def test():
print("----- Unit Test ----- ")
a = randint(1, 100000)
b = randint(1, 100000)
assert em.lb(a) == int(math.log(a, 2)), "lb() assert failed!"
assert em.log(a, 8) == int(math.log(a, 8)), "log() assert failed!"
assert em.sqrt(a) == int(math.sqrt(a)), "sqrt() assert failed!"
assert em.gcd(a, b) == math.gcd(a, b), "powmod() assert failed!"
assert em.mulmod(a, b, 100) == a * b % 100, "mulmod() assert failed!"
assert em.powmod(a, b, 100) == pow(a, b, 100), "powmod() assert failed!"
t = em.randrange(min(a, b), max(a, b))
assert min(a, b) <= t and t < max(a, b), "randrange() assert failed!"
print("numeric passed!")
assert em.isprime(primet)
assert all(prime50[i] == em.primes(50)[i] for i in range(len(prime50)))
assert all(prime100[i] == em.primes(100)[i] for i in range(len(prime100)))
em.clearprimes()
assert all(prime100[i] == em.nprimes(len(prime100))[i] for i in range(len(prime100)))
plist = list(islice(em.iterprimes(), len(prime100)))
assert all(prime100[i] == plist[i] for i in range(len(prime100)))
assert em.isprime(primet)
em.clearprimes()
assert em.factors(123456789) == fac123456789
print("prime passed!")
def check(number):
if isprime(number):
return True # skip non-composite
for i in count(1):
s = number - 2 * i * i
if s <= 0:
return False
elif isprime(s):
return True
def count_primes(ab):
a, b = ab
if not isprime(b):
return 0
counter = 0
current = b
while current > 1 and isprime(current):
current += counter * 2 + 1 + a
counter += 1
return counter
def check(target):
# left truncatable
divider = 10
while divider <= target:
if not isprime(target % divider):
return False
divider *= 10
# right truncatable
target //= 10
while target > 0:
if not isprime(target):
return False
target //= 10
return True
def solve(target = TARGET):
from em import iterprimes, isprime
from itertools import product
families = set()
digits = [str(d) for d in range(10)]
for prime in iterprimes():
if prime < 10000:
continue
sprime = str(prime)
masks = [(digit, '*') for digit in sprime]
for mask in product(*masks):
family = ''.join(mask)
if family == sprime: continue # no replaceable digits
if len(set(sprime[i] for i, d in enumerate(family) if d == '*')) > 1:
continue
if family in families:
continue
else:
# This condition is awkwardly implied by the problem description.
# Without this condition, the result is 111109
if mask[0] == '*':
replacer = digits[1:] # remove 0
else:
replacer = digits
total = sum(isprime(int(family.replace('*', d))) for d in replacer)
if total >= target:
return prime
families.add(family)
def solve(thres=THRES):
total = 1.
total_prime = 0
d1, d2, d3, d4 = 3, 5, 7, 9
for n in count(1):
total += 4
total_prime += isprime(d1) + isprime(d2) + isprime(d3) + isprime(d4)
d1 += 8 * n + 2
d2 += 8 * n + 4
d3 += 8 * n + 6
d4 += 8 * n + 8
if total_prime / total < thres:
break
return 2 * n + 1
def solve():
'''
Brute-force solution
'''
digits = [str(d) for d in range(1, 10)]
for size in reversed(range(10)):
for number in reversed(sorted(permutations(digits[:size]))):
number = int(''.join(number))
if isprime(number):
return number
def solve(limit=LIMIT):
from em import primes, isprime
from itertools import count
lprimes = primes(limit)
maxlen = 21
psum = 0
for plen in count(maxlen, 2):
if sum(lprimes[:plen]) > limit:
return psum
for start in range(len(lprimes) - plen):
current = sum(lprimes[start:start + plen])
if current > limit:
break
if isprime(current) and plen > maxlen:
psum = current
maxlen = plen
def test2(a, b):
return isprime(int(str(a) + str(b))) and isprime(int(str(b) + str(a)))