def main():
primes = GPE.sieve(int(10**3.5) + 1)
for a in range(len(primes)):
for b in range(a + 1, len(primes)):
i = primes[a]
j = primes[b]
n = i * j
ep = GPE.Euler_Phi(n, primes)
if str(sorted(str(ep))) == str(sorted(str(n))):
print(n, ep)
def main():
candidate = GPE.sieve(10**3)
curbest = 0
curbestcand = (0, 0)
for b in candidate:
for a in range(-999, 1001, 2):
if GPE.is_prime(a + b + 1):
n = 0
while GPE.is_prime(n * n + n * a + b):
n += 1
if n > curbest:
curbest = n
curbestcand = (a, b)
print(curbestcand[0] * curbestcand[1])
def main():
f = open("102.txt", 'r')
ans = 0
for line in f:
cord = list(map(int, line.split(',')))
a = GPE.Point(cord[0], cord[1])
b = GPE.Point(cord[2], cord[3])
c = GPE.Point(cord[4], cord[5])
S = GPE.triangle_area(a, b, c)
s1 = GPE.triangle_area(a, b, GPE.Point(0, 0))
s2 = GPE.triangle_area(c, b, GPE.Point(0, 0))
s3 = GPE.triangle_area(a, c, GPE.Point(0, 0))
if S == s1 + s2 + s3:
ans += 1
print(ans)
def main():
ub = 50000000
P = set()
primes2 = GPE.sieve(int(pow(ub, 1 / 2)) + 1)
primes3 = GPE.sieve(int(pow(ub, 1 / 3)) + 1)
primes4 = GPE.sieve(int(pow(ub, 1 / 4)) + 1)
c = 0
for (i, j, k) in itertools.product(primes2, primes3, primes4):
c += 1
x = i**2 + j**3 + k**4
if x > ub:
continue
else:
P.add(x)
print(len(P))
def main():
count = 0
primes = GPE.sieve(10**6)
for p in primes:
u = len(str(p))
flag = True
for i in range(u):
if GPE.BinarySearch(int(rotation(i, p)), primes) > -1:
flag = True
else:
flag = False
break
if flag:
print(p)
count += 1
print("answer is", count)
def main(): ans = 0 primes = GPE.sieve(10**8) for p in primes: if p==2 or p==3: continue ans += euler_381(p) print(ans)
def main():
ans = 0
abundants = []
for x in range(1, 28123):
if sum(GPE.allDivisors(x)) > 2 * x:
abundants.append(x)
for cand in range(1, 28123):
flag = 0
for check in abundants:
if check > cand:
break
if GPE.BinarySearch(cand - check, abundants) != -1:
flag = 1
break
if flag == 0:
ans += cand
print(ans)
def main():
ans = 10**7
result = [False] * 1001
for i in range(1, 1000):
x = i
while True:
x = GPE.sum_on_digit(x, sq)
if x is 89:
result[i] = False
break
if x is 1:
result[i] = True
break
for i in range(1, 10**7 + 1):
x = GPE.sum_on_digit(i, sq)
if result[x]:
ans -= 1
print(ans)
def main():
r = "7654321"
for s in itertools.permutations(r):
a = ''
for x in s:
a += (''.join(x))
a = int(a)
if GPE.is_prime(a):
print(a)
return
def main():
plist = GPE.sieve(100000)
twosq = []
for i in range(1, 300):
twosq.append(i * i * 2)
for task in range(3, 100000, 2):
if GPE.BinarySearch(task, plist) == -1:
flag = False
for p in plist:
if task - p <= 0:
break
if GPE.BinarySearch(task - p, twosq) >= 0:
flag = True
break
if not flag:
print(task)
return
else:
continue
def main():
dp = [0]*1005
dp[0] = 1
primes = GPE.sieve(1000)
for p in primes:
for i in range(p, 1000):
dp[i] += dp[i-p]
for i in range(1,1000):
if dp[i]>5000:
print(f"ANSWER : {i}")
break
def main():
genp = 0
tg = 8
prls = []
for i in range(1, 1000000):
cand = [j for j in range(len(str(i)))]
cd = GPE.powerset(cand)
bst = 0
for st in cd:
if len(st) > 0:
cls = gen(i, st)
ct = 0
for p in cls:
if isprime(p):
ct += 1
if ct == tg:
print(cls[0])
return
def is_pentagonal(x):
if GPE.BinarySearch(x, pentagonal_numbers) == -1:
return False
else:
return True
def int_palindrome(n):
return GPE.check_palindrome(str(n))
def isprime(x):
return GPE.BinarySearch(x, pr) != -1
import time
from lib import Gratus_PE_Util as GPE
pr = GPE.sieve(1000000)
vst = [False] * 1000000
def isprime(x):
return GPE.BinarySearch(x, pr) != -1
def gen(x, checklist):
ls = [[]] * 10
for i in range(10):
ls[i] = list(str(x))
rls = [0] * 10
mk = False
for i in range(10):
for k in checklist:
ls[i][k] = chr(ord('0') + i)
if k == 0 and i == 0:
mk = True
rls[i] = int("".join(ls[i]))
if mk:
rls.remove(rls[0])
return rls
def main():
genp = 0
tg = 8