def solve():
piter = allprimes()
next(piter)
i = 3
for node in generateAsc([Node(piter)], Node.next):
if node.val > i:
return i
elif node.val == i:
i += 2
def solve():
piter = allprimes()
next(piter)
next(piter)
p1 = next(piter)
p2 = next(piter)
nextMag = 10
accum = 0
while p1 <= 1000000:
while nextMag < p1:
nextMag *= 10
accum += p1 + nextMag * ((p2 - p1) * modInverse(nextMag, p2) % p2)
(p1, p2) = (p2, next(piter))
return accum
def solve():
for p in allprimes():
pstr = str(p)
for d in '012':
indices = [i for i,c in enumerate(pstr) if c == d]
if indices:
for subdex in subsets(indices, nonempty=True):
qty = 1
for d2 in range(int(d)+1, 10):
s2 = pstr
for i in subdex:
s2 = s2[:i] + str(d2) + s2[i+1:]
if isPrime(int(s2)):
qty += 1
if qty == 8:
return p
def solve():
for p in allprimes():
while n % p == 0:
n //= p
if n == 1:
return p
def solve():
for n,p in islice(enumerate(allprimes(), start=1), 0, None, 2):
if 2 * n * p > 10**10:
return n