(original) (raw)

p

p=2^k +/- 1
or
p=4^k +/- 3

2^p - 1 prime

(2^p + 1)/3 prime

3

yes (-1)

yes

yes

5

yes (+1)

yes

yes

7

yes (-1/+3)

yes

yes

11

no

no factor: 23

yes

13

yes (-3)

yes

yes

17

yes (+1)

yes

yes

19

yes (+3)

yes

yes

23

no

no factor: 47

yes

31

yes (-1)

yes

yes

43

no

no factor: 431

yes

61

yes (-3)

yes

yes

67

yes (+3)

no factor: 193707721

no
factor: 7327657

79

no

no factor: 2687

yes

89

no

yes

no
factor: 179

101

no

no factor: 7432339208719

yes

107

no

yes

no
factor: 643

127

yes (-1)

yes

yes

167

no

no factor: 2349023

yes

191

no

no factor: 383

yes

199

no

no factor: 164504919713

yes

257

yes (+1)

no factor: 535006138814359

no
factor: 37239639534523

313

no

no factor: 10960009

yes

347

no

no factor: 14143189112952632419639

yes

521

no

yes

no
factor: 501203

607

no

yes

no
factor: 115331

701

no

no factor: 796337

yes

1021

yes (-3)

no factor: 40841

no
factor: 10211

1279

no

yes

no
factor: 706009

1709

no

no factor: 379399

yes

2203

no

yes

no
factor: 13219

2281

no

yes

no
factor: 22811

2617

no

no factor: 78511

yes

3217

no

yes

no
factor: 7489177

3539

no

no factor: 7079

yes

4093

yes (-3)

no factor: 2397911088359

no
factor: 3732912210059

4099

yes (+3)

no factor: 73783

no
factor: 2164273

4253

no

yes

no
factor: 118071787

4423

no

yes

no
factor: 2827782322058633

5807

no

no factor: 139369

yes

8191

yes (-1)

no factor: 338193759479

no (prp test)
no factor (P-1 B1=10^10 B2=10^12)

9689

no

yes

no
factor: 19379

9941

no

yes

no
factor: 11120148512909357034073

10501

no

no factor: 2160708549249199

yes

10691

no

no factor: 21383

yes

11213

no

yes

no
factor: 181122707148161338644285289935461939

11279

no

no factor: 2198029886879

yes

12391

no

no factor: 198257

yes

14479

no

no factor: 27885728233673

yes

16381

yes (-3)

no factor: 8114899840326779533679915276470289950126585679

no
factor: 163811

19937

no

yes

no (prp test)
no factor < 2^59 (ECM t=50digits)

21701

no

yes

no
factor: 43403

23209

no

yes

no
factor: 4688219

42737

no

no factor: 542280975142237477071005102443059419300063

yes

44497

no

yes

no
factor: 2135857

65537

yes (+1)

no factor: 513668017883326358119

no
factor: 13091975735977

65539

yes (+3)

no factor: 3354489977369

no
factor: 58599599603

83339

no

no factor: 166679

yes

86243

no

yes

no
factor: 1627710365249

95369

no

no factor: 297995890279

yes

110503

no

yes

no
factor: 48832113344350037579071829046935480686609

117239

no

no no factor < 2^65 (ECM t=35digits)

yes

127031

no

no factor: 12194977

yes (prp)

131071

yes (-1)

no factor: 231733529

no
factor: 2883563

132049

no

yes

no
factor: 618913299601153

138937

no

no factor: 100068818503

yes (prp)

141079

no

no factor: 458506751

yes (prp)

216091

no

yes

no
factor: 10704103333093885136919332089553661899

262147

yes (+3)

no factor: 268179002471

no
factor: 4194353

267017

no

no factor: 1602103

yes (prp)

269987

no

no factor: 1940498230606195707774295455176153

yes (prp)

374321

no

no no factor < 2^65 (ECM t=35digits)

yes (prp)

524287

yes (+1)

no factor: 62914441

no (prp test)
no factor < 2^70

756839

no

yes

no
factor: 1640826953

859433

no

yes

no
factor: 1718867

986191

no

no no factor < 2^67 (ECM t=35digits)

yes (prp)

1048573

yes (-3)

no factor: 73400111

no (prp test)
no factor < 2^70

1257787

no

yes

no
factor: 20124593

1398269

no

yes

no
factor: 23609117451215727502931

2976221

no

yes

no
factor: 434313978089

3021377

no

yes

no
factor: 95264016811

4031399

no

no factor: 8062799

yes (prp)

4194301

yes (-3)

no factor: 2873888432993463577

no
factor: 14294177809

6972593

no

yes

no
factor: 142921867730820791335455211

13347311

no

no factor: 26694623

yes (prp)

13372531

no

no factor: 451135705817

yes (prp)

13466917

no

yes

no
factor: 781081187

15135397

no

no no factor < 2^70

yes (prp)

16777213

yes (-3)

no no factor < 2^75

no
factor: 68470872139190782171

20996011

no

yes

no
factor: 50965926368055564259063193

24036583

no

yes

no
factor: 11681779339

25964951

no

yes

no
factor: 155789707

30402457

no

yes

no (prp test)
no factor < 2^70 (ECM t=25digits)

32582657

no

yes

no
factor: 13526662966442476828963

37156667

no

yes

no
factor: 297253337

42643801

no

yes

no
factor: 405661842777846034141594389769

43112609

no

yes

no
factor: 86225219

57885161

no

yes

no
factor: 7061989643

74207281

no

yes

no (prp test)
no factor < 2^79 (ECM t=25digits)

77232917

no

yes

no
factor: 3460697185562027

82589933

no

yes

no
factor: 17973642059656480077259129

268435459

yes (+3)

no (prp test) no factor < 2^83

no
factor: 414099276471761

1073741827

yes (+3)

no
factor: 16084529043983099051873383

unknown
no factor < 2^84

2147483647

yes (-1)

no
factor: 295257526626031

unknown
no factor < 2^86

M61

yes (-1)

unknown no factor < 2^119.6 (2*220,000,000,000,000,000*M61)

no
factor: 1328165573307087715777

M127

yes (-1)

unknown no factor < 2^185 (2*145,000,000,000,000,000*M127)

no
factor:
886407410000361345663448535540258622490179142922169401