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changed documentation of isprime(n::Integer) -> Bool #147

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Nov 15, 2023
Merged

changed documentation of isprime(n::Integer) -> Bool #147

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changed documentation of isprime(n::Integer) -> Bool
fepaul Nov 15, 2023
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fepaul Nov 15, 2023
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13 changes: 11 additions & 2 deletions src/Primes.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -156,8 +156,14 @@ end
"""
isprime(n::Integer) -> Bool

Returns `true` if `n` is prime, and `false` otherwise.

Returns for values in the range of an INT64 variable: `true` if `n` is prime, and `false` otherwise
for bigger values: `true` if `n` is probably prime, and `false` otherwise (false-positive rate = 0.25^reps with reps=25 --> considerered safe)

More detailed:
for even numbers: returns deterministic and correct results
for values in the range of an INT64 variable: returns deterministic and correct results (by Lookup-tables, trial-division, Miller-Rabin, Lucas-Test)
for bigger values: returns probabilistic resultsfrom GNU Multiple Precision Arithmetic Library

```julia
julia> isprime(3)
true
Expand Down Expand Up @@ -290,6 +296,9 @@ end
Probabilistic primality test. Returns `true` if `x` is prime with high probability (pseudoprime);
and `false` if `x` is composite (not prime). The false positive rate is about `0.25^reps`.
`reps = 25` is considered safe for cryptographic applications (Knuth, Seminumerical Algorithms).

is_probably_prime is inherited from the module IntegerMathUtils that provides a wrapper to access
functionality from the GNU Multiple Precision Arithmetic Library (GMP) library
```julia
julia> isprime(big(3))
true
Expand Down