def main():
nums = []
p_gen = prime_generator()
primes = [next(p_gen)]
for i in count(1):
factors = 0
while i/30 >= primes[-1]:
primes.append(next(p_gen))
for n in primes:
temp = i
once = True
while temp % n == 0:
if once:
factors += 1
once = False
temp /= n
if i/30 < n or 4 < factors:
break
logging.debug('{} has {} factors'.format(i, factors))
if factors == 4:
nums.append(i)
else:
nums = []
if len(nums) == 4:
break
print('Answer: {}'.format(nums))
def main():
prime_list = []
trunc_prime_sum = 0
trunc_prime_count = 0
for prime in prime_generator():
prime_list.append(prime)
if prime < 10:
continue
logging.debug("Checking prime {}".format(prime))
trunc_prime = True
for i in range(1,len(str(prime))):
left = int(str(prime)[:i])
right = int(str(prime)[i:])
logging.debug("Testing {} and {}".format(left, right))
if left not in prime_list or right not in prime_list:
logging.debug("Nope!")
trunc_prime = False
break
if trunc_prime:
trunc_prime_count += 1
logging.info(prime)
trunc_prime_sum += prime
if trunc_prime_count >= 11:
break
print('Answer: {}'.format(trunc_prime_sum))
def main(): limit = 2e6 prime_sum = 0 for prime in prime_generator(): if prime > limit: break prime_sum += prime print prime_sum
def main():
prime_list = []
trunc_prime_sum = 0
trunc_prime_count = 0
for prime in prime_generator():
prime_list.append(prime)
if prime < 10:
continue
logging.debug("Checking prime {}".format(prime))
trunc_prime = True
for i in range(1, len(str(prime))):
left = int(str(prime)[:i])
right = int(str(prime)[i:])
logging.debug("Testing {} and {}".format(left, right))
if left not in prime_list or right not in prime_list:
logging.debug("Nope!")
trunc_prime = False
break
if trunc_prime:
trunc_prime_count += 1
logging.info(prime)
trunc_prime_sum += prime
if trunc_prime_count >= 11:
break
print('Answer: {}'.format(trunc_prime_sum))
def main():
nums = []
p_gen = prime_generator()
primes = [next(p_gen)]
for i in count(1):
factors = 0
while i / 30 >= primes[-1]:
primes.append(next(p_gen))
for n in primes:
temp = i
once = True
while temp % n == 0:
if once:
factors += 1
once = False
temp /= n
if i / 30 < n or 4 < factors:
break
logging.debug('{} has {} factors'.format(i, factors))
if factors == 4:
nums.append(i)
else:
nums = []
if len(nums) == 4:
break
print('Answer: {}'.format(nums))
def prime_pairs(lim, block = 1000100): pg = prime_generator(block) large = pg.next() for p in pg: (large, small) = (p, large) if small >= lim: return if large - small == 2: yield (large, small)
def prime_pairs(lim, block=1000100):
pg = prime_generator(block)
large = pg.next()
for p in pg:
(large, small) = (p, large)
if small >= lim: return
if large - small == 2:
yield (large, small)
def main():
max_pan_len = (0,0)
for prime in prime_generator():
if prime > 987654321: break
pan_len = pandigital_len(str(prime))
if pan_len > max_pan_len[0]:
max_pan_len = (pan_len, prime)
logging.info(max_pan_len)
print('Answer: {}'.format(max_pan_len))
def main():
max_pan_len = (0, 0)
for prime in prime_generator():
if prime > 987654321: break
pan_len = pandigital_len(str(prime))
if pan_len > max_pan_len[0]:
max_pan_len = (pan_len, prime)
logging.info(max_pan_len)
print('Answer: {}'.format(max_pan_len))
def brute(): lim = 100000 for p in prime_generator(): if p >= lim: break for n in range(1,lim): m = n**2 * (n + p) if is_cube(m): if is_cube(n): nu = round(n ** (1.0/3)) print "%d^9 + %d^2 * %d = %d^3" %(nu,n,p,round(m**(1.0/3)))
def main():
big_num = 100000
prime_sum = 2 + 3 + 5
for p in prime_generator(block=100100):
if p <= 5: continue
if p >= big_num: break
stdout.write("%d\r" %(p))
stdout.flush()
if not match(p):
prime_sum += p
print "Sum of all primes with property is %d" %(prime_sum)
def main():
big_num = 100000
prime_sum = 2 + 3 + 5
for p in prime_generator(block=100100):
if p <= 5: continue
if p >= big_num: break
stdout.write("%d\r" % (p))
stdout.flush()
if not match(p):
prime_sum += p
print "Sum of all primes with property is %d" % (prime_sum)
def main():
n_prime = prime_generator()
primes = [next(n_prime)]
max_conseq = 0
for a in range(-999,1000):
for b in range(-999,1000):
consec = consec_quad_primes(a,b,primes,n_prime)
if max_conseq < consec:
max_conseq = consec
coeff = (a,b)
print("{}: from {}".format(max_conseq, str(coeff)))
def factor(n): f = [] p_gen = prime_generator() while not is_prime(n) and n > 1: p = p_gen.next() while n % p == 0: n /= p f.append(p) print n if n != 1: f.append(int(n)) return f
def main():
big_num = 10**10
for n,p in enumerate(prime_generator(block=10000000), start=1):
if p**2 < big_num: continue
r = prime_remainder(p,n)
stdout.write("%d: %d: %d\r" %(n,p,r))
stdout.flush()
if r > big_num:
stdout.write(" " * 40 + "\r")
print "%d: %d: %d" %(n, p, r)
return
def factor(n):
f = []
p_gen = prime_generator()
while not is_prime(n) and n > 1:
p = p_gen.next()
while n % p == 0:
n /= p
f.append(p)
print n
if n != 1: f.append(int(n))
return f
def brute():
lim = 100000
for p in prime_generator():
if p >= lim: break
for n in range(1, lim):
m = n**2 * (n + p)
if is_cube(m):
if is_cube(n):
nu = round(n**(1.0 / 3))
print "%d^9 + %d^2 * %d = %d^3" % (nu, n, p, round(
m**(1.0 / 3)))
def main():
lim = 1000000
ans = 0
for p in prime_generator(block=lim + 1000):
if p >= lim: break
(m, args) = match(p)
if m:
(a, c) = args
stdout.write("%d^3 + %d^2 * %d = %d^3\r" % (a, a, p, c))
stdout.flush()
ans += 1
print "There are %d primes with propery below %d" % (ans, lim),
print " " * 10
def main():
n = 1
p_gen = prime_generator()
prime_list = [next(p_gen)]
while True:
n += 2
while n > prime_list[-1]:
prime_list.append(next(p_gen))
if n in prime_list:
continue
if not fits_conjecture(n, prime_list):
print('Answer: {}'.format(n))
break
def main():
lim = 1000000
ans = 0
for p in prime_generator(block = lim + 1000):
if p >= lim: break
(m, args) = match(p)
if m:
(a,c) = args
stdout.write("%d^3 + %d^2 * %d = %d^3\r" %(a,a,p,c))
stdout.flush()
ans += 1
print "There are %d primes with propery below %d" %(ans, lim),
print " " * 10
def main():
n = 1
p_gen = prime_generator()
prime_list = [next(p_gen)]
while True:
n += 2
while n > prime_list[-1]:
prime_list.append(next(p_gen))
if n in prime_list:
continue
if not fits_conjecture(n, prime_list):
print('Answer: {}'.format(n))
break
def main():
big_num = 10**9
lim = 40
c = 0
prime_sum = 0
for p in prime_generator(block=10000000):
if p == 5 or p == 2: continue
a = A(p)
stdout.write("%d: %d\r" % (c, p))
stdout.flush()
if big_num % a == 0:
#print p
prime_sum += p
c += 1
print "%d: %d" % (c, p)
if c >= lim: break
print "Sum of the first %d primes is %d" % (lim, prime_sum)
def main():
big_num = 10**9
lim = 40
c = 0
prime_sum = 0
for p in prime_generator(block=10000000):
if p == 5 or p == 2: continue
a = A(p)
stdout.write("%d: %d\r" %(c,p))
stdout.flush()
if big_num % a == 0:
#print p
prime_sum += p
c += 1
print "%d: %d" %(c, p)
if c >= lim: break
print "Sum of the first %d primes is %d" %(lim, prime_sum)
def main():
#big_num = 10000
big_num = 1000000
s_sum = 0
pg = prime_generator(big_num + 1000)
large = pg.next()
large = pg.next()
large = pg.next()
#print large
for p in pg:
(large, small) = (p, large)
if small > big_num: break
stdout.write("%d: %d\r" % (large, small))
stdout.flush()
s_sum += get_s(large, small)
#if get_s(large,small) != slow_get_s(large, small):
# print "Problem: (%d, %d)" %(large,small)
print "Sum of all s is %d" % (s_sum)
def main():
#big_num = 10000
big_num = 1000000
s_sum = 0
pg = prime_generator(big_num + 1000)
large = pg.next()
large = pg.next()
large = pg.next()
#print large
for p in pg:
(large, small) = (p, large)
if small > big_num: break
stdout.write("%d: %d\r" %(large, small))
stdout.flush()
s_sum += get_s(large, small)
#if get_s(large,small) != slow_get_s(large, small):
# print "Problem: (%d, %d)" %(large,small)
print "Sum of all s is %d" %(s_sum)
def main():
set_dict = {}
limit = False
max_elements = [1e6] * 5
i = 0
for prime in prime_generator(block=1000000):
i += 1
if i % 100000 == 0: logging.info("Testing {}".format(prime))
if limit and limit < prime: break
[p, q] = populate(set_dict, prime)
logging.debug(set_dict)
logging.debug("p: {}\nq: {}".format(str(p), str(q)))
element_set = has_valid_set(set_dict, [p, q])
if element_set and sum(element_set) < sum(max_elements):
element_set.sort()
print("{:d}: {!s}".format(sum(element_set), element_set))
k = str(element_set[-1])
limit = int(k + k)
max_elements = element_set
def wheel_sieve(diffs, lim, stop):
wheel = {}
for p in prime_generator(block=(stop+100)):
stdout.write("%9d\r" %(p))
stdout.flush()
if p > stop: break
if p == 2 or p == 5: continue
spoke = wheel_worker(p, diffs)
# print "%2d: %s" %(p, spoke)
wheel[p] = spoke
primes = sorted(wheel.keys())
for i in range(lim//10):
for p in primes:
flag = True
if not wheel[p][i % p]:
if i == 1: print "%d: %d: %s" %(p,i%p,wheel[p])
flag = False
break
if flag: yield i*10
def wheel_sieve(diffs, lim, stop):
wheel = {}
for p in prime_generator(block=(stop + 100)):
stdout.write("%9d\r" % (p))
stdout.flush()
if p > stop: break
if p == 2 or p == 5: continue
spoke = wheel_worker(p, diffs)
# print "%2d: %s" %(p, spoke)
wheel[p] = spoke
primes = sorted(wheel.keys())
for i in range(lim // 10):
for p in primes:
flag = True
if not wheel[p][i % p]:
if i == 1: print "%d: %d: %s" % (p, i % p, wheel[p])
flag = False
break
if flag: yield i * 10
def main():
prime_gen = prime_generator()
prime_list = [next(prime_gen)]
circular_count = 0
logging.info("Starting")
for i in count():
while i >= len(prime_list):
logging.debug("Extending primes array")
new_prime = next(prime_gen)
prime_list.append(new_prime)
circular = True
if prime_list[i] >= 1000000: break
logging.debug("Testing " + str(prime_list[i]))
for circ in circ_gen(prime_list[i]):
while circ > prime_list[-1]:
prime_list.append(next(prime_gen))
if circ not in prime_list:
circular = False
break
if circular:
logging.info("This prime is circular " + str(prime_list[i]))
circular_count += 1
print('There are {} circular primes'.format(circular_count))
def nth_prime(n):
i = 1
for prime in prime_generator():
i += 1
if i > n: return prime
def nth_prime(n): i = 1 for prime in prime_generator(): i += 1 if i > n: return prime
