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Old 2021-10-30, 15:45   #1
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Arrow 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.
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File Type: pdf A_Restricted_Domain_Lucas_Probable_Prime_Test.pdf (64.0 KB, 23 views)

Last fiddled with by paulunderwood on 2021-11-20 at 13:54
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Old 2021-10-30, 18:39   #2
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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?
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Old 2021-10-31, 10:19   #3
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Quote:
Originally Posted by Dobri View Post
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.

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Old 2021-10-31, 11:52   #4
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Quote:
Originally Posted by paulunderwood View Post
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.
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Old 2021-10-31, 12:03   #5
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Thanks again. This academic point has been corrected in my copy to be the paltry $30. A cheque for it would be worth more!

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Old 2021-11-01, 09:54   #6
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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.

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Old 2021-11-03, 02:56   #7
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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.

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Old 2021-11-04, 19:27   #8
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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.
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Old 2021-11-04, 19:50   #9
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Quote:
Originally Posted by paulunderwood View Post
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.
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Old 2021-11-04, 22:11   #10
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Quote:
Originally Posted by chalsall View Post
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?
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Old 2021-11-04, 23:11   #11
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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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