gaspersic/freeCodeCamp
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

chore: manual translations (#42811)

Browse Source
This commit is contained in:
Nicholas Carrigan (he/him)
2021-07-09 21:23:54 -07:00
committed by GitHub
parent a3395269a0
commit c4fd49e5b7
806 changed files with 8935 additions and 4378 deletions
Download Patch File Download Diff File Expand all files Collapse all files

4
curriculum/challenges/italian/10-coding-interview-prep/rosetta-code/factors-of-a-mersenne-number.md
View File

@ -12,7 +12,7 @@ A Mersenne number is a number in the form of <code>2<sup>P</sup>-1</code>.
If `P` is prime, the Mersenne number may be a Mersenne prime. (If `P` is not prime, the Mersenne number is also not prime.)
In the search for Mersenne prime numbers it is advantageous to eliminate exponents by finding a small factor before starting a, potentially lengthy, [Lucas-Lehmer test](<https://rosettacode.org/wiki/Lucas-Lehmer test> "Lucas-Lehmer test").
In the search for Mersenne prime numbers it is advantageous to eliminate exponents by finding a small factor before starting a, potentially lengthy, [Lucas-Lehmer test](https://rosettacode.org/wiki/Lucas-Lehmer test "Lucas-Lehmer test").
There are very efficient algorithms for determining if a number divides <code>2<sup>P</sup>-1</code> (or equivalently, if <code>2<sup>P</sup> mod (the number) = 1</code>).
@ -48,7 +48,7 @@ Further properties of Mersenne numbers allow us to refine the process even more.
Any factor `q` of <code>2<sup>P</sup>-1</code> must be of the form `2kP+1`, `k` being a positive integer or zero. Furthermore, `q` must be `1` or `7 mod 8`.
Finally any potential factor `q` must be [prime](<https://rosettacode.org/wiki/Primality by Trial Division> "Primality by Trial Division").
Finally any potential factor `q` must be [prime](https://rosettacode.org/wiki/Primality by Trial Division "Primality by Trial Division").
As in other trial division algorithms, the algorithm stops when `2kP+1 > sqrt(N)`.These primarily tests only work on Mersenne numbers where `P` is prime. For example, <code>M<sub>4</sub>=15</code> yields no factors using these techniques, but factors into 3 and 5, neither of which fit `2kP+1`.