55 lines
1.2 KiB
Python
55 lines
1.2 KiB
Python
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#!/usr/bin/env python3
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from itertools import combinations
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from operator import mul
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def candidates(sieve):
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n = len(sieve)
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for i in range(4, n, 4):
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sieve[i] = True
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for p in range(3, n, 2):
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if sieve[p]:
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continue
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for i in range(p**2, n, 2*p):
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sieve[i] = p
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for i in range(2*p**2, n, 2*p**2):
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sieve[i] = True
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if not sieve[p-1]:
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yield p-1
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def is_prime(n):
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return not sieve[n] and n%2
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def factors(n):
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r = []
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while not n%2:
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r.append(2)
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n //= 2
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while sieve[n] != False:
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r.append(sieve[n])
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n //= sieve[n]
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return r + [n]
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def test_alt(n):
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fctrs = [f for f in factors(n)]
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for i in range(len(fctrs)//2):
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for c in combinations(fctrs, i+1):
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d = reduce(mul, c)
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if not is_prime(d + n//d):
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return False
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return True
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def test(n, fctrs, p=1, i=0, depth=1):
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if depth > len(fctrs) // 2:
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return True
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for j, f in enumerate(fctrs[i:]):
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if not is_prime(p*f + n//(p*f)) or not test(n, fctrs, p*f, j+1, depth+1):
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return False
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return True
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N = 10**8 + 2
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sieve = [False] * N
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print(sum(c for c in candidates(sieve) if test(c, factors(c))) + 1)
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