def solve(n=100, verbose=False):
result = 0
pfound = 0
results = []
i = 8
while pfound < 11:
if is_prime(i): # and ['4','6','8','0'] not in str(i):
if verbose:
print 'checking prime ', i
s = str(i)
relevance = 1
for j in xrange(len(s)):
num = s[j:]
if verbose:
print '\t truncating from left, now checking ', num
if not is_prime(int(num)):
relevance = 0
break
num = s[:j + 1]
if verbose:
print '\t truncating from right, now checking ', num
if not is_prime(int(num)):
relevance = 0
break
#j = j + 1
if relevance:
if verbose:
print 'found it: ', i
results.append(i)
pfound = pfound + 1
i = i + 1
result = sum(results)
return result
def greatest_pandigital():
#Note: Nine numbers cannot be done
#(1+2+3+4+5+6+7+8+9=45 => always dividable by 3)
#Note: Eight numbers cannot be done
#(1+2+3+4+5+6+7+8=36 => always dividable by 3)
for n in range(1, 8)[::-1]:
s = ''.join([str(a) for a in range(1, n + 1)[::-1]])
if verbose:
print 'checking %i pandigital numbers: ' % n, s
for e in permutations(s):
e = ''.join(e)
if verbose:
print e
if is_prime(int(e)):
return e
def check_sums_for_prime():
result = 0
l = 0
for (prim, i) in zip(__primes[:20], range(20)):
s = 0
j = i
while s + __primes[j] < n:
s += __primes[j]
if is_prime(s):
if j - i > l:
l = j - i
result = s
if args.verbose:
print prim, result, s, l, j - i
j = j + 1
return result
def solve(n=1000000, verbose=False):
results = []
for num in sieve(n):
if num not in results:
if verbose:
print "checking prime %i for circularity ..." % num
relevant = True
for rotated_prime in all_rotations(str(num)):
if not is_prime(int(rotated_prime)):
relevant = False
if relevant:
if verbose:
print " ... it is circular!"
print rotations
results += [int(e) for e in all_rotations(str(num))]
result = len(np.unique(results))
return result
def solve(n=4, verbose=True):
result = 0
i = 0
count = n
while not result:
i += 1
if not is_prime(i):
if len(set(factors2(i))) == n:
count -= 1
else:
count = n
else:
count = n
if not count:
result = i - n
if verbose:
print i, count
return result
def solve(verbose=True):
"""
Find the smallest odd composite number that cannot be written
as the sum of a prime and a two times a square.
"""
upperLimit = 100000
result = 1
for num in xrange(2, upperLimit):
if not is_prime(num) and num % 2:
result = 0
for e in sieve(num):
for f in xrange(int(np.ceil(np.sqrt((num - e) / 2)) + 1)):
if verbose:
print num, e, f, result
result += num == e + 2 * f**2
if not result:
result = num
break
return result
if True:
target = 10001
from Primes import is_prime
i, answer = 0, 1
while(i < target):
answer += 1
if is_prime(answer):
i += 1
print(answer)
raw_input("Press ENTER")
if True:
target = 600851475143
from Primes import is_prime, low_prime
while True:
if is_prime(target):
answer = target
break
target //= low_prime(target)
print(answer)
raw_input('Press ENTER')