mersenneforum.org A Restricted Domain Lucas Probable Prime Test paper
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2021-10-30, 15:45   #1
paulunderwood

Sep 2002
Database er0rr

10001000111012 Posts
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!

After 103 downloads of February 2022 pre-print, I have updated the "Test Results" section.
Attached Files
 A_Restricted_Domain_Lucas_Probable_Prime_Test.pdf (65.4 KB, 9 views) data_10e10.txt.7z (350.1 KB, 56 views)

Last fiddled with by paulunderwood on 2022-11-09 at 02:25

 2021-10-30, 18:39 #2 Dobri   "Καλός" May 2018 23·5·11 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?
2021-10-31, 10:19   #3
paulunderwood

Sep 2002
Database er0rr

104358 Posts

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. Last fiddled with by paulunderwood on 2021-10-31 at 10:24 2021-10-31, 11:52 #4 Dobri "Καλός" May 2018 6708 Posts 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.  2021-10-31, 12:03 #5 paulunderwood Sep 2002 Database er0rr 111D16 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
2021-11-01, 09:54   #6
paulunderwood

Sep 2002
Database er0rr

13·337 Posts

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

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.

Last fiddled with by paulunderwood on 2021-11-01 at 10:01

 2021-11-03, 02:56 #7 paulunderwood     Sep 2002 Database er0rr 13·337 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
 2021-11-04, 19:27 #8 paulunderwood     Sep 2002 Database er0rr 438110 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, 19:50   #9
chalsall
If I May

"Chris Halsall"
Sep 2002

22·2,719 Posts

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.

2021-11-04, 22:11   #10
paulunderwood

Sep 2002
Database er0rr

438110 Posts

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?

 2021-11-04, 23:11 #11 Nick     Dec 2012 The Netherlands 6E516 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.

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