project-euler/134_prime_pair_connection.py

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2023-03-26 17:21:44 +02:00
#!/usr/bin/env python3
def primes(n):
sieve = [False]*n
for p in range(2, int(n**0.5)):
if sieve[p]:
continue
for i in range(p**2, n, p):
sieve[i] = True
return [p for p, t in enumerate(sieve) if not t][2:]
def solve(p1, p2, k):
t = extended_euclid(p2, k)
return ((t * p1) % k) * p2
def extended_euclid(p2, k):
a = k
b = p2
t1, t2 = 0, 1
while b != 0:
k = a // b
a, b = b, a % b
t1, t2 = t2, t1 - k*t2
return t1
n = 10**6
nums = primes(n + 1000)
nums = [nums[i] for i in range(1, len(nums)) if nums[i-1] <= n]
k = 10
s = 0
for p1, p2 in zip(nums[1:], nums[2:]):
if p1 > k:
k *= 10
s += solve(p1, p2, k)
print(s)