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47 lines
1.3 KiB
Python
47 lines
1.3 KiB
Python
"""
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The first known prime found to exceed one million digits was discovered in 1999,
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and is a Mersenne prime of the form 2**6972593 − 1; it contains exactly 2,098,960
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digits. Subsequently other Mersenne primes, of the form 2**p − 1, have been found
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which contain more digits.
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However, in 2004 there was found a massive non-Mersenne prime which contains
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2,357,207 digits: (28433 * (2 ** 7830457 + 1)).
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Find the last ten digits of this prime number.
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"""
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def solution(n: int = 10) -> str:
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"""
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Returns the last n digits of NUMBER.
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>>> solution()
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'8739992577'
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>>> solution(8)
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'39992577'
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>>> solution(1)
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'7'
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>>> solution(-1)
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Traceback (most recent call last):
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...
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ValueError: Invalid input
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>>> solution(8.3)
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Traceback (most recent call last):
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...
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ValueError: Invalid input
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>>> solution("a")
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Traceback (most recent call last):
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...
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ValueError: Invalid input
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"""
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if not isinstance(n, int) or n < 0:
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raise ValueError("Invalid input")
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MODULUS = 10**n
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NUMBER = 28433 * (pow(2, 7830457, MODULUS)) + 1
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return str(NUMBER % MODULUS)
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if __name__ == "__main__":
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from doctest import testmod
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testmod()
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print(f"{solution(10) = }")
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