Solve 133 and 134.
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c3f24f445e
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from lib_prime import primes
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def r_modulo_closed_form(n, m):
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assert n > 0 and m > 0
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return ((pow(10, n, 9 * m) - 1) // 9) % m
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def euler_132():
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n = 10**20
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r = 0
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for p in primes(100_000):
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if r_modulo_closed_form(n, p) == 0:
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pass
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else:
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r += p
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return r
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if __name__ == "__main__":
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solution = euler_132()
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print("e132.py: " + str(solution))
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assert solution == 453647705
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from lib_prime import primes
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from math import log, ceil
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def s(p1, p2):
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p1l = ceil(log(p1, 10))
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base = 10**p1l
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for lhs in range(base, 10**12, base):
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r = lhs + p1
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if r % p2 == 0:
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return r
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assert False
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def s2(p1, p2):
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# Invert, always invert ;)
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p1l = ceil(log(p1, 10))
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base = 10**p1l
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c = p2
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while True:
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if c % base == p1:
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return c
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c += p2
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def euler_134():
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r = 0
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ps = primes(10**6 + 10) # p1 < 10**6 but p2 is the first p > 10**6
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for i in range(2, len(ps) - 1):
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p1, p2 = ps[i], ps[i + 1]
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sc = s(p1, p2)
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r += sc
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return r
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if __name__ == "__main__":
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solution = euler_134()
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print("e134.py: " + str(solution))
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assert solution == 18613426663617118
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