def main():
# for all prime**4ths
# for all primes**3s
# if there's a prime**2 add one
lim = 50000000
num_list = [False] * lim
prime_list = prime_sieve( int(lim**0.5) )
for a in prime_list:
if a**4 > lim:
print "Done at %d" % a
break
for b in prime_list:
if a**4 + b**3 > lim: break
for c in prime_list:
stdout.write("%2d, %5d, %10d, %d\r" %(a,b,c,a**4+b**3+c**2))
stdout.flush()
num = a**4 + b**3 + c**2
if num > lim: break
# print "%d^4+%d^3+%d^2=%d" %(a,b,c,a**4+b**3+c**2)
num_list[num] = True
count = 0
for n in num_list:
if n:
count += 1
print "There are %d" % count
def primes_less_then(n):
global prime_list
block = 100000
for i in count(1):
if i >= len(prime_list):
prime_list.extend(prime_sieve(block, prime_list))
if prime_list[i] > n: break
yield prime_list[i]
def main():
count = 1
n_primes = 0
primes = prime_sieve(100000)
for s in spiral_gen():
if s**0.5 > primes[-1]:
logging.debug("extending {}: {}".format(primes[-1], s))
primes.extend(prime_sieve(100000, primes))
if is_prime(s,primes):
n_primes += 1
logging.debug("new prime {}".format(s))
count += 1
if float(n_primes)/count < 0.1:
side_len = 2 * ((count + 2)// 4) + 1
print("Prime ratio is {:5.4f} when the side length is {}".format(
100 * float(n_primes)/count, side_len))
return None
def primes_less_then(n): global prime_list block = 100000 for i in count(1): if i >= len(prime_list): prime_list.extend(prime_sieve(block, prime_list)) if prime_list[i] > n: break yield prime_list[i]
def main():
block = 10000
n = 3
lim = 5000000
prime_list = prime_sieve(block)
p_bar = ProgressBar(maxval=lim).start()
while True:
ways = changes(n, prime_list)
# print "%d: %d: %s" %(n,ways,str(prime_list))
if ways > lim:
p_bar.finish()
print "%d can be written over %d ways" % (n, lim)
return
p_bar.update(ways)
n += 1
if prime_list[-1] < n:
new_primes = prime_sieve(i + block, prime_list)
prime_list.append(new_primes)
def main(): block = 10000 n = 3 lim = 5000000 prime_list = prime_sieve(block) p_bar = ProgressBar(maxval=lim).start() while True: ways = changes(n,prime_list) # print "%d: %d: %s" %(n,ways,str(prime_list)) if ways > lim: p_bar.finish() print "%d can be written over %d ways" %(n,lim) return p_bar.update(ways) n += 1 if prime_list[-1] < n: new_primes = prime_sieve(i+block,prime_list) prime_list.append(new_primes)
def main():
N = 4000000
primes = prime_sieve(100)
m = int(log(2 * N, 3)) + 1
factors = [1] * m
best = (quick_num(factors, primes), factors)
done = [factors]
for i in reversed(range(m)):
queue = done
done = set()
for f in queue:
for new in replace(f[:], primes, i, N):
done.add(new)
s = quick_num(new, primes)
best = min(best, (s, new))
print "%d: %d" % (number(best[1], primes), solutions(best[1]))
def circular_primes():
sieve = set(common.prime_sieve(1000000))
num_circular = 0
for prime in sieve:
digits = common.get_num_digits(prime)
circular = True
for i in xrange(digits):
first = prime / 10**(digits - 1)
rest = prime % 10**(digits - 1)
prime = rest * 10 + first
if prime not in sieve:
circular = False
break
if circular:
num_circular += 1
return num_circular
def main(): N = 4000000 primes = prime_sieve(100) m = int(log(2*N,3)) + 1 factors = [1] * m best = (quick_num(factors, primes), factors) done = [factors] for i in reversed(range(m)): queue = done done = set() for f in queue: for new in replace(f[:], primes, i, N): done.add(new) s = quick_num(new, primes) best = min(best, (s, new)) print "%d: %d" %(number(best[1], primes), solutions(best[1]))
def truncatable_primes():
primes = common.prime_sieve(1000000)
prime_set = set(primes)
# under_10 = set(primes[:4])
primes = primes[4:] # Ignore single digits primes
# Filter primes where first and last digit are not prime
# primes = filter(lambda x: first_last_digit_prime(x, under_10), primes)
truncatable_sum = 0
for p in primes:
if truncate(p, prime_set):
truncatable_sum += p
return truncatable_sum
def main():
big_num = 100000
primes = prime_sieve(int(big_num**0.5+1))
# Find distinct prime factors
nums = [set([x]) for x in range(big_num+1)]
for n in range(1,big_num+1):
if n in primes: continue
for p in primes:
if n % p == 0:
nums[n] = set([p]) | nums[n//p]
break
elif n**0.5 < p: break
# Calculate rad from distinct prime factors
for i, fact in enumerate(nums[1:], start=1):
nums[i] = (prod(fact), i)
nums.pop(0)
# sort
nums.sort()
# print
print "E(10000)=%d" %(nums[10000-1][1])
def main():
big_num = 100000
primes = prime_sieve(int(big_num**0.5 + 1))
# Find distinct prime factors
nums = [set([x]) for x in range(big_num + 1)]
for n in range(1, big_num + 1):
if n in primes: continue
for p in primes:
if n % p == 0:
nums[n] = set([p]) | nums[n // p]
break
elif n**0.5 < p:
break
# Calculate rad from distinct prime factors
for i, fact in enumerate(nums[1:], start=1):
nums[i] = (prod(fact), i)
nums.pop(0)
# sort
nums.sort()
# print
print "E(10000)=%d" % (nums[10000 - 1][1])
#!/usr/bin/python
from common import split_num, prime_sieve
result = 0
sieve = prime_sieve(87654321)
for i in range(2, len(sieve)):
if sieve[i] == False:
continue
nums = split_num(i)
if sorted(nums) == list(range(1, len(nums) + 1)):
if i > result:
result = i
print(result)
#!/usr/bin/python
from common import prime_sieve, factors
def prime_factors(n, sieve):
f = factors(n)
f.remove(1)
f.remove(n)
return [i for i in f if sieve[i]]
result = 0
sieve = prime_sieve()
for i in range(647, 1000000):
found = True
for j in range(4):
n = i + j
pf = prime_factors(n, sieve)
if len(pf) != 4:
found = False
if found is True:
result = i
break
print(result)
def test_truncate_3792(self):
self.assertFalse(truncate(3792, prime_sieve(1000000)))
def test_truncate_3797(self):
self.assertTrue(truncate(3797, prime_sieve(1000000)))
def test_truncate_748317(self):
self.assertFalse(truncate(748317, prime_sieve(1000000)))
def test_truncate_311(self):
self.assertFalse(truncate(311, prime_sieve(1000000)))
