mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-27 23:11:09 +00:00
47 lines
1.3 KiB
Python
47 lines
1.3 KiB
Python
|
"""
|
|||
|
|
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) = }")
|