Issue #16468 has been updated by steveb3210 (Stephen Blackstone).

Dan0042 (Daniel DeLorme) wrote in #note-15:
> I think it would be interesting to expose the algorithm for larger numbers. So you could have `miller_rabin` which allows any integer, and `prime?` which checks the value and either call `miller_rabin` or raise ArgumentError.

Unforunately Miller-Rabin is not a deterministic test for arbitrarily large n - its only the work in the paper https://arxiv.org/pdf/1509.00864.pdf that allows us to provide functionality up to a bound.

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Feature #16468: Switch to Miller-Rabin for Prime.prime?
https://bugs.ruby-lang.org/issues/16468#change-84330

* Author: steveb3210 (Stephen Blackstone)
* Status: Open
* Priority: Normal
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The miller-rabin algorithm is a non-deterministic primality test, however it is known that below 2**64, you can always get a deterministic answer by only checking a=[2,3,5,7,11,13,17,19,23, 29, 31, 37]

Given that Prime.prime? would never respond in a reasonable amount of time for larger numbers, we can gain much more utility and performance by  switching..

```
user     system      total        real
miller_rabin: random set                   0.150000   0.000000   0.150000 (  0.152212)
Prime.prime?: random set                   0.270000   0.000000   0.270000 (  0.281257)

user     system      total        real
miller_rabin: 16 digits                    0.010000   0.000000   0.010000 (  0.000300)
Prime.prime? 16 digits                     2.200000   0.020000   2.220000 (  2.368247)

user     system      total        real
miller_rabin: 2-10000                      0.030000   0.000000   0.030000 (  0.035752)
Prime.prime? 2-10000                       0.020000   0.000000   0.020000 (  0.022948)

---Files--------------------------------
patch_with_argument_error_and_tests.diff (2.17 KB)

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