20211030, 15:45  #1 
Sep 2002
Database er0rr
2^{2}×3^{2}×7×17 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! 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. Last fiddled with by paulunderwood on 20220219 at 13:14 
20211030, 18:39  #2 
"Καλός"
May 2018
3×11^{2} 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? 
20211031, 10:19  #3  
Sep 2002
Database er0rr
2^{2}·3^{2}·7·17 Posts 
Quote:
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 20211031 at 10:24 

20211031, 11:52  #4  
"Καλός"
May 2018
3×11^{2} Posts 
Quote:
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 BailliePSW primality test" was deposited in arXiv in June 2021. Their email addresses are available in the pdf file, see https://arxiv.org/pdf/2006.14425.pdf. 

20211031, 12:03  #5 
Sep 2002
Database er0rr
10BC_{16} 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 20211031 at 22:57 
20211101, 09:54  #6  
Sep 2002
Database er0rr
1000010111100_{2} Posts 
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:
Last fiddled with by paulunderwood on 20211101 at 10:01 

20211103, 02:56  #7 
Sep 2002
Database er0rr
2^{2}·3^{2}·7·17 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 20211103 at 03:01 
20211104, 19:27  #8 
Sep 2002
Database er0rr
4284_{10} 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. 
20211104, 19:50  #9  
If I May
"Chris Halsall"
Sep 2002
Barbados
2×5,333 Posts 
Quote:
But, I would like to commend you for stepping forward. It's how the Scientific Method works. 

20211104, 22:11  #10  
Sep 2002
Database er0rr
2^{2}·3^{2}·7·17 Posts 
Quote:
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? 

20211104, 23:11  #11 
Dec 2012
The Netherlands
5×353 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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