def main():
coins, checker = sieve_of_eratosthenes(100)
print(coins)
n = 10
while True:
ways = [1] + [0] * n
for coin in coins[1:]:
for i in range(len(ways) - coin):
ways[i + coin] += ways[i]
if ways[-1] > 5000:
return n
n += 1
def main():
sum1 = 0
primes, prime_table = sieve_of_eratosthenes(10**8)
print("tables ready")
for p in primes[1:]:
n = p - 1
i = 1
flag = True
while i <= n**0.5:
if n % i == 0:
if not prime_table[int(i + n / i)]:
flag = False
break
i += 1
if flag:
sum1 += n
print(sum1)
def main3(n, MOD):
primes, sieve = sieve_of_eratosthenes(50 * n)
primes_idx = 2
heap = []
heapq.heappush(heap, 2)
print(heap)
pre_mod = 2
for i in range(1, n):
temp = heap[0] * heap[0]
if temp < primes[primes_idx]:
pre_mod *= temp % MOD
heapq.heappushpop(heap, temp)
else:
pre_mod *= primes[primes_idx]
heapq.heappush(heap, primes[primes_idx])
primes_idx += 1
print("ksekinaei to mod") # 335.5031895637512
print(pre_mod % MOD)
def main2(n):
primes, sieve = sieve_of_eratosthenes(n * 15)
print("sieve complete")
prime_idx = 2
changing_idx = 0
base_in_power = [[2, 1]]
candidates = [4]
h = []
heapq.heappush(h, 4)
number_of_candidates = 0
next_entry = 3
counter = 2
while counter <= n:
# print(counter)
changing_idx = candidates.index(h[0])
if changing_idx == number_of_candidates and candidates[
changing_idx] > next_entry:
base_in_power.append([next_entry, 1])
candidates.append(next_entry**2)
heapq.heappush(h, next_entry**2)
prime_idx += 1
next_entry = primes[prime_idx]
counter += 1
number_of_candidates += 1
else:
base_in_power[changing_idx][
1] += base_in_power[changing_idx][1] + 1
candidates[changing_idx] = base_in_power[changing_idx][0]**(
base_in_power[changing_idx][1] + 1)
heapq.heappushpop(h, candidates[changing_idx])
counter += 1
answer = 1
answer_s = ""
for i in base_in_power:
answer *= i[0]**i[1]
# answer_s += " " + str(i[0]) + "^"+ str(i[1]) + " x"
# print(answer_s)
print(answer % 500500507)
def main(n):
primes, sieve = sieve_of_eratosthenes(n * 10)
print("sieve complete")
prime_idx = 2
changing_idx = 0
base_in_power = [[2, 1]]
candidates = [4]
number_of_candidates = 0
next_entry = 3
counter = 2
while counter <= n:
# print(counter)
if changing_idx == 0 and number_of_candidates == 0:
if candidates[0] < next_entry:
base_in_power[changing_idx][1] += (
base_in_power[changing_idx][1] + 1)
candidates[0] = base_in_power[0][0]**(base_in_power[0][1] + 1)
else:
number_of_candidates += 1
candidates.append(next_entry**2)
base_in_power.append([primes[prime_idx], 1])
prime_idx += 1
next_entry = primes[prime_idx]
changing_idx += 1
counter += 1
elif changing_idx == 0:
if candidates[0] < candidates[1]:
base_in_power[0][1] += (base_in_power[0][1] + 1)
candidates[0] = base_in_power[0][0]**(base_in_power[0][1] + 1)
else:
changing_idx += 1
base_in_power[changing_idx][
1] += base_in_power[changing_idx][1] + 1
candidates[changing_idx] = base_in_power[changing_idx][0]**(
base_in_power[changing_idx][1] + 1)
counter += 1
elif changing_idx == number_of_candidates:
if candidates[changing_idx] > candidates[changing_idx - 1]:
changing_idx -= 1
base_in_power[changing_idx][
1] += base_in_power[changing_idx][1] + 1
candidates[changing_idx] = base_in_power[changing_idx][0]**(
base_in_power[changing_idx][1] + 1)
else:
number_of_candidates += 1
candidates.append(next_entry**2)
base_in_power.append([primes[prime_idx], 1])
prime_idx += 1
next_entry = primes[prime_idx]
changing_idx += 1
counter += 1
else:
if candidates[changing_idx] > candidates[changing_idx - 1]:
changing_idx -= 1
base_in_power[changing_idx][
1] += base_in_power[changing_idx][1] + 1
candidates[changing_idx] = base_in_power[changing_idx][0]**(
base_in_power[changing_idx][1] + 1)
elif candidates[changing_idx] > candidates[changing_idx + 1]:
changing_idx += 1
base_in_power[changing_idx][
1] += base_in_power[changing_idx][1] + 1
candidates[changing_idx] = base_in_power[changing_idx][0]**(
base_in_power[changing_idx][1] + 1)
else:
base_in_power[changing_idx][
1] += base_in_power[changing_idx][1] + 1
candidates[changing_idx] = base_in_power[changing_idx][0]**(
base_in_power[changing_idx][1] + 1)
counter += 1
changing_idx = candidates.index(min(candidates))
# print(changing_idx)
# for j in base_in_power:
# new_candidate = j[0] ** (j[1] + 1)
# if primes[prime_idx] < new_candidate:
# base_in_power.append([primes[prime_idx],1])
# prime_idx +=1
# break
# else
answer = 1
answer_s = ""
for i in base_in_power:
answer *= i[0]**i[1]
answer_s += " " + str(i[0]) + "^" + str(i[1]) + " x"
print(answer_s)
print(answer % 500500507)