mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-24 12:10:16 +00:00
44254cf112
* Rename all Project Euler directories: Reason: The change was done to maintain consistency throughout the directory and to keep all directories in sorted order. Due to the above change, some config files had to be modified: 'problem_22` -> `problem_022` * Update scripts to pad zeroes in PE directories
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) = }")
|