def e343(n=2 * 10 ** 6):
alist = [1 + k ** 3 for k in range(n + 1)]
primes = primesd3(n + 2)
print()
for p in primes:
for i in roots(p):
for j in range(i, n + 1, p):
while alist[j] > p and alist[j] % p == 0:
alist[j] //= p
return sum(alist) - n - 1
def e343(n = 2*10**6):
alist = [1 + k**3 for k in range(n + 1)]
primes = primesd3(n + 2)
print()
for p in primes:
for i in roots(p):
for j in range(i, n + 1, p):
while alist[j] > p and alist[j] % p == 0:
alist[j] //= p
return sum(alist) - n - 1
def Euler_7(n = 10001):
p = primesd3(10**6)
print()
return p[n-1]
i =1
num = 0;
while i<n:
num +=1
if isprime(num):
i +=1
return num
def Euler_7(n=10001):
p = primesd3(10**6)
print()
return p[n - 1]
i = 1
num = 0
while i < n:
num += 1
if isprime(num):
i += 1
return num
def e187(top = 10**8//2):
print(time()-ti)
#p = list(primesd2(top))
#print(len(p))
alist = primesd3(top)
count = len(alist)
print('start',time()-ti)
b = True
for i in range(1,len(alist)):
tx = time()-ti
m = tx//60
s = tx-(m*60)
if i<10**5:print(i,'{}min {}sec'.format(m,s),end='\r')
if i%10**5==0:print(i,'{}min {}sec'.format(m,s),end='\r')
for j in range(i,len(alist)):
if alist[i]*alist[j]>10**8:break
count+=1
return count
def e187(top=10**8 // 2):
print(time() - ti)
#p = list(primesd2(top))
#print(len(p))
alist = primesd3(top)
count = len(alist)
print('start', time() - ti)
b = True
for i in range(1, len(alist)):
tx = time() - ti
m = tx // 60
s = tx - (m * 60)
if i < 10**5: print(i, '{}min {}sec'.format(m, s), end='\r')
if i % 10**5 == 0: print(i, '{}min {}sec'.format(m, s), end='\r')
for j in range(i, len(alist)):
if alist[i] * alist[j] > 10**8: break
count += 1
return count
def e343_test(top=2*10**6):
global primes
primes = primesd3(top+1)
print()
vect = [i**3+1 for i in range(1,top+1)]
result = 0
t = time()
for i in range(len(vect)):
if i%100==0:print(i)
vect[i]=max(factors(vect[i]))
vect[i]=phi(vect[i])
return sum(vect)
for k in range(1,top+1):
i = k**3+1
j = round(i**(1/3))
if j%100==0:print(j)
global primes
tmp = max(factors(i))#,primes))
result+=phi(tmp)
return result
def e343_test(top=2 * 10 ** 6):
global primes
primes = primesd3(top + 1)
print()
vect = [i ** 3 + 1 for i in range(1, top + 1)]
result = 0
t = time()
for i in range(len(vect)):
if i % 100 == 0:
print(i)
vect[i] = max(factors(vect[i]))
vect[i] = phi(vect[i])
return sum(vect)
for k in range(1, top + 1):
i = k ** 3 + 1
j = round(i ** (1 / 3))
if j % 100 == 0:
print(j)
global primes
tmp = max(factors(i)) # ,primes))
result += phi(tmp)
return result
def Euler_10(top=2 * 10**6):
return sum(maths.primesd3(top))
def Euler_10(top = 2*10**6):
return sum(maths.primesd3(top))