Find a Book About Prime Number Distribution

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Discussion Overview

The discussion centers around recommendations for books that cover the distribution of prime numbers, exploring various texts and their levels of comprehensiveness and accessibility. Participants share their experiences with different books and express opinions on their content and difficulty.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant seeks a comprehensive book on prime number distribution.
  • Another suggests "The Distribution Of Prime Numbers" by A.E. Ingham, noting it as a good but potentially limited choice.
  • A different participant agrees on Ingham's value but emphasizes that no single book can cover "everything" about prime distribution.
  • This participant also recommends "The Prime Numbers and their distribution" by Tenenbaum et al. for a more introductory approach, along with other texts like Davenport's "Multiplicative Number Theory" and Apostol's "Introduction to Analytic Number Theory".
  • They mention "Analytic Number Theory" by Iwaniec and Kowalski as a comprehensive but challenging resource.
  • Guy's "Unsolved Problems In Number Theory" is noted for providing current results and references, though it may be discouraging to read due to its remarks on the difficulty of solving certain problems.
  • Another participant mentions enjoying "Prime Numbers: The Most Mysterious Figures in Math," comparing it to Guy's book but noting it includes both solved and unsolved topics.
  • Concerns are raised about the extensive effort in number theory yielding minimal progress towards understanding prime distribution.

Areas of Agreement / Disagreement

Participants express a range of opinions on the adequacy and accessibility of various texts, indicating that while some books are favored, there is no consensus on a single definitive resource for prime number distribution.

Contextual Notes

Participants acknowledge the limitations of individual texts and the challenges inherent in the field of number theory, particularly regarding the depth and complexity of the subject matter.

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I'm looking for a book that will do a thorough exposition of everything we know about the distribution of primes. Can anyone recommend one?
 
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'The Distribution Of Prime Numbers' - A.E.Ingham is pretty good, but then it's the only one I've used so there may be better suggestions out there..
 
I don't think there is a book that contains "everything".

Ingham's book is old, but also one of my favorites, it's a great introduction though at an advanced level. "The Prime Numbers and their distribution" by Tenenbaum, et al. is a nice book as well, more on an introductory level but still covering a good range of topics.

Almost all number theory texts beyond the "elementary" ones will have info on the distribution of primes. Davenport's "Multiplicative Number theory" and Apostols "Introduction to Analytic Number Theory" are good. "Analytic Number Theory" by Iwaniec and Kowalski is a phenomenal resource for all things related to it's title, though perhaps not the easiest to learn about a topic from scratch.

Guy's "Unsolved Problems In Number Theory" is self explanatory. It usually gives the most current results on a topic and will provide ample references.

If you plan to buy a book, you should go to the library and try to read some of it first to see if it's at an appropriate level.
 
Thanks for the suggestions. I've discovered a book called "Prime Numbers: The Most Mysterious Figures in Math" which I really like. It may sound like a popularized math book, but it's actually like "Unsolved Problems in Number Theory" by Guy, though it lists topics that are solved and unsolved. "The New Book of Prime Number Records" is pretty good too.

Guy's book is very discouraging to read. At the end of many sections, he often includes a remark like "it is unlikely that this problem will be solved within our lifetime".
 
In number theory, hundreds and thousands of pages of work can result in reducing an exponent by a minuscule amount and still you seem hopelessly distant from what is believed to be the truth.
 

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