Lehmer-Ramanujan Numbers
Ν. Λυγερός
Lehmer-Ramanujan Numbers
N. Lygeros, O. Rozier
|2cos(theta(p))|
|
p
|
q
|
size
|
primality
|
good/bad |
Discovery
|
Program
|
Date
|
Contributors
|
Time | Total CPU time |
0.822567
|
251
|
3
|
26
|
P
|
very bad (13)
|
Lehmer 01
|
1965
|
Lehmer
|
|||
0.381879
|
677
|
3
|
32
|
P
|
–
|
LR 02
|
2011
|
LR
|
|||
0.798883
|
971
|
3
|
33
|
P
|
bad
|
LR 03
|
2011
|
||||
0.413262
|
983
|
3
|
33
|
P
|
bad
|
LR 04
|
2011
|
||||
1.709172
|
47
|
5
|
37
|
P
|
very good (11)
|
LR 05
|
2011
|
||||
0.690618
|
197
|
5
|
50
|
P
|
–
|
LR 06
|
2011
|
||||
0.149742
|
227
|
11
|
130
|
P
|
bad
|
LR 07
|
2011
|
||||
0.962083
|
379
|
11
|
142
|
P
|
–
|
LR 08
|
2011
|
||||
1.600770
|
829
|
11
|
161
|
P
|
–
|
LR 09
|
2011
|
||||
1.229474
|
607
|
13
|
184
|
P
|
–
|
LR 10
|
2011
|
||||
1.099902
|
761
|
13
|
190
|
P
|
–
|
LR 11
|
2011
|
||||
1.162514
|
29
|
31
|
242
|
P
|
–
|
LR 12
|
2011
|
||||
0.716263
|
281
|
19
|
243
|
P
|
–
|
LR 13
|
2011
|
||||
0.084978
|
439
|
29
|
407
|
P
|
–
|
LR 14
|
2011
|
||||
1.709172
|
47
|
47
|
424
|
P
|
–
|
LR 15
|
2011
|
||||
1.216486
|
947
|
41
|
654
|
P
|
–
|
LR 16
|
2011
|
||||
1.162514
|
29
|
83
|
660
|
P
|
–
|
LR 17
|
2011
|
||||
0.508967
|
811
|
43
|
671
|
P
|
bad
|
LR 18
|
2011
|
||||
1.153966
|
613
|
47
|
706
|
P
|
very bad (17)
|
LR 19
|
2011
|
||||
0.474429
|
89
|
73
|
772
|
P
|
very good (29)
|
LR 20
|
2011
|
||||
0.642521
|
401
|
59
|
831
|
P
|
–
|
LR 21
|
2011
|
||||
1.747589
|
937
|
59
|
949
|
P
|
–
|
LR 22
|
2011
|
||||
0.314073
|
977
|
59
|
954
|
P
|
–
|
LR 23
|
2011
|
||||
1.452457
|
773
|
67
|
1049
|
P
|
–
|
LR Titan 24
|
gp
|
2011
|
|||
0.701505
|
503
|
73
|
1070
|
P
|
very good (29)
|
LR Titan 25
|
gp
|
2011
|
|||
1.561722
|
787
|
73
|
1147
|
P
|
–
|
LR Titan 26
|
gp
|
2011
|
|||
0.466280
|
173
|
103
|
1256
|
P
|
–
|
LR Titan 27
|
gp
|
2011
|
|||
0.630563
|
421
|
89
|
1271
|
P
|
–
|
LR Titan 28
|
gp
|
2011
|
|||
0.890666
|
223
|
101
|
1292
|
P
|
–
|
LR Titan 29
|
gp
|
2011
|
|||
0.592221
|
239
|
107
|
1387
|
P
|
–
|
LR Titan 30
|
gp
|
2011
|
|||
0.148174
|
557
|
109
|
1631
|
P
|
–
|
LR Titan 31
|
gp
|
2011
|
|||
1.000872
|
11
|
317
|
1810
|
P
|
very bad (11)
|
LR Titan 32
|
gp
|
2011
|
|||
1.162514
|
29
|
229
|
1834
|
P
|
–
|
LR Titan 33
|
gp
|
2011
|
|||
0.434747
|
113
|
197
|
2214
|
P
|
good
|
LR Titan 34
|
gp
|
2011
|
|||
0.568639
|
809
|
149
|
2367
|
P
|
very good (11)
|
LR Titan 35
|
gp
|
2011
|
|||
0.765198
|
491
|
167
|
2457
|
P
|
–
|
LR Titan 36
|
gp
|
2011
|
|||
1.179650
|
17
|
433
|
2924
|
P
|
–
|
LR Titan 37
|
gp
|
2011
|
|||
0.241885
|
353
|
239
|
3335
|
P
|
–
|
LR Titan 38
|
gp
|
2011
|
|||
0.886942
|
97
|
331
|
3606
|
P
|
–
|
LR Titan 39
|
gp
|
2011
|
31h
|
||
0.890666
|
223
|
281
|
3617
|
P
|
–
|
LR Titan 40
|
gp
|
2011
|
32h
|
||
0.268015
|
881
|
241
|
3888
|
P
|
very good (11)
|
LR Titan 41
|
primo
|
16/04/2013
|
Gérasimos
|
29h
|
59h
|
0.268015
|
881
|
251
|
4050
|
P
|
–
|
LR Titan 42
|
primo
|
16/04/2013
|
Neoklis
|
29h
|
29h
|
0.457445
|
109
|
373
|
4169
|
P
|
–
|
LR Titan 43
|
primo
|
16/04/2013
|
Olivier
|
11h
|
46h
|
0.630563
|
421
|
317
|
4561
|
P
|
–
|
LR Titan 44
|
primo
|
17/04/2013
|
Neoklis
|
21h
|
41h
|
1.541981
|
941
|
349
|
5692
|
P
|
good
|
LR Titan 45
|
primo
|
28/04/2013
|
Gérasimos
|
||
0.265111
|
349
|
409
|
5706
|
P
|
–
|
LR Titan 46
|
primo
|
19/04/2013
|
Olivier
|
44h
|
174h
|
0.363777
|
487
|
479
|
7066
|
P
|
–
|
LR Titan 47
|
primo
|
25/04/2013
|
Neoklis
|
7d
|
13d
|
0.798883
|
971
|
433
|
7098
|
P
|
very bad (11)
|
LR Titan 48
|
primo
|
20/05/2013
|
Dimitris
|
||
1.583644
|
449
|
547
|
7965
|
P
|
–
|
LR Titan 49
|
primo
|
23/05/2013
|
Olivier
|
5d
|
35d
|
1.649726
|
953
|
557
|
9111
|
P
|
good
|
LR Titan 50
|
primo
|
05/08/2013
|
Theodora
|
||
0.886942
|
97
|
887
|
9682
|
P
|
–
|
LR Titan 51
|
primo
|
26/05/2013
|
Keira
|
||
1.644580
|
857
|
683
|
11002
|
P
|
–
|
LR Giant 52
|
primo
|
20/07/2013
|
Socratis
|
||
0.944962
|
59
|
1381
|
13441
|
P
|
very good (11)
|
LR Giant 53
|
primo
|
12/10/2013
|
Gérasimos
|
83d
|
326d
|
0.109065
|
643
|
953
|
14703
|
P
|
–
|
LR Giant 54
|
FastECPP
|
01/02/2011
|
François
|
13d
|
313d+42d
|
1.153966
|
613
|
1013
|
15515
|
P
|
–
|
LR Giant 55
|
primo
|
02/09/2014
|
Kostas/Keira
|
||
0.822567
|
251
|
1193
|
15733
|
P
|
very bad (11)
|
LR Giant 56
|
FastECPP
|
12/03/2018
|
François
|
123d
|
22d
|
1.323747
|
673
|
1019
|
15834
|
P
|
–
|
LR Giant 57
|
primo
|
19/06/2013
|
Patrice
|
30d
|
892d
|
1.393695
|
79
|
1571
|
16386
|
P
|
–
|
LR Giant 58
|
primo
|
07/02/2014
|
Gérasimos
|
||
0.987446
|
571
|
1091
|
16526
|
P
|
–
|
LR Giant 59
|
primo
|
05/12/2013
|
Dimitris
|
||
1.441636
|
587
|
1093
|
16629
|
P
|
good
|
LR Giant 60
|
primo
|
24/05/2018
|
Philippe & Pierre
|
||
0.026114
|
821
|
1163
|
18626
|
P
|
LR Giant 61
|
primo
|
04/07/2014
|
Keira
|
|||
1.868850
|
619
|
1297
|
19900
|
P
|
very good (17)
|
LR Giant 62
|
primo
|
07/08/2014
|
Patrice
|
||
0.415345
|
41
|
2297
|
20367
|
P
|
very bad (11)
|
LR Giant 63
|
FastECPP
|
06/04/2018
|
François
|
24d
|
321d+53d
|
1.333141
|
257
|
1699
|
22506
|
P
|
–
|
LR Giant 64
|
primo
|
23/04/2014
|
Patrice
|
180d
|
4573d
|
0.663405
|
691
|
1523
|
23770
|
P
|
–
|
LR Giant 65
|
primo
|
27/02/2014
|
André, Philippe & Pierre
|
238d
|
7179d
|
1.100312
|
157
|
2207
|
26643
|
P
|
–
|
LR Giant 66
|
FastECPP
|
03/04/2011
|
François
|
59d
|
1963d+392d
|
0.879617
|
331
|
2129
|
29492
|
P
|
–
|
LR Giant 67
|
primo
|
15/09/2015
|
André, Philippe & Pierre
|
559d
|
17888d
|
1.709172
|
47
|
4177
|
38404
|
P
|
very good (11)
|
LR Giant
|
ECPP
|
23/06/2022
|
Andreas Enge
|
||
1.403115
|
739
|
2503
|
39475
|
pp
|
–
|
LR Giant
|
|||||
0.266890
|
463
|
2753
|
40347
|
pp
|
–
|
LR Giant
|
|||||
1.631383
|
461
|
3019
|
44215
|
pp
|
–
|
LR Giant
|
2011
|
||||
0.165452
|
199
|
4519
|
57125
|
P
|
good
|
LR Super Giant
|
ECPP
|
09/09/2022
|
Andreas Enge
|
||
1.829136
|
877
|
3617
|
58531
|
pp
|
–
|
LR Super Giant
|
2011
|
||||
1.644580
|
857
|
3847
|
62042
|
pp
|
–
|
LR Super Giant
|
2011
|
||||
0.890722
|
409
|
4423
|
63520
|
pp
|
–
|
LR Super Giant
|
2011
|
||||
1.393695
|
79
|
6317
|
65920
|
pp
|
–
|
LR Super Giant
|
2011
|
||||
0.661184
|
839
|
4177
|
67153
|
pp
|
very good (17)
|
LR Super Giant
|
2011
|
||||
0.944962
|
59
|
8971
|
87365
|
pp
|
very good (11)
|
LR Super Giant
|
2011
|
||||
0.568639
|
809
|
6029
|
96410
|
pp
|
–
|
LR Super Giant
|
2013 | ||||
0.890666
|
223
|
9431
|
121795
|
pp
|
–
|
LR Hyper Giant
|
2011
|
||||
1.462783
|
317
|
10331
|
142098
|
pp
|
–
|
LR Hyper Giant
|
2013 | ||||
1.918814
|
103
|
14939
|
165374
|
pp
|
–
|
LR Hyper Giant
|
2013
|
||||
0.109065
|
643
|
11689
|
180524
|
prp
|
–
|
LR Hyper Giant
|
2015 | ||||
0.395585
|
373
|
15187
|
214796
|
prp
|
–
|
LR Hyper Giant
|
2013 | ||||
0.972080
|
311
|
15787
|
216429
|
pp
|
–
|
LR Hyper Giant
|
2013 | ||||
0.972080
|
311
|
16453 |
225560
|
pp
|
–
|
LR Hyper Giant
|
2013 | ||||
0.415345
|
41
|
28289
|
250924
|
pp
|
very good (19)
|
LR Hyper Giant
|
2011 | ||||
0.798883
|
971
|
15739
|
258571
|
pp
|
good
|
LR Hyper Giant
|
2015 | ||||
0.111250
|
509
|
18947
|
282048
|
pp
|
–
|
LR Hyper Giant
|
2015
|
||||
0.004564
|
907
|
20849
|
339132
|
pp
|
–
|
LR Hyper Giant
|
2016
|
||||
0.768786
|
863
|
24631
|
397727
|
pp
|
–
|
LR Hyper Giant
|
2015
|
||||
1.696603
|
631
|
32371
|
498503
|
pp
|
–
|
LR Hyper Giant
|
2015 | ||||
1.452000
|
773
|
34961
|
555339
|
pp
|
–
|
LR Hyper Giant
|
2015 | ||||
0.268015
|
881
|
38993
|
631568
|
pp
|
–
|
LR Hyper Giant
|
2015 | ||||
0.413262
|
983
|
38933
|
640784
|
pp
|
–
|
LR Hyper Giant
|
2016 | ||||
0.854653
|
151
|
56087
|
672156
|
pp
|
–
|
LR Hyper Giant
|
2017 | ||||
1.24075
|
229
|
63499
|
824146
|
prp
|
–
|
LR Hyper Giant
|
2020 | ||||
0.381386
|
181
|
72559
|
900969
|
prp
|
–
|
LR Hyper Giant
|
2018 |