def is_truncatable_prime(n):
if n in ["2", "3", "5", "7"]: return False
l = len(n)
for i in range(0, l):
m = int(n[i:])
if not lib.is_prime(m): return False
m = int(n[0:l-i])
if not lib.is_prime(m): return False
return True
def ok(a, b):
x = lib.concat(a, b)
if x < N:
if not sieve[x]:
return False
elif not lib.is_prime(x):
return False
y = lib.concat(b, a)
if y < N:
if not sieve[y]:
return False
elif not lib.is_prime(y):
return False
return True
def count_quandratic_primes(a, b):
count = 0
n = 0
while n == count:
count += int(is_prime(n ** 2 + a * n + b))
n += 1
return count
def get_prime_n(n):
count = 0
num = 1
while count != n:
num += 1
if (is_prime(num)):
count += 1
return num
def euler_27(max_a, max_b):
a = range(-max_a, max_a + 1)
#n = 0 means that the equation simplifies to b, so b must be prime.
b = filter(lambda x: lib.is_prime(abs(x)), range(-max_b, max_b + 1))
vars = filter(a_filter, itertools.product(a, b))
solution = max((consec_primes_for_eq(*var), var) for var in vars)[1]
return operator.mul(*solution)
def euler_46():
r = itertools.count(3, 2)
composite_odd = filter(lambda x: not lib.is_prime(x), r)
for n in composite_odd:
squares = itertools.takewhile(lambda x: x < n,
(2 * (i ** 2) for i in itertools.count()))
if not any(map(lib.is_prime, (n - s for s in squares))):
return n
def prime_factorization(n):
primes = []
candidates = xrange(2, n + 1)
candidate = 2
while not primes and candidate in candidates:
if n % candidate == 0 and lib.is_prime(candidate):
primes = primes + [candidate] + prime_factorization(n / candidate)
candidate += 1
return primes
def prime_factorization(n):
primes = []
candidates = xrange(2, n+1)
candidate = 2
while not primes and candidate in candidates:
if n%candidate == 0 and lib.is_prime(candidate):
primes = primes + [candidate] + prime_factorization(n/candidate)
candidate += 1
return primes
def main():
pandigital_length = 9
while pandigital_length > 1:
pandigitals = generate_pandigitals(pandigital_length)
pandigitals.sort(reverse=True)
for pandigital in pandigitals:
if lib.is_prime(pandigital):
print(pandigital)
pandigital_length = 0
break
pandigital_length -= 1
return 0
def is_prime_cached(n, primes):
"""
Checks if a number is prime. Caches primes found in primes
:param n: the number to check
:param primes: list of known primes
:return: True if prime, False otherwise
"""
if n in primes:
return True
if lib.is_prime(n):
primes.add(n)
return True
return False
def main():
circular_primes = [2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97]
for i in range(101, 1000000, 2):
n = i
digit_count = 0
while n > 0:
if n % 5 == 0 or n % 2 == 0:
digit_count = -1
break
n //= 10
digit_count += 1
if digit_count == -1 or i in circular_primes or not is_prime(i):
continue
rotated_primes = [i]
n = (i % 10 * 10 ** (digit_count - 1)) + (i // 10)
while n != i:
if not is_prime(n):
break
rotated_primes.append(n)
n = (n % 10 * 10 ** (digit_count - 1)) + (n // 10)
else:
circular_primes += rotated_primes
print(len(circular_primes))
fig, axs = plt.subplots(2, 2, figsize=(20.0/2.54, 20.0/2.54))
ax1, ax2, ax3, ax4 = axs.flat
print('Mean Error Real FFT (Non-Primes)')
i = 0
markers = ['>', '<', '+', 'x', '^']
styles = ['--', ':', '-.', '--', ':']
for k in sorted(results.keys()):
v = results[k]
kwargs = dict(label=k, marker=markers[i], ls=styles[i])
n = np.array(v['sizes'][:], dtype=np.int)
# the values which are a power of two
f = (n != 0) & ((n & (n - 1)) == 0)
# the primes
fp = lib.is_prime(n)
# the non-power of two, non-primes -> regular (or Hamming) numbers
f2 = ~(f | fp)
lc1, = ax1.plot(n[f], v['real_l2'][f], **kwargs)
lc2, = ax2.plot(n[f2], v['real_l2'][f2], **kwargs)
lc3, = ax3.plot(n[fp], v['real_linf'][fp], **kwargs)
lc4, = ax4.plot(v['identity_sizes'], v['real_identity'], **kwargs)
i += 1
# ignore prime sizes as the error grows strongly with N
print(k.ljust(20), np.mean(v['real_l2'][~fp]))
ax1.set_title('Power of Two')
ax2.set_title('Regular Numbers')
ax3.set_title('Primes')
ax4.set_title('Identity Error')
def test2(self):
self.assertTrue(lib.is_prime(3))
def test11(self):
self.assertFalse(lib.is_prime(6))
def test13(self):
self.assertFalse(lib.is_prime(9))
def test7(self):
self.assertTrue(lib.is_prime(17))
def test9(self):
self.assertTrue(lib.is_prime(23))
def test7(self):
self.assertTrue(lib.is_prime(17))
for consecutive values of n, starting with n = 0
"""
from lib import is_prime
def count_quandratic_primes(a, b):
count = 0
n = 0
while n == count:
count += int(is_prime(n ** 2 + a * n + b))
n += 1
return count
max_n = 0
max_i = 0
max_j = 0
for i in range(-999, 1000):
if not is_prime(abs(i)):
continue
for j in reversed(range(-999, 1000)):
if not is_prime(abs(j)):
continue
n_count = count_quandratic_primes(i, j)
if max_n < n_count:
max_n = n_count
max_i = i
max_j = j
print(max_i * max_j)
def test9(self):
self.assertTrue(lib.is_prime(23))
def test8(self):
self.assertTrue(lib.is_prime(19))
def test15(self):
self.assertFalse(lib.is_prime(100))
def test13(self):
self.assertFalse(lib.is_prime(9))
def test12(self):
self.assertFalse(lib.is_prime(8))
import lib
lib._prime_limit = 10000
for x in range(1001, 10000, 2):
if not lib.is_prime(x):
continue
inc_limit = ((10000 - x) / 2)
for inc in range(10, inc_limit, 2):
seq = x + inc, x + inc + inc
if lib.is_prime(seq[0]) and lib.is_prime(seq[1]):
s1 = sorted(str(x))
if s1 == sorted(str(seq[0])) and s1 == sorted(str(seq[1])):
print "%d%d%d" % (x, x+inc, x+inc+inc)
""" The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. """ from lib import is_prime limit = 2000000 primesum = 0 for i in range(1, limit+1): if(is_prime(i)): primesum += i print(primesum)
import lib
sum = 2
below = 2000000
for i in range(3, below, 2):
if lib.is_prime(i):
sum += i
print(sum)
def test6(self):
self.assertTrue(lib.is_prime(13))
def test11(self):
self.assertFalse(lib.is_prime(6))
def test5(self):
self.assertTrue(lib.is_prime(11))
def test8(self):
self.assertTrue(lib.is_prime(19))
def test4(self):
self.assertTrue(lib.is_prime(7))
def test10(self):
self.assertFalse(lib.is_prime(4))
import lib
lim = 1000000
primes = list(lib.get_primes(lim))
max_prime = (0, 0, 0)
for idx, start in enumerate(primes):
total = start
for num, p in enumerate(primes[idx+1:]):
if total >= lim:
break
if lib.is_prime(total):
max_prime = max(max_prime, (num + 1, total, start))
total += p
print max_prime
def test12(self):
self.assertFalse(lib.is_prime(8))
def consecutive_prime(a, b):
n, length = 0, 0
while (n * n + a * n + b) > 1 and is_prime(n * n + a * n + b):
n += 1
length += 1
return length
def test15(self):
self.assertFalse(lib.is_prime(100))
def test3(self):
self.assertTrue(lib.is_prime(5))
def num_euler(a, b):
for n in itertools.count():
if not lib.is_prime(n*n + a*n + b):
return n
def test3(self):
self.assertTrue(lib.is_prime(5))
def test1(self):
self.assertTrue(lib.is_prime(2))
def test4(self):
self.assertTrue(lib.is_prime(7))
def circular_filter(n):
return all((lib.is_prime(x) for x in rotate_gen(n)))
def test5(self):
self.assertTrue(lib.is_prime(11))
"""
Largest prime factor
Problem 3
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143 ?
"""
from math import sqrt, ceil
from lib import is_prime, iterate_odd
number = 600851475143
limit = ceil(sqrt(number))
pf = []
for n in range(3, limit):
if number % n == 0 and is_prime(n):
pf.append(n)
print(max(pf))
def test6(self):
self.assertTrue(lib.is_prime(13))
def test1(self):
self.assertTrue(lib.is_prime(2))
def test10(self):
self.assertFalse(lib.is_prime(4))
"""
Summation of primes
Problem 10
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
Find the sum of all the primes below two million.
"""
from lib import is_prime
p = [2]
p_sum = 2
max_n = 2000000
for n in range(3, max_n, 2):
if is_prime(n):
p.append(n)
p_sum += n
print(p_sum)
def test2(self):
self.assertTrue(lib.is_prime(3))