Crandall & Pomerance

Numbers · 2005-09-10, 12:16

As Crandall and Pomerance is, with good reason, plugged on this forum so often, I thought it might be useful to post this link here. You can order not just the book, but also download a free Mathematica add-on that will do all the algorithms for you.

http://www.perfsci.com/primenumbers.htm#primekit

This may already be well known, I don�t know, but I thought it might be useful.

akruppa · 2005-09-10, 12:37

Btw, afaik the 2nd edition is due soon. A few months ago Carl Pomerance told me that they were proofreading the galleys. They expected that it would be out "this summer" but apparantly there was some delay.

Alex

T.Rex · 2005-09-10, 12:52

The 2nd Edition is available now !
Tony

ET_ · 2005-09-29, 21:35

Quote:

Originally Posted by T.Rex

The 2nd Edition is available now !
Tony

Before spending 55 euros (I have the first edition), couuld someone tell me which parts have been rewritten-modified-added?

Luigi

Peter Nelson · 2005-09-29, 22:19

What's NEW in the second edition?

That's easy.

I compared the contents pages from the first and second editions.

New in the second edition are.....

4.5 The primality test of Agrawal, Kayal and Saxena (AKS test)

4.5.1 Primality testing with roots of unity
4.5.2 The complexity of Algorithm 4.5.1
4.5.3 Primality testing with Gaussian periods
4.5.4 A quartic time primality test

and

7.6.3 Fast primality-proving via elliptic curvest (fastECPP)

The rest of the contents headings are IDENTICAL.

I ORDERED SECOND EDITION MYSELF LAST FRIDAY

Cost £42.50 in UK money.

Still waiting for my order to arrive at my local bookstore.

Publisher springer website say it ships in about 3 days (Germany).

Various websites like amazon have some ability to read sample contents, chapter(s) and preface so I like what I read already.

People who already own first edition may not find it worthwhile to invest in second edition.

I liked the notes of people acknowledged and tried to see how many names I recognised :-)

Including some "Woltman" chap, whoever HE is ;-)

T.Rex · 2005-10-01, 14:16

I've ordered it.
The following Book Review (2002) describes the first version of the book in details.
I'll let you know my opinion about it.
Tony

T.Rex · 2005-10-12, 18:46

I've got it !
The day before my anniversary ! How did they know ?

I'll let you know my opinion in some days or weeks.
Tony

Peter Nelson · 2005-10-14, 01:45

My copy of second edition arrived too.

I would say that this is NOT an entry level text.

It does assume some maths knowledge such as integral notation, and eg

gcd=greatest common divisor
lcm=least common multiple

and knowing what complex/imaginary numbers are.

Fortunately my school education and some undergraduate math study had equipped me thus.

There are SOME things it does explain from foundations like definitions of what a prime is.

However they use the term "coprime" without defining what that is.

I started with "define coprime" in google search engine.

Having looked it up coprime appears to be synonymous with "mutually prime" and "relatively prime", and none of these ARE prime.

http://en.wikipedia.org/wiki/Coprime

C&P would therefore do better to define this term coprime before using it as it is relevant to their particular field and therefore may not be known to those who know general maths but are quite new to primes.

Some parts of the book I find easy to follow, whereas other parts lose me (at first reading). Perhaps they will make more sense when I re-read them.

Parts of the very first chapter confuse me! Perhaps they could gradually make it progressively harder or rearrange the chapters :-)

Nonetheless this book is a valuable resource and collects together many good and relevant things. As far as I am qualified to judge, the book appears authoritative.

Also its very up to date with the latest discoveries, records etc.

Recommended for those with the prerequisite math knowledge.

I am pleased that this book is developing my knowledge rather than being a book of things I knew already. It also is a nice reference of proofs and conjectures regarding primes.

There is a section near the end of the preface to this edition which describes the many things they have improved upon the previous edition.

ColdFury · 2005-10-14, 03:46

Coprime is a pretty standard synonym of relatively prime. I've seen it used everywhere.

Peter Nelson · 2005-10-14, 17:18

I'm just saying to present a definition wouldn't do any harm.

They bother to define "smooth".

This edition has extended and revised exercises.

The exercises and "research problems" are well worth reading through (even if one cannot attempt or fully complete them) because they hint at or describe further factual and informative results not found in the main text.

ET_ · 2005-10-14, 20:52

Quote:

Originally Posted by Peter Nelson

I'm just saying to present a definition wouldn't do any harm.

They bother to define "smooth".

I've had the same problem reading our Mersenne.org math page, and had to ask George the meaning of that word in that contest.

Luigi

2005-09-10, 12:16	#1
Numbers Jun 2005 Near Beetlegeuse 2²×97 Posts	Crandall & Pomerance As Crandall and Pomerance is, with good reason, plugged on this forum so often, I thought it might be useful to post this link here. You can order not just the book, but also download a free Mathematica add-on that will do all the algorithms for you. http://www.perfsci.com/primenumbers.htm#primekit This may already be well known, I don�t know, but I thought it might be useful.

2005-09-10, 12:37	#2
akruppa "Nancy" Aug 2002 Alexandria 2,467 Posts	Btw, afaik the 2nd edition is due soon. A few months ago Carl Pomerance told me that they were proofreading the galleys. They expected that it would be out "this summer" but apparantly there was some delay. Alex Last fiddled with by akruppa on 2005-09-10 at 12:38

2005-09-10, 12:52	#3
T.Rex Feb 2004 France 1110110000₂ Posts	2nd edition is available now ! The 2nd Edition is available now ! Tony

2005-09-29, 22:19	#5
Peter Nelson Oct 2004 23² Posts	Prime Numbers A computational perspective SECOND EDITION What's NEW in the second edition? That's easy. I compared the contents pages from the first and second editions. New in the second edition are..... 4.5 The primality test of Agrawal, Kayal and Saxena (AKS test) 4.5.1 Primality testing with roots of unity 4.5.2 The complexity of Algorithm 4.5.1 4.5.3 Primality testing with Gaussian periods 4.5.4 A quartic time primality test and 7.6.3 Fast primality-proving via elliptic curvest (fastECPP) The rest of the contents headings are IDENTICAL. I ORDERED SECOND EDITION MYSELF LAST FRIDAY Cost £42.50 in UK money. Still waiting for my order to arrive at my local bookstore. Publisher springer website say it ships in about 3 days (Germany). Various websites like amazon have some ability to read sample contents, chapter(s) and preface so I like what I read already. People who already own first edition may not find it worthwhile to invest in second edition. I liked the notes of people acknowledged and tried to see how many names I recognised :-) Including some "Woltman" chap, whoever HE is ;-)

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2005-10-01, 14:16	#6
T.Rex Feb 2004 France 2⁴×59 Posts	I've ordered it. The following Book Review (2002) describes the first version of the book in details. I'll let you know my opinion about it. Tony

2005-10-12, 18:46	#7
T.Rex Feb 2004 France 2⁴×59 Posts	I've got it ! The day before my anniversary ! How did they know ? I'll let you know my opinion in some days or weeks. Tony

2005-10-14, 01:45	#8
Peter Nelson Oct 2004 1021₈ Posts	My copy of second edition arrived too. I would say that this is NOT an entry level text. It does assume some maths knowledge such as integral notation, and eg gcd=greatest common divisor lcm=least common multiple and knowing what complex/imaginary numbers are. Fortunately my school education and some undergraduate math study had equipped me thus. There are SOME things it does explain from foundations like definitions of what a prime is. However they use the term "coprime" without defining what that is. I started with "define coprime" in google search engine. Having looked it up coprime appears to be synonymous with "mutually prime" and "relatively prime", and none of these ARE prime. http://en.wikipedia.org/wiki/Coprime C&P would therefore do better to define this term coprime before using it as it is relevant to their particular field and therefore may not be known to those who know general maths but are quite new to primes. Some parts of the book I find easy to follow, whereas other parts lose me (at first reading). Perhaps they will make more sense when I re-read them. Parts of the very first chapter confuse me! Perhaps they could gradually make it progressively harder or rearrange the chapters :-) Nonetheless this book is a valuable resource and collects together many good and relevant things. As far as I am qualified to judge, the book appears authoritative. Also its very up to date with the latest discoveries, records etc. Recommended for those with the prerequisite math knowledge. I am pleased that this book is developing my knowledge rather than being a book of things I knew already. It also is a nice reference of proofs and conjectures regarding primes. There is a section near the end of the preface to this edition which describes the many things they have improved upon the previous edition.

2005-10-14, 03:46	#9
ColdFury Aug 2002 101000000₂ Posts	Coprime is a pretty standard synonym of relatively prime. I've seen it used everywhere.

2005-10-14, 17:18	#10
Peter Nelson Oct 2004 23² Posts	I'm just saying to present a definition wouldn't do any harm. They bother to define "smooth". This edition has extended and revised exercises. The exercises and "research problems" are well worth reading through (even if one cannot attempt or fully complete them) because they hint at or describe further factual and informative results not found in the main text.