def solve():
INIT = 100000
INC = 100000
primes = mathlib.getPrimes(INIT)
while True:
if len(primes) >= 10001:
return primes[10000]
else:
INIT = INIT + INC
primes = mathlib.getPrimes(INIT)
def solve():
primes = mathlib.getPrimes(1000)
primes.reverse()
for p in primes:
c = 1
while (10**c - 1) % p != 0:
c += 1
if (p-c) == 1:
return p
return -1
def solve():
primes = mathlib.getPrimes(100)
target = 10
while True:
ways = [0] * (target + 1)
ways[0] = 1
for num in primes:
for i in range(num, target + 1):
ways[i] += ways[i - num]
result = ways[target]
if result > 5000:
break
target += 1
return target
def solve():
primes = mathlib.getPrimes(1000000)
primesum = [0]
s = 0
count = 0
while s < 1000000:
s += primes[count]
primesum.append(s)
count += 1
terms = 1
for i in range(count):
for j in range(i + terms, count):
n = primesum[j] - primesum[i]
if (j-i>terms and mathlib.isPrime(n)):
terms, maxprime = j-i, n
return maxprime
def solve():
MAXNUM = 1000000 + 1
eulerlist = [0] * MAXNUM
# Sieve of Eratosthenes getting to get list of primes under 10^6
primes = mathlib.getPrimes(MAXNUM)
# compute the ¦Õ(n) of the primes
# ¦Õ(n) = n-1 if n is a prime
for p in primes:
eulerlist[p] = p - 1
# compute the ¦Õ(n) of other number
for i in range(2, MAXNUM):
if eulerlist[i] != 0:
pass
else:
for p in primes:
# ¦Õ(pq) = ¦Õ(p)*¦Õ(q) if p is a relatively prime to q,
# if p is a prime, it is a relatively prime to any number.
if i % p == 0:
if int(i/p) % p == 0:
eulerlist[i] = eulerlist[int(i/p)] * p
else:
eulerlist[i] = eulerlist[int(i/p)] * (p - 1)
break
else:
pass
# find the max ratio
reault = 6
maxRatio = 1.66666
# computer all ratio
for i in range(11, MAXNUM):
if float(i) / eulerlist[i] > maxRatio:
result = i
maxRatio = float(i) / eulerlist[i]
else:
pass
return result, maxRatio
def solve():
return sum(mathlib.getPrimes(2000000))
def solve():
D = 1000
return max([(pellEquation(d), d) for d in mathlib.getPrimes(D)])[1]
