Lehmer-Ramanujan Numbers

Ν. Λυγερός

Lehmer-Ramanujan Numbers

N. Lygeros, O. Rozier

Odd prime values of the Ramanujan tau function in The Ramanujan Journal , 15/03/2013– Pdf

LR Data.

|2cos(theta(p))|
p
q
size
primality

good/bad
numbers

Discovery
Program
Date
Contributors
TimeTotal 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
pp
very good (11)
LR Giant
1.403115
739
2503
39475
pp
LR Giant
0.266890
463
2753
40347
pp
LR Giant
1.631383
461
3019
44215
pp
LR Giant
0.165452
199
4519
57125
pp
good
LR Super Giant
1.829136
877
3617
58531
pp
LR Super Giant
1.644580
857
3847
62042
pp
LR Super Giant
0.890722
409
4423
63520
pp
LR Super Giant
1.393695
79
6317
65920
pp
LR Super Giant
0.661184
839
4177
67153
pp
very good (17)
LR Super Giant
0.944962
59
8971
87365
pp
very good (11)
LR Super Giant
0.568639
809
6029
96410
pp
LR Super Giant
0.890666
223
9431
121795
pp
LR Hyper Giant
1.462783
317
10331
142098
pp
LR Hyper Giant
1.918814
103
14939
165374
pp
LR Hyper Giant
0.109065
643
11689
180524
prp
LR Hyper Giant
0.395585
373
15187
214796
prp
LR Hyper Giant
0.972080
311
15787
216429
pp
LR Hyper Giant
0.972080
311
16453
225560
pp
LR Hyper Giant
0.415345
41
28289
250924
pp
very good (19)
LR Hyper Giant
0.798883
971
15739
258571
pp
good
LR Hyper Giant
0.111250
509
18947
282048
pp
LR Hyper Giant
0.004564
907
20849
339132
pp
LR Hyper Giant
0.768786
863
24631
397727
pp
LR Hyper Giant
1.696603
631
32371
498503
pp
LR Hyper Giant
1.452000
773
34961
555339
pp
LR Hyper Giant
0.268015
881
38993
631568
pp
LR Hyper Giant
0.413262
983
38933
640784
pp
LR Hyper Giant
0.854653
151
56087
672156
pp
LR Hyper Giant
0.381386
181
72559
900969
prp
LR Hyper Giant
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