Prime Time Tactics—Sieve Tweaks and Boosters
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors
The Authors present a detailed description and analysis of all fundamental algorithms for sieving prime numbers. The paper is well written and can be interested for many readers. I read it with a pleasure, at least the general parts. The subject is, in spite of reservations of the Authors themselves, quite actual and living. However, my impression is that this kind of research shifted from a regular scientific debate to some circles of passionates and computer fans.
I am not able to check technical details in so short time (all the more so that part of them is out of my expertise) but my overall impression is rather good.
My suggestion is to change the label from "article" to "review". Although the paper contains some novel material (and I am not so sure whether similar computations appeared somewhere earlier) but its main merit and value is in a comprehensive account of historical and technical aspects of existing algorithms.
Also, the paper seems to be too long. In some places, especially in technical appendices it could be made more concise.
Conclusions are... doubled. Please the unnecessary repetition.
Comments on the Quality of English Language
I am not a native speaker, so I do not have any specific remarks (not obvious issues detected) but a general style of the paper is a little bit strage to me, too bold in a sense. It would be good to if a native speaker in the role of a technical editor see it and check its correctness.
Author Response
Thank you very much for your thoughtful review!
Comments 1: Conclusions are doubled. Please the unnecessary repetition.
Response 1: Fixed
Comments 2: My impression is that this kind of research shifted from a regular scientific debate to some circles of passionates and computer fans.
Response 2: We totally agree, and we also stated this in our systematic review published earlier in this journal. I added a paragraph in the introduction to emphasize this idea.
Comments 3: Change the label from "article" to "review"
Response 3: We tend to agree, and we believe this is a decision best left to the Editor.
Reviewer 2 Report
Comments and Suggestions for Authors
See pdf file
Comments for author File: 
Comments.pdf
Author Response
Thank you very much for your thoughtful review!
Comment 1: Introduction and Reference list could be wider.
Response 1: Agree. We will add more details in the introduction, which will include additional references. We will also incorporate more references in the main body of the paper.
Comment 2: Text of Conclusions is repeated twice
Response 2: We shall correct the repetition there.
Reviewer 3 Report
Comments and Suggestions for Authors
Please see the report attached.
Comments for author File: Comments.pdf
Author Response
Thank you very much for your thoughtful review!
Comments 1: In Conclusion, 15 lines are repeated and are to be removed.
Response 1: Fixed
Comments 2: Give the original terms for many short-hands. E.g., Sieve of Atkin (SoA) or SISD (Single Instruction, Single Data), SIMD, GPGPU, GPU.
Response 2: Added complete terms at the first occurrence of the term.
Reviewer 4 Report
Comments and Suggestions for Authors
In the paper under review, the authors seek to make a contribution by giving a diverse compilation of general modifications and boosters targeted at rejuvenating prime sieving approaches, based upon years of intensive study and testing. They reveal a wide range of tactics intended to improve the effectiveness, precision, and scalability of prime sieving algorithms. These adjustments and boosters represent a synthesis of new findings and old wisdom, providing useful direction for researchers as well as practitioners. They do this by drawing on a wealth of rediscovered knowledge and refined sieving algorithms, techniques, and optimizations. Overall, the content of the paper seems to be interesting and publishable. The following are my suggestions to improve the paper:
Line 27, write complete form of "COVID".
Line 28, write complete form of "GPGPU".
Lines 34-35, "we tested our mettle"?
Line 51, write complete form of "SIMD".
Line 97, "like this" -> "like the following". Similar change is suggested on Line 162.
Lines 180-181, the sentence "the pattern will repeat every..."needs to be revised.
Figure 3, is there any function different from 1/x that can be used here? If yes, it should be pointed out in the text.
Lines 530-532, some text of the code goes outside the margin.
Conclusion: Of the six paragraphs, every paragraph is repeated twice.
Author Response
Thank you very much for your thoughtful review!
Comments 1: Line 27, write complete form of "COVID".
Response 1: Rephrased and replaced with “pandemic”
Comments 2: Line 28, write complete form of "GPGPU".
Response 2: Added „General-purpose computing on Graphics Processing Units” at the first occurrence.
Comments 3: Lines 34-35, "we tested our mettle"?
Response 3: Rephrased and replaced with “we measured our capabilities”
Comments 4: Line 51, write complete form of "SIMD".
Response 4: Added „ Single instruction, multiple data” at the first occurrence.
Comments 5: Line 97, "like this" -> "like the following". Similar change is suggested on Line 162.
Response 5: Modified accordingly in both places, also at lines 83, 100, 373, 557, 565.
Comments 6: Lines 180-181, the sentence "the pattern will repeat every..."needs to be revised.
Response 6: Rephrased for improved clarity.
Comments 7: Figure 3, is there any function different from 1/x that can be used here? If yes, it should be pointed out in the text.
Response 7: Added clarification in a footnote – the function is used just to give an idea of the profile of the curve; the actual function is more complex and of no particular interest here.
Comments 8: Lines 530-532, some text of the code goes outside the margin.
Response 8: Fixed everywhere.
Comments 9: Conclusion: Of the six paragraphs, every paragraph is repeated twice.
Response 9: Fixed.
Round 2
Reviewer 4 Report
Comments and Suggestions for Authors
The revised version seems to be publishable in its current form.
