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 solve(limit = LIMIT):
from em import primes
pset = set(primes(limit))
# be careful for that '71993' is a rotation of `930719`
result = [prime for prime in pset if all(
int(str(prime)[i:] + str(prime)[:i]) in pset
for i in range(1, len(str(prime)))
)]
return len(result)
def solve():
lprimes = [p for p in primes(10000) if p > 1000]
for idx, p1 in enumerate(lprimes):
for p2 in lprimes[:idx]:
if not isperm(p1, p2):
continue
p3 = 2 * p2 - p1
if p3 in lprimes and isperm(p2, p3):
if p3 != 1487: # given by problem
return str(p3) + str(p2) + str(p1)
def pfactor(target):
flist = set()
for prime in primes(sqrt(target) + 1):
if target % prime == 0:
flist.add(prime)
target //= prime
while target % prime == 0:
target //= prime
if target == 1 or prime > target:
break
if target != 1:
flist.add(target)
return flist
def solve():
# In this order we prevent duplicate computation
for a in iterprimes():
for plist in cache[4]:
if testn(a, plist):
return sum([a] + plist)
for plist in cache[3]:
if testn(a, plist):
cache[4].append([a] + plist)
for plist in cache[2]:
if testn(a, plist):
cache[3].append([a] + plist)
for p in primes(a):
if test2(a, p):
cache[2].append([a, p])
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
from em import iterprimes, primes, isprime
from functools import lru_cache
# primes that fulfill the property is far more less, so store true values
cache = {2: list(), 3: list(), 4: list()}
primes(1e6, True)
@lru_cache(maxsize=None)
def test2(a, b):
return isprime(int(str(a) + str(b))) and isprime(int(str(b) + str(a)))
def testn(a, l):
for p in l:
if not test2(a, p):
return False
return True
def solve():
# In this order we prevent duplicate computation
for a in iterprimes():
for plist in cache[4]:
if testn(a, plist):
return sum([a] + plist)
for plist in cache[3]:
if testn(a, plist):
cache[4].append([a] + plist)
for plist in cache[2]:
if testn(a, plist):
def solve(limit=LIMIT):
from em import primes
return sum(primes(limit))
