def main(args):
if args.test:
m = 10
else:
m = 1000*1000
prime = PrimeNumberPool()
md = 5
mn = 2
for d in range(2, m):
if d == 7:
continue
n = d * 3 // 7
if (n>mn*d/md and HCF(n, d, prime)):
mn = n
md = d
logging.debug("{}/{}".format(mn, md))
logging.info("answer: {}/{}".format(mn, md))
logging.debug(prime.Factorize(mn))
logging.debug(prime.getPrimeFactor(mn))
logging.debug(prime.Factorize(md))
logging.debug(prime.getPrimeFactor(md))
def main(args):
description = '''
Largest prime factor
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143 ?
'''
if args.test:
number = 13195
else:
number = 600851475143
logging.debug('test with {}'.format(number))
maxp = round(math.sqrt(number)) + 1
ts1 = time.time()
primes = PrimeNumberPool(maxp)
ts2 = time.time()
logging.debug('time for build prime number pool: {}'.format(ts2-ts1))
factors = primes.getPrimeFactor(number)
logging.debug('factors:{}'.format(factors))
ts3 = time.time()
logging.debug('time for factorize: {}'.format(ts3-ts2))
solution = 'largest prime factor of the number {} is {}'.format(number, factors[-1])
logging.info(solution)
def main(args):
if args.test:
m = 3000
max_phi = 1
max_n = 1
brute_force = 1
else:
m = 1000 * 1000
max_phi = 3
max_n = 6
brute_force = 0
prime = PrimeNumberPool(m)
'''
A strait forward way is to calculate the product of primes
'''
answer = 1
for p in prime.numbers:
while answer < m:
answer *= p
logging.info("answer:{}".format(answer))
return 0
max_num_prime_factors = 1
for n in range(2, m + 1):
if brute_force:
phi = Phi(n, prime)
else:
'''
Analysis:
A lower phi happens when the number n has many prime factors
'''
factors = prime.getPrimeFactor(n)
if len(factors) > max_num_prime_factors:
max_num_prime_factors = len(factors)
phi = Phi(n, prime)
logging.debug("{} factors: {}, phi: {}".format(
n, factors, phi))
else:
continue
logging.debug("{} phi = {}".format(n, phi))
if (phi * max_phi < n):
max_n = n
max_phi = float(n) / phi
logging.debug((max_n, max_phi))
logging.info("answer:{}".format(max_n))
def main(args):
if args.test:
m = 8 + 1
else:
m = 1000 * 12 + 1
prime = PrimeNumberPool(m // 2)
num = 0
for d in range(3, m):
d1 = d // 2 + 1
pd = prime.getPrimeFactor(d)
for n in range(d // 3 + 1, d1):
if (HCF(n, pd)):
logging.debug("{}/{}".format(n, d))
num += 1
logging.info("answer: {}".format(num))
def main(args):
prime = PrimeNumberPool()
n = 100000
rod = {}
for k in range(1, n+1):
f = prime.getPrimeFactor(k)
p = np.product(f)
if (p in rod):
rod_p = rod[p]
rod_p.append(k)
else:
rod[p] = [k]
# assume rod's key is sorted
e_n = []
for k in sorted(list(rod.keys())):
e_n += rod[k]
logger.info("answer: {}".format(e_n[10000-1]))