"Extra strong" Lucas pseudoprime

[Arpan612]

"Extra strong" Lucas pseudoprime 2nd condition corrected

References to other Issues or PRs

Fixes #18921

Brief description of what is fixed or changed

In the cited paper "Frobenius Pseudoprimes" p. 876, the second condition on being an "extra strong" Lucas pseudoprime reads:

V_{2^ts} ≡ 0 mod n, where 0 ≤ t < r-1

When V == 0 and s == 1, by the above definition ("s" is "r" there), the number should not be declared as a pseudoprime. Hence the change is needed.

Other comments

Release Notes

• ntheory
  • Corrects the condition for "Extra strong" Lucas pseudoprime

[codecov]

Codecov Report

Merging #18946 into master will decrease coverage by 0.002%.
The diff coverage is 0%.

@@              Coverage Diff              @@
##            master    #18946       +/-   ##
=============================================
- Coverage   75.741%   75.738%   -0.003%     
=============================================
  Files          647       647               
  Lines       168584    168599       +15     
  Branches     39723     39728        +5     
=============================================
+ Hits        127688    127695        +7     
- Misses       35344     35347        +3     
- Partials      5552      5557        +5

[Arpan612]

@sylee957 Sir, could you please review the PR.

[sylee957]

I think that there is no way to make this change visible.
If s is 1, V seems like always not divisible by n. But I haven't got through how to prove this.

[Arpan612]

@sylee957 Sir, do you expect a change in PR? Or at least could you share some documents for me to explore on this issue?

[sylee957]

I think that you should squash the commits because there are more redundant commits than the code itself.

My comment above is about the difficulty to getting the counterexample that is fixed.

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• ntheory
  • Corrects the condition for "Extra strong" Lucas pseudoprime (#18946 by @Arpan612 and @sylee957)

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<!-- Your title above should be a short description of what
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"Extra strong" Lucas pseudoprime 2nd condition corrected
#### References to other Issues or PRs
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Fixes #18921 

#### Brief description of what is fixed or changed
In the cited paper "Frobenius Pseudoprimes" p. 876, the second condition on being an "extra strong" Lucas pseudoprime reads:

V_{2^ts} ≡ 0 mod n, where 0 ≤ t < r-1

When V == 0 and s == 1, by the above definition ("s" is "r" there), the number should not be declared as a pseudoprime. Hence the change is needed.

#### Other comments


#### Release Notes

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<!-- BEGIN RELEASE NOTES -->
* ntheory
   * Corrects the condition for "Extra strong" Lucas pseudoprime
<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

[czgdp1807]

I have cleared the commits. Just make some minor changes so that your name is recorded as well in the git history.

[czgdp1807]

Is there any test case that can be added for this fix?

[Arpan612]

@czgdp1807 Sir, could you please tell me how did you manage the squash commit? My attempt was continuously showing compatibility issues.

[Arpan612]

@czgdp1807 Sir, I have added the test cases.

[mohitacecode]

you have to add test in test_primetest.py file.

[mohitacecode]

This is not how you should write test take a look at test_primetest.py you will get it.

[Arpan612]

@mohitacecode Got it. Working on it.

[Arpan612]

@sylee957 @czgdp1807 Could you please review the changes?

[Arpan612]

@sylee957 Thank you for the correction.