A Restricted Domain Lucas Probable Prime Test paper

paulunderwood · 2021-10-30, 15:45

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!

After 103 downloads of February 2022 pre-print, I have updated the "Test Results" section.

Dobri · 2021-10-30, 18:39

It seems that the actual reward for a counterexample of the BPSW test was $30 but not $620, see https://en.wikipedia.org/wiki/Bailli...primality_test.

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?

paulunderwood · 2021-10-31, 10:19

Quote:

Originally Posted by Dobri

It seems that the actual reward for a counterexample of the BPSW test was $30 but not $620, see https://en.wikipedia.org/wiki/Bailli...primality_test.

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?

According to this 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.

Dobri · 2021-10-31, 11:52

Quote:

Originally Posted by paulunderwood

According to this it is a $620 prize for a counterexample, but also for a proof that none exist.

It seems that the $620 reward is concerned with the PSW conjecture but not the BPSW conjecture, see https://en.wikipedia.org/wiki/John_S...mality_Testing.
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 https://arxiv.org/pdf/2006.14425.pdf.

paulunderwood · 2021-10-31, 12:03

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

paulunderwood · 2021-11-01, 09:54

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.

paulunderwood · 2021-11-03, 02:56

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.

paulunderwood · 2021-11-04, 19:27

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.

chalsall · 2021-11-04, 19:50

Quote:

Originally Posted by paulunderwood

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.

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.

paulunderwood · 2021-11-04, 22:11

Quote:

Originally Posted by chalsall

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.

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?

Nick · 2021-11-04, 23:11

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.

2021-10-31, 12:03	#5
paulunderwood Sep 2002 Database er0rr 7×23×29 Posts	Thanks again. This academic point has been corrected in my copy to be the paltry $30. A cheque for it would be worth more! Last fiddled with by paulunderwood on 2021-10-31 at 22:57

2021-11-03, 02:56	#7
paulunderwood Sep 2002 Database er0rr 7·23·29 Posts	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. Last fiddled with by paulunderwood on 2021-11-03 at 03:01

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2021-10-30, 18:39	#2
Dobri "ม้าไฟ" May 2018 2·5·53 Posts	It seems that the actual reward for a counterexample of the BPSW test was $30 but not $620, see https://en.wikipedia.org/wiki/Bailli...primality_test. 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?

2021-11-04, 19:27	#8
paulunderwood Sep 2002 Database er0rr 7×23×29 Posts	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.

2021-11-04, 23:11	#11
Nick Dec 2012 The Netherlands 3452₈ Posts	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.