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