import math
from sieve_prime import get_all_primes
all_primes = get_all_primes(10000000)
all_primes[-1]
len(all_primes)
def is_relative_prime(num1, num2):
return math.gcd(num1, num2) == 1
def phi(n):
return sum(is_relative_prime(i, n) for i in range(1,n))
def is_perm(num1, num2):
num1_str = str(num1)
num2_str = str(num2)
for c in '0123456789':
if num1_str.count(c) != num2_str.count(c):
return False
return True
#max(i/phi(i) for i in range(2,upper_bound) if i % 2 == 0)
print(17*13)
phi(17*13)
def phi2(m,n):
return m * n - m - n + 1
from sieve_prime import get_all_primes
from bisect import bisect_right
all_primes = get_all_primes(50000)
def find_max_prime(n):
return all_primes[bisect_right(all_primes, n) - 1]
def ways(n, p):
if n == 0:
return 1
if n == 1:
return 0
if p > n:
return ways(n, find_max_prime(n))
else:
if p == 2:
if n % 2 == 0:
return 1
else:
return 0
else:
total = 0
temp_prime = p
while temp_prime > 2:
total += sub_ways(n, temp_prime)
temp_prime = find_max_prime(temp_prime - 1)
if n % 2 == 0:
total += 1
return sum(math.gcd(i, n) == 1 for i in range(1, n))
def prime_factors(num):
f = set()
if get_index(all_primes, num) > -1:
f.add(num)
return f
else:
remaining = num
for p in all_primes:
while remaining % p == 0:
f.add(p)
remaining //= p
if remaining == 1:
return f
def phi2(n):
result = n
factors = prime_factors(n)
for f in factors:
result *= f - 1
result //= f
return result
limit = 1000000
all_primes = get_all_primes(limit)
sum(phi2(i) for i in range(2, limit + 1))
def prime_factors(num):
f = set()
if get_index(all_primes, num) > -1:
f.add(num)
return f
else:
remaining = num
for p in all_primes:
while remaining % p == 0:
f.add(p)
remaining //= p
if remaining == 1:
return f
def phi2(n):
result = n
factors = prime_factors(n)
for f in factors:
result *= f - 1
result //= f
return result
limit = 1000000
all_primes = get_all_primes(limit)
sum(phi2(i) for i in range(2, limit+1))
from sieve_prime import get_all_primes
from bisect import bisect_right
all_primes = get_all_primes(50000)
def find_max_prime(n):
return all_primes[bisect_right(all_primes, n) - 1]
def ways(n, p):
if n == 0:
return 1
if n == 1:
return 0
if p > n:
return ways(n, find_max_prime(n))
else:
if p == 2:
if n % 2 == 0:
return 1
else:
return 0
else:
total = 0
temp_prime = p
while temp_prime > 2:
total += sub_ways(n, temp_prime)
temp_prime = find_max_prime(temp_prime - 1)
if n % 2 == 0:
total += 1
return total
import math
from bisect import bisect_right
from sieve_prime import get_all_primes
upper_bound = 50000000
p4_bound = int(upper_bound ** (1/4))
p3_bound = int(upper_bound ** (1/3))
p2_bound = int(upper_bound ** (1/2))
p2_primes = get_all_primes(p2_bound)
p3_index = bisect_right(p2_primes, p3_bound)
p4_index = bisect_right(p2_primes, p4_bound)
p3_primes = p2_primes[:p3_index]
p4_primes = p2_primes[:p4_index]
print(len(p2_primes), len(p3_primes), len(p4_primes))
sum_set = set()
for p2 in p2_primes:
for p3 in p3_primes:
for p4 in p4_primes:
total = p2 ** 2 + p3 ** 3 + p4 ** 4
if total <= upper_bound:
sum_set.add(total)
else:
import math
from bisect import bisect_right
from sieve_prime import get_all_primes
upper_bound = 50000000
p4_bound = int(upper_bound**(1 / 4))
p3_bound = int(upper_bound**(1 / 3))
p2_bound = int(upper_bound**(1 / 2))
p2_primes = get_all_primes(p2_bound)
p3_index = bisect_right(p2_primes, p3_bound)
p4_index = bisect_right(p2_primes, p4_bound)
p3_primes = p2_primes[:p3_index]
p4_primes = p2_primes[:p4_index]
print(len(p2_primes), len(p3_primes), len(p4_primes))
sum_set = set()
for p2 in p2_primes:
for p3 in p3_primes:
for p4 in p4_primes:
total = p2**2 + p3**3 + p4**4
if total <= upper_bound:
sum_set.add(total)
else:
break
import math
import numpy as np
from sieve_prime import get_all_primes
from bisect import bisect_left
def index(a, x):
'Locate the leftmost value exactly equal to x'
i = bisect_left(a, x)
if i != len(a) and a[i] == x:
return i
return -1
upper_bound = 900000000
all_primes = get_all_primes(upper_bound)
len(all_primes)
def get_corner(i, j, corners):
if i == 0:
return 1 + 8 * i + j * 2 + 2
else:
return corners[i-1][j] + 8 * i + j * 2 + 2
def get_ratio(n, corners):
for i in range(n):
for j in range(4):
corners[i][j] = get_corner(i, j, corners)
from sieve_prime import get_all_primes
from bisect import bisect_left
def index(a, x):
'Locate the leftmost value exactly equal to x'
i = bisect_left(a, x)
if i != len(a) and a[i] == x:
return i
return -1
upper_bound = 900000000
all_primes = get_all_primes(upper_bound)
len(all_primes)
def get_corner(i, j, corners):
if i == 0:
return 1 + 8 * i + j * 2 + 2
else:
return corners[i - 1][j] + 8 * i + j * 2 + 2
def get_ratio(n, corners):
for i in range(n):
for j in range(4):