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I. Introduction to the ShortTables . . . . . . . . . . . . . . . . . . xi

II. Convenient Short Tables

Short 2􀀀: 2n 􀀀 1; n_400 . . . . . . . . . . . . . . . . xiii

Short 2+ : 2n + 1; n_400 . . . . . . . . . . . . . . . . xxiv

Short 10􀀀: 10n 􀀀 1; n_150 . . . . . . . . . . . . . . . xxxv

Short 10+ : 10n + 1; n_150 . . . . . . . . . . . . . . . . . xl

III. Introduction to the Main Tables

A. The Cunningham-Woodall Tables and Their Inuence|

The Cunningham Project . . . . . . . . . . . . . . . . . . xlv

B. Developments Contributing to the Present Tables

1. Developments inTechnology . . . . . . . . . . . . . . . . xlvii

2. Developments inFactorization . . . . . . . . . . . . . . . . . lv

3. Developments in Primality Testing

(a)TheTheory . . . . . . . . . . . . . . . . . . . . . . lix

(b)ThePrograms . . . . . . . . . . . . . . . . . . . . . lxv

(c)TheProofSummaries . . . . . . . . . . . . . . . . . . lxvi

C. Multiplicative Structure of bn _ 1

1. Algebraic andPrimitiveFactors . . . . . . . . . . . . . . lxviii

2. Aurifeuillian Factorizations . . . . . . . . . . . . . . . . . lxix

D.Acknowledgements . . . . . . . . . . . . . . . . . . . . . lxxiii

E.References . . . . . . . . . . . . . . . . . . . . . . . . lxxiv

IV.Update to the Introduction for the SecondEdition . . . . . . . . lxxix

A. Developments Contributing to the Second Edition

1. Developments inTechnology . . . . . . . . . . . . . . . . lxxx

2. Developments inFactorization . . . . . . . . . . . . . . . lxxxi

3. Developments inPrimalityTesting . . . . . . . . . . . . . lxxxiv

B.Acknowledgements for the SecondEdition . . . . . . . . . . lxxxv

C.References for the SecondEdition . . . . . . . . . . . . . . lxxxvi

CONTENTS x

V.Update to the Introduction for theThirdEdition . . . . . . . . . lxxxix

A. Developments Contributing to the Third Edition

1. Developments inTechnology . . . . . . . . . . . . . . . lxxxix

2. Developments inFactorization . . . . . . . . . . . . . . . . . xc

3. Developments inPrimalityTesting . . . . . . . . . . . . . . xci

B. Status of theProject and of ImportantFactorizations . . . . . . xcii

C.Acknowledgements for theThirdEdition . . . . . . . . . . . . xcvi

D.References for theThirdEdition . . . . . . . . . . . . . . . xcviii

VI.HowtoUse theMainTables . . . . . . . . . . . . . . . . . . . c

VII. The Main Tables

2n 􀀀 1 n odd n < 1200 . . . . . . . . . . . . . . . . . . . 1

2n + 1 n odd n < 1200 . . . . . . . . . . . . . . . . . . 14

2n + 1 n = 4k 􀀀 2 n < 2400 L, M . . . . . . . . . . . . . . 27

2n + 1 n = 4k n_ 1200 . . . . . . . . . . . . . . . . . . 53

3n 􀀀 1 n odd n <540 . . . . . . . . . . . . . . . . . . 60

3n + 1 n _ 540 L, M for n = 6k 􀀀 3 _ 1077 . . . . 66

5n 􀀀 1 n odd n < 375 L, M for n = 10k 􀀀 5 _745 . . . . 86

5n + 1 n _375 . . . . . . . . . . . . . . . . . . 94

6n 􀀀 1 n odd n <330 . . . . . . . . . . . . . . . . . . 102

6n + 1 n _ 330 L, M for n = 12k 􀀀 6 _654 . . . . 106

7n 􀀀 1 n odd n <300 . . . . . . . . . . . . . . . . . . 116

7n + 1 n _ 300 L, M for n = 14k 􀀀 7 _595 . . . . 120

10n 􀀀 1 n odd n <330 . . . . . . . . . . . . . . . . . . 129

10n + 1 n _ 330 L, M for n = 20k 􀀀 10 _650 . . . . 133

11n 􀀀 1 n odd n <240 . . . . . . . . . . . . . . . . . . 142

11n + 1 n _ 240 L, M for n = 22k 􀀀 11 _473 . . . . 145

12n 􀀀 1 n odd n <240 . . . . . . . . . . . . . . . . . . 152

12n + 1 n _ 240 L, M for n = 6k 􀀀 3 _477 . . . . . 155

VIII. Introduction to theAppendices . . . . . . . . . . . . . . . . . 165

A.Primes andProbablePrimes . . . . . . . . . . . . . . . . . 167

B.PrimalityProofSummaries . . . . . . . . . . . . . . . . . . 189

C.CompositeCofactors . . . . . . . . . . . . . . . . . . . . . 235

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