def find_primes(*, up_to=100):
primes = []
for p in prime_number_generator():
if p >= up_to:
break
primes.append(p)
return primes
def primes_range(start, stop):
primes = []
for p in takewhile(
lambda x: x < stop,
dropwhile(lambda y: y <= start, prime_number_generator())):
primes.append(p)
return primes
def run_exercise(*, n=6):
primes = []
for p in prime_number_generator():
primes.append(p)
n -= 1
if not n > 0:
break
print('Solution =', primes[-1])
def run_exercise(*, limit=10):
prime = prime_number_generator()
primes = []
while True:
p = next(prime)
if p >= limit:
break
primes.append(p)
print(sum(primes))
def attempt():
limit = 10**6
prime = 0
terms = 1
prime_sums = [0]
for p in prime_number_generator():
prime_sums.append(prime_sums[-1] + p)
if prime_sums[-1] >= limit:
break
candidates = []
for j in range(len(prime_sums)):
for k in range(j):
candidate = prime_sums[j] - prime_sums[k]
if is_prime(candidate):
candidates.append((candidate, j - k))
break
return max(candidates, key=lambda x: x[terms])[prime]
def run_solution(n=13195):
prime = prime_number_generator()
factors = []
p = next(prime)
while n > 1:
while (n % p) == 0:
n //= p
factors.append(p)
p = next(prime)
counter = Counter(factors)
print('all prime factors:', counter)
print('maximum prime factor:', max(counter))
def attempt():
max_truncatable_primes = 11
truncatable_primes = []
for prime in prime_number_generator():
if len(truncatable_primes) >= max_truncatable_primes:
break
if prime < 10:
continue
trunks = find_all_trunks(prime)
if all(map(is_prime, trunks)):
print('prime =', prime, ', trunks =', list(sorted(trunks)))
truncatable_primes.append(prime)
return sum(truncatable_primes)
def attempt():
"""Builds a product from consecutive ascending primes until we not longer exceed the limit.
Then goes back by dividing the denominator so far by the last prime, and then stepping up
by multiplying by two (i.e. growing the denominator the smallest possible step) for
several rounds.
CAVEAT! To be sure really having found the smallest denominator, some testing and
optimizing is necessary. There might still be smaller denominators in the wild.
"""
limit = Fraction(15499, 94744)
# limit = Fraction(4, 10)
prime = prime_number_generator()
denominator = next(prime)
while denominator_resilience(denominator) >= limit:
p = next(prime)
denominator *= p
denominator //= p
# prime = prime_number_generator()
while denominator_resilience(denominator) >= limit:
# denominator *= next(prime)
denominator *= 2
print('R({}) = {} and is less than {}.'.format(
denominator, denominator_resilience(denominator), limit))