def problem35(n):
"""
>>> problem35(1000000)
55
"""
primes = [2, 3]
prime.primesBelow_fast(50, primes)
prime.primesBelow_fast(100000, primes)
prime.primesBelow_fast(n, primes)
primes = [str(p) for p in primes]
#to make it fast comment out above lines
#uncomment below line
#primes = prime.get_primes_from_file()
evens = ['0', '2', '4', '6', '8']
required_primes = filter(lambda s: not set(s).intersection(evens), primes)
result = 1
for num in required_primes:
value = lib.rotation(list(num), required_primes)
result = result + value
return result
def problem37(n):
"""
>>> problem37(1000000)
748317
"""
primes_below_bilion = [2, 3]
prime.primesBelow_fast(50, primes_below_bilion)
prime.primesBelow_fast(100000, primes_below_bilion)
prime.primesBelow_fast(n, primes_below_bilion)
primes = {}
for p in primes_below_bilion:
primes.setdefault(len(str(p)), []).append(str(p))
#to make it fast comment out above lines
#uncomment below line
#primes = prime.get_primes_dict_from_file()
result = []
for L in primes.values():
call_is_truncatable_prime = lambda n: lib.is_truncatable_prime(n, primes)
result.extend(filter(call_is_truncatable_prime, L))
return sum(map(lambda x: int(x), result))
def problem50():
primesList = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]
prime.primesBelow_fast(1000000, primesList)
primesDict = dict.fromkeys(primesList)
resultDict = {}
length, count, limit = len(primesList), 1, primesList[-1]
currentList = primesList[:]
diffList = [0]*length
while length:
result = [x+y-z for x,y,z in zip(currentList[:-1],currentList[1:], diffList) if x+y-z<limit]
length, count = len(result), count+1
diffList, currentList = currentList[1:length], result[:]
if count%2:
resultDict[count] = [n for n in result[1:] if primesDict.has_key(n)]
else:
n = result and result[0] or 0
resultDict[count] = primesDict.has_key(n) and [n] or []
R = filter(lambda x: resultDict[x], resultDict.keys())
R.sort()
return R[-1], resultDict[R[-1]]
def problem27():
"""http://projecteuler.net/index.php?section=problems&id=27
>>> problem27()
-59231
"""
max_pair = (0,0,0)
primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]
for a in xrange(-999, 1000):
for b in xrange(max(2, 1-a), 1000): # b >= 2, a + b + 1 >= 2
n, count = 0, 0
while True:
v = n*n + a*n + b
v = v <=0 and -v or v
if v > primes[-1]:
prime.primesBelow_fast(v, primes)
if prime.isprime_fast(v, primes): count = count + 1
else: break
else:
if not prime.hasFactors(v, primes): count = count + 1
else: break
n = n + 1
if count > max_pair[2]:
max_pair = (a,b,count)
return max_pair[0] * max_pair[1]
import prime
primes = [2,3,5,7,11,13,17,19,23,29]
prime.primesBelow_fast(int(1000**0.5+1), primes)
def problem47():
n, count = 6882, 0#2*3*31*37
while count != 4:
primeFactors = prime.primeFactors(n, primes)
if len(primeFactors)==4:
count = count+1
else:
count=0
n=n+1
return n-4
print problem47()
import prime
primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]
prime.primesBelow_fast(103, primes)
def problem49():
choice = xrange(1489, 3340, 2)
for n in choice:
if not prime.hasFactors(n, primes):
m1, strn = n+3330, str(n)
strm1, setn = str(m1), set(strn)
if set(strm1)==setn and not prime.hasFactors(m1, primes):
m2 = m1+3330
if set(str(m2))==setn and not prime.hasFactors(m2, primes):
return strn+strm1+str(m2)
print problem49()
import prime
primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]
squares = dict.fromkeys((x*x for x in xrange(1, 10000)), 1)
prime.primesBelow_fast(10000, primes)
for x in xrange(35, 10000, 2):
if not prime.isprime(x):
is_goldbach = 0
for p in primes[1:]:
if p >= x: break
if squares.has_key((x - p)/2):
is_goldbach = 1
break
if not is_goldbach:
print x
break