-1)-1):
count = 1
count2 = 0
for k in range(j+1, 10):
strr = str(k)
rstr = ""
for jj in range(length-1):
if ((ii>>jj)&1) == 1:
rstr += tmpList[jj]+stro
else:
rstr += tmpList[jj]+strr
rnum = int(rstr + tmpList[-1])
if rnum not in primeList:
count2 += 1
else:
count += 1
if 10-8-j < count2:
break
if count == 8:
print i
return True
return False
def main():
t = getPrimeList(1000000)
totallen = len(t)
length = 0
for i in range(totallen):
if i+length >= totallen:
break
Sum = sum(t[i:i+length])
for j in range(i+length, totallen):
Sum += t[j]
if Sum > 1000000:
break
if j-i+1 > length and isPrime(Sum):
length = j-i+1
Max = Sum
print Max