A Restricted Domain Lucas Probable Prime Test paper
 

The attached paper is distilled from several threads. So I thought I'd start a new one specifically to criticize the paper. Any corrections to typos, spelling mistakes, grammatical errors, inaccuracies, ellipsis of ideas etc will be most welcome.

I am hoping this paper is good enough to put on arXiv. What do you think to that?

Enjoy!

I have noticed it was a method due to Pomerance and not to Wagstaff in the BPSW paper. Fixed in my copy.

Also a stray ")" has been deleted in my copy.

I will refrain from a new upload until I get some feedback.

It seems that the actual reward for a counterexample of the BPSW test was $30 but not $620, see [URL]https://en.wikipedia.org/wiki/Baillie%E2%80%93PSW_primality_test[/URL].

Concerning the use of an indefinite article, shouldn't it be "an LPRP test" instead of "a LPRP test" because even though 'L' is a consonant, the actual pronunciation 'eL' in the abbreviation starts with a vowel?

[QUOTE=Dobri;592076]It seems that the actual reward for a counterexample of the BPSW test was $30 but not $620, see [URL]https://en.wikipedia.org/wiki/Baillie%E2%80%93PSW_primality_test[/URL].

Concerning the use of an indefinite article, shouldn't it be "an LPRP test" instead of "a LPRP test" because even though 'L' is a consonant, the actual pronunciation 'eL' in the abbreviation starts with a vowel?[/QUOTE]

According to [URL="http://openproblemgarden.org/op/counterexamples_to_the_baillie_psw_primality_test"]this[/URL] it is a $620 prize for a counterexample, but also for a proof that none exist.

Along with many other changes, I have made it read "an LPRP". Thanks.

The paper in the OP is updated.

[QUOTE=paulunderwood;592114]According to [URL="http://openproblemgarden.org/op/counterexamples_to_the_baillie_psw_primality_test"]this[/URL] it is a $620 prize for a counterexample, but also for a proof that none exist.[/QUOTE]
It seems that the $620 reward is concerned with the PSW conjecture but not the BPSW conjecture, see [URL]https://en.wikipedia.org/wiki/John_Selfridge#Selfridge's_Conjecture_about_Primality_Testing[/URL].
Perhaps it would be appropriate to ask Baillie and Wagstaff about this matter.
An article by Robert Baillie, Andrew Fiori, and Samuel S. Wagstaff, Jr. entitled "Strengthening the Baillie-PSW primality test" was deposited in arXiv in June 2021. Their e-mail addresses are available in the pdf file, see [URL]https://arxiv.org/pdf/2006.14425.pdf[/URL].

Thanks again. This academic point has been corrected in my copy to be the paltry $30. A cheque for it would be worth more!

The paper is finished as far as I am concerned, but feedback from others might make me develop it more.

In the lastest upload I have added the sentence:

[QUOTE]For example, for an average 100 digit base 2 Fermat pseudoprime the chance of finding it pseudoprime for the Lucas
component of the test is, by extrapolation, reduced by a factor of about 10^80.6 over a linear method of choosing parameters, such as is calculated for the BPSW test.[/QUOTE]

I have moderated my outlandish claims. "Test Results" of the paper has been rewritten. I show now that a few GCDs is equivalent to two Euler PRP tests! At least in effect. Of course a few GCDs can be computed way quicker than a couple of EPRP tests.

The new paper is uploaded in post #1.

I have made my arguments clearer, but I am still unsure about my premise and of my analysis in "Test Results".

The latest incarnation is uploaded in post #1.

[QUOTE=paulunderwood;592444]I have made my arguments clearer, but I am still unsure about my premise and of my analysis in "Test Results". The latest incarnation is uploaded in post #1.[/QUOTE]

I cannot offer any insight. The Maths is well beyond me.

But, I would like to commend you for stepping forward.

It's how the Scientific Method works.

[QUOTE=chalsall;592447]I cannot offer any insight. The Maths is well beyond me.

But, I would like to commend you for stepping forward.

It's how the Scientific Method works.[/QUOTE]

Thanks for those kind words.

Maybe I should just drop my analysis and present the algorithm without it. Maybe an analyst would like to write a joint author the paper. What a quandary! Intuitively I know the test is very good. But how good in comparison to BPSW?

This is not my area (as you know!) but I would say broadly speaking that you have 2 paths forward: either a mathematical proof that your method performs better or, alternatively, using formal statistical methods to show that the testing you have done is sufficient to be significant.