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.
Zeta5Irrational
.
Table
.
U56
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Imports
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LeanPool.Zeta5Irrational.Table.UpperCertificate
Imported by
Zeta5Irrational
.
U_676_1
Zeta5Irrational
.
U_676_2
Zeta5Irrational
.
U_676_3
Zeta5Irrational
.
U_676_4
Zeta5Irrational
.
U_676_5
Zeta5Irrational
.
U_676_6
Zeta5Irrational
.
U_676_7
Zeta5Irrational
.
U_676_8
Zeta5Irrational
.
U_676_9
Zeta5Irrational
.
U_676_10
Zeta5Irrational
.
U_676_11
Zeta5Irrational
.
U_676_12
Zeta5Irrational
.
U_676_13
Zeta5Irrational
.
U_676_14
Zeta5Irrational
.
U_676_15
Zeta5Irrational
.
U_676_16
Zeta5Irrational
.
U_676
Zeta5Irrational
.
U_677_1
Zeta5Irrational
.
U_677_2
Zeta5Irrational
.
U_677_3
Zeta5Irrational
.
U_677_4
Zeta5Irrational
.
U_677_5
Zeta5Irrational
.
U_677_6
Zeta5Irrational
.
U_677_7
Zeta5Irrational
.
U_677_8
Zeta5Irrational
.
U_677_9
Zeta5Irrational
.
U_677_10
Zeta5Irrational
.
U_677_11
Zeta5Irrational
.
U_677_12
Zeta5Irrational
.
U_677_13
Zeta5Irrational
.
U_677_14
Zeta5Irrational
.
U_677_15
Zeta5Irrational
.
U_677_16
Zeta5Irrational
.
U_677
Zeta5Irrational
.
U_678_1
Zeta5Irrational
.
U_678_2
Zeta5Irrational
.
U_678_3
Zeta5Irrational
.
U_678_4
Zeta5Irrational
.
U_678_5
Zeta5Irrational
.
U_678_6
Zeta5Irrational
.
U_678_7
Zeta5Irrational
.
U_678_8
Zeta5Irrational
.
U_678_9
Zeta5Irrational
.
U_678_10
Zeta5Irrational
.
U_678_11
Zeta5Irrational
.
U_678_12
Zeta5Irrational
.
U_678_13
Zeta5Irrational
.
U_678_14
Zeta5Irrational
.
U_678_15
Zeta5Irrational
.
U_678_16
Zeta5Irrational
.
U_678
Zeta5Irrational
.
U_679_1
Zeta5Irrational
.
U_679_2
Zeta5Irrational
.
U_679_3
Zeta5Irrational
.
U_679_4
Zeta5Irrational
.
U_679_5
Zeta5Irrational
.
U_679_6
Zeta5Irrational
.
U_679_7
Zeta5Irrational
.
U_679_8
Zeta5Irrational
.
U_679_9
Zeta5Irrational
.
U_679_10
Zeta5Irrational
.
U_679_11
Zeta5Irrational
.
U_679_12
Zeta5Irrational
.
U_679_13
Zeta5Irrational
.
U_679_14
Zeta5Irrational
.
U_679_15
Zeta5Irrational
.
U_679_16
Zeta5Irrational
.
U_679
Zeta5Irrational
.
U_680_1
Zeta5Irrational
.
U_680_2
Zeta5Irrational
.
U_680_3
Zeta5Irrational
.
U_680_4
Zeta5Irrational
.
U_680_5
Zeta5Irrational
.
U_680_6
Zeta5Irrational
.
U_680_7
Zeta5Irrational
.
U_680_8
Zeta5Irrational
.
U_680_9
Zeta5Irrational
.
U_680_10
Zeta5Irrational
.
U_680_11
Zeta5Irrational
.
U_680_12
Zeta5Irrational
.
U_680_13
Zeta5Irrational
.
U_680_14
Zeta5Irrational
.
U_680_15
Zeta5Irrational
.
U_680_16
Zeta5Irrational
.
U_680
Zeta5Irrational
.
U_681_1
Zeta5Irrational
.
U_681_2
Zeta5Irrational
.
U_681_3
Zeta5Irrational
.
U_681_4
Zeta5Irrational
.
U_681_5
Zeta5Irrational
.
U_681_6
Zeta5Irrational
.
U_681_7
Zeta5Irrational
.
U_681_8
Zeta5Irrational
.
U_681_9
Zeta5Irrational
.
U_681_10
Zeta5Irrational
.
U_681_11
Zeta5Irrational
.
U_681_12
Zeta5Irrational
.
U_681_13
Zeta5Irrational
.
U_681_14
Zeta5Irrational
.
U_681_15
Zeta5Irrational
.
U_681_16
Zeta5Irrational
.
U_681
Zeta5Irrational
.
U_682_1
Zeta5Irrational
.
U_682_2
Zeta5Irrational
.
U_682_3
Zeta5Irrational
.
U_682_4
Zeta5Irrational
.
U_682_5
Zeta5Irrational
.
U_682_6
Zeta5Irrational
.
U_682_7
Zeta5Irrational
.
U_682_8
Zeta5Irrational
.
U_682_9
Zeta5Irrational
.
U_682_10
Zeta5Irrational
.
U_682_11
Zeta5Irrational
.
U_682_12
Zeta5Irrational
.
U_682_13
Zeta5Irrational
.
U_682_14
Zeta5Irrational
.
U_682_15
Zeta5Irrational
.
U_682_16
Zeta5Irrational
.
U_682
Zeta5Irrational
.
U_683_1
Zeta5Irrational
.
U_683_2
Zeta5Irrational
.
U_683_3
Zeta5Irrational
.
U_683_4
Zeta5Irrational
.
U_683_5
Zeta5Irrational
.
U_683_6
Zeta5Irrational
.
U_683_7
Zeta5Irrational
.
U_683_8
Zeta5Irrational
.
U_683_9
Zeta5Irrational
.
U_683_10
Zeta5Irrational
.
U_683_11
Zeta5Irrational
.
U_683_12
Zeta5Irrational
.
U_683_13
Zeta5Irrational
.
U_683_14
Zeta5Irrational
.
U_683_15
Zeta5Irrational
.
U_683_16
Zeta5Irrational
.
U_683
Zeta5Irrational
.
U_684_1
Zeta5Irrational
.
U_684_2
Zeta5Irrational
.
U_684_3
Zeta5Irrational
.
U_684_4
Zeta5Irrational
.
U_684_5
Zeta5Irrational
.
U_684_6
Zeta5Irrational
.
U_684_7
Zeta5Irrational
.
U_684_8
Zeta5Irrational
.
U_684_9
Zeta5Irrational
.
U_684_10
Zeta5Irrational
.
U_684_11
Zeta5Irrational
.
U_684_12
Zeta5Irrational
.
U_684_13
Zeta5Irrational
.
U_684_14
Zeta5Irrational
.
U_684_15
Zeta5Irrational
.
U_684_16
Zeta5Irrational
.
U_684
Certified arcsine potential bounds (U56)
#
source
theorem
Zeta5Irrational
.
U_676_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
7226461069683
/
8000000000000
)
≤
-
(
108859842802811722997
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_676_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
7226461069683
/
8000000000000
)
≤
-
(
223049730527027750149
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_676_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
7226461069683
/
8000000000000
)
≤
-
(
1168711495788115444963
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_676_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
7226461069683
/
8000000000000
)
≤
-
(
628991572116585160863
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_676_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
7226461069683
/
8000000000000
)
≤
-
(
55802843000971698371
/
400000000000000000000
)
source
theorem
Zeta5Irrational
.
U_676_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
7226461069683
/
8000000000000
)
≤
-
(
398517382703400588829
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_676_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
7226461069683
/
8000000000000
)
≤
-
(
1870052209910470026807
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_676_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
7226461069683
/
8000000000000
)
≤
-
(
1118883342221099544697
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_676_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
7226461069683
/
8000000000000
)
≤
-
(
2710035841923158558309
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_676_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
7226461069683
/
8000000000000
)
≤
-
(
3295663745591862291993
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_676_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
7226461069683
/
8000000000000
)
≤
-
(
999108980076215164303
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_676_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
7226461069683
/
8000000000000
)
≤
-
(
4802404152764222826933
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_676_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
7226461069683
/
8000000000000
)
≤
-
(
2842013848850894396079
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_676_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
7226461069683
/
8000000000000
)
≤
-
(
6579422346950211503277
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_676_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
7226461069683
/
8000000000000
)
≤
-
(
7377973537692901902479
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_676_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
7226461069683
/
8000000000000
)
≤
-
(
7917178800593945107141
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_676
:
Uρ
(
7226461069683
/
8000000000000
)
≤
-
(
352383937996564167861
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_677_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
30159206983063
/
32000000000000
)
≤
-
(
82643010106364090371
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_677_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
30159206983063
/
32000000000000
)
≤
-
(
85834148424330625231
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_677_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
30159206983063
/
32000000000000
)
≤
-
(
368936939244914093781
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_677_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
30159206983063
/
32000000000000
)
≤
-
(
82332884107747569223
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_677_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
30159206983063
/
32000000000000
)
≤
-
(
477229023155082316277
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_677_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
30159206983063
/
32000000000000
)
≤
-
(
1144589866729602112133
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_677_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
30159206983063
/
32000000000000
)
≤
-
(
1407832126127480045027
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_677_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
30159206983063
/
32000000000000
)
≤
-
(
1757720990443800197271
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_677_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
30159206983063
/
32000000000000
)
≤
-
(
2205550341869910017897
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_677_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
30159206983063
/
32000000000000
)
≤
-
(
2758186921991172196263
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_677_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
30159206983063
/
32000000000000
)
≤
-
(
426875502031516809391
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_677_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
30159206983063
/
32000000000000
)
≤
-
(
4163275610179741765353
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_677_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
30159206983063
/
32000000000000
)
≤
-
(
4971061494768781944211
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_677_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
30159206983063
/
32000000000000
)
≤
-
(
2888495107361552193757
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_677_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
30159206983063
/
32000000000000
)
≤
-
(
810002854756473131841
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_677_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
30159206983063
/
32000000000000
)
≤
-
(
434015474906195459093
/
625000000000000000000
)
source
theorem
Zeta5Irrational
.
U_677
:
Uρ
(
30159206983063
/
32000000000000
)
≤
-
(
2318547818050359873459
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_678_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
15706284843697
/
16000000000000
)
≤
-
(
31401869492385685679
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_678_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
15706284843697
/
16000000000000
)
≤
-
(
275713462460201346549
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_678_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
15706284843697
/
16000000000000
)
≤
-
(
20302229308895077003
/
625000000000000000000
)
source
theorem
Zeta5Irrational
.
U_678_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
15706284843697
/
16000000000000
)
≤
-
(
81357388672044063251
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_678_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
15706284843697
/
16000000000000
)
≤
-
(
532453962168235848837
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_678_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
15706284843697
/
16000000000000
)
≤
-
(
357237988318402216991
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_678_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
15706284843697
/
16000000000000
)
≤
-
(
966103549437018389189
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_678_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
15706284843697
/
16000000000000
)
≤
-
(
1299819252231914866819
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_678_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
15706284843697
/
16000000000000
)
≤
-
(
172562545086624586799
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_678_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
15706284843697
/
16000000000000
)
≤
-
(
2248820499400769661627
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_678_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
15706284843697
/
16000000000000
)
≤
-
(
286694897106712835459
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_678_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
15706284843697
/
16000000000000
)
≤
-
(
44567725956253433693
/
125000000000000000000
)
source
theorem
Zeta5Irrational
.
U_678_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
15706284843697
/
16000000000000
)
≤
-
(
4311189061635353508999
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_678_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
15706284843697
/
16000000000000
)
≤
-
(
504471450642891062021
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_678_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
15706284843697
/
16000000000000
)
≤
-
(
1134783711466407468651
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_678_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
15706284843697
/
16000000000000
)
≤
-
(
1520695928810576621543
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_678
:
Uρ
(
15706284843697
/
16000000000000
)
≤
-
(
92343274023702849147
/
500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_679_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
4239911887007
/
4000000000000
)
≤
32589570407983029189
/
625000000000000000000
source
theorem
Zeta5Irrational
.
U_679_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
4239911887007
/
4000000000000
)
≤
99752968003727494617
/
2000000000000000000000
source
theorem
Zeta5Irrational
.
U_679_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
4239911887007
/
4000000000000
)
≤
226665678130179312083
/
5000000000000000000000
source
theorem
Zeta5Irrational
.
U_679_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
4239911887007
/
4000000000000
)
≤
75518162225807609173
/
2000000000000000000000
source
theorem
Zeta5Irrational
.
U_679_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
4239911887007
/
4000000000000
)
≤
261587752722163667687
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_679_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
4239911887007
/
4000000000000
)
≤
23468035726243644037
/
2500000000000000000000
source
theorem
Zeta5Irrational
.
U_679_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
4239911887007
/
4000000000000
)
≤
-
(
17169293930414594967
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_679_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
4239911887007
/
4000000000000
)
≤
-
(
13838695655646965701
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_679_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
4239911887007
/
4000000000000
)
≤
-
(
4152692092358634187
/
50000000000000000000
)
source
theorem
Zeta5Irrational
.
U_679_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
4239911887007
/
4000000000000
)
≤
-
(
325854264266228926319
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_679_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
4239911887007
/
4000000000000
)
≤
-
(
928275361804200092781
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_679_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
4239911887007
/
4000000000000
)
≤
-
(
98932252879129752837
/
400000000000000000000
)
source
theorem
Zeta5Irrational
.
U_679_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
4239911887007
/
4000000000000
)
≤
-
(
1560256889330704127261
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_679_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
4239911887007
/
4000000000000
)
≤
-
(
748717128402485919173
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_679_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
4239911887007
/
4000000000000
)
≤
-
(
2132701068385280181461
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_679_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
4239911887007
/
4000000000000
)
≤
-
(
2298623924628737086939
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_679
:
Uρ
(
4239911887007
/
4000000000000
)
≤
-
(
976182167040415310791
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_680_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
18213010252359
/
16000000000000
)
≤
1238640559424707941031
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_680_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
18213010252359
/
16000000000000
)
≤
121754804071227033031
/
1000000000000000000000
source
theorem
Zeta5Irrational
.
U_680_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
18213010252359
/
16000000000000
)
≤
117528797438582498587
/
1000000000000000000000
source
theorem
Zeta5Irrational
.
U_680_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
18213010252359
/
16000000000000
)
≤
17263797762555920119
/
156250000000000000000
source
theorem
Zeta5Irrational
.
U_680_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
18213010252359
/
16000000000000
)
≤
49858176718355945399
/
500000000000000000000
source
theorem
Zeta5Irrational
.
U_680_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
18213010252359
/
16000000000000
)
≤
841668503982988491161
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_680_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
18213010252359
/
16000000000000
)
≤
125556082777140847159
/
2000000000000000000000
source
theorem
Zeta5Irrational
.
U_680_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
18213010252359
/
16000000000000
)
≤
34611624805998184127
/
1000000000000000000000
source
theorem
Zeta5Irrational
.
U_680_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
18213010252359
/
16000000000000
)
≤
-
(
9759515284691867981
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_680_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
18213010252359
/
16000000000000
)
≤
-
(
441205039158688405329
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_680_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
18213010252359
/
16000000000000
)
≤
-
(
235459762249886509823
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_680_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
18213010252359
/
16000000000000
)
≤
-
(
186784175247454332741
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_680_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
18213010252359
/
16000000000000
)
≤
-
(
2066466640027391588759
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_680_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
18213010252359
/
16000000000000
)
≤
-
(
521780271597462009859
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_680_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
18213010252359
/
16000000000000
)
≤
-
(
3055850814904569992253
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_680_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
18213010252359
/
16000000000000
)
≤
-
(
834040341612878975103
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_680
:
Uρ
(
18213010252359
/
16000000000000
)
≤
-
(
185691588642492027487
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_681_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
1946637295669
/
1600000000000
)
≤
381566729181073695513
/
2000000000000000000000
source
theorem
Zeta5Irrational
.
U_681_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
1946637295669
/
1600000000000
)
≤
944056028915092092057
/
5000000000000000000000
source
theorem
Zeta5Irrational
.
U_681_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
1946637295669
/
1600000000000
)
≤
1848611035360319879371
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_681_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
1946637295669
/
1600000000000
)
≤
44570985859756852759
/
250000000000000000000
source
theorem
Zeta5Irrational
.
U_681_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
1946637295669
/
1600000000000
)
≤
210287390033879084137
/
1250000000000000000000
source
theorem
Zeta5Irrational
.
U_681_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
1946637295669
/
1600000000000
)
≤
38434103813816542803
/
250000000000000000000
source
theorem
Zeta5Irrational
.
U_681_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
1946637295669
/
1600000000000
)
≤
1338393787175108167323
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_681_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
1946637295669
/
1600000000000
)
≤
538549030281882261609
/
5000000000000000000000
source
theorem
Zeta5Irrational
.
U_681_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
1946637295669
/
1600000000000
)
≤
748204042513207311507
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_681_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
1946637295669
/
1600000000000
)
≤
351480511177384359847
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_681_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
1946637295669
/
1600000000000
)
≤
-
(
26459032811501839539
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_681_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
1946637295669
/
1600000000000
)
≤
-
(
151566259945222584619
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_681_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
1946637295669
/
1600000000000
)
≤
-
(
1119336165660419824783
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_681_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
1946637295669
/
1600000000000
)
≤
-
(
800052579600481050621
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_681_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
1946637295669
/
1600000000000
)
≤
-
(
1991591901709806684277
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_681_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
1946637295669
/
1600000000000
)
≤
-
(
1117370294237785446319
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_681
:
Uρ
(
1946637295669
/
1600000000000
)
≤
539206832017378636869
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_682_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
2746637295669
/
2000000000000
)
≤
1562609017187395006033
/
5000000000000000000000
source
theorem
Zeta5Irrational
.
U_682_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
2746637295669
/
2000000000000
)
≤
621553036055481657661
/
2000000000000000000000
source
theorem
Zeta5Irrational
.
U_682_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
2746637295669
/
2000000000000
)
≤
768206569321752291863
/
2500000000000000000000
source
theorem
Zeta5Irrational
.
U_682_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
2746637295669
/
2000000000000
)
≤
3014704537217327050923
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_682_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
2746637295669
/
2000000000000
)
≤
585197835390417916143
/
2000000000000000000000
source
theorem
Zeta5Irrational
.
U_682_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
2746637295669
/
2000000000000
)
≤
1399192462686000616281
/
5000000000000000000000
source
theorem
Zeta5Irrational
.
U_682_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
2746637295669
/
2000000000000
)
≤
40996380119763539301
/
156250000000000000000
source
theorem
Zeta5Irrational
.
U_682_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
2746637295669
/
2000000000000
)
≤
2395479286330499915887
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_682_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
2746637295669
/
2000000000000
)
≤
2109866511084314583863
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_682_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
2746637295669
/
2000000000000
)
≤
1768087379828123108613
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_682_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
2746637295669
/
2000000000000
)
≤
1378108348866220666213
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_682_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
2746637295669
/
2000000000000
)
≤
956720482436799679737
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_682_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
2746637295669
/
2000000000000
)
≤
531080877900712560969
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_682_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
2746637295669
/
2000000000000
)
≤
34680649393365873701
/
2500000000000000000000
source
theorem
Zeta5Irrational
.
U_682_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
2746637295669
/
2000000000000
)
≤
-
(
175689130303678076623
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_682_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
2746637295669
/
2000000000000
)
≤
-
(
368491277579048029599
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_682
:
Uρ
(
2746637295669
/
2000000000000
)
≤
1832301135489243993659
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_683_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
6746637295669
/
4000000000000
)
≤
648647470165495546441
/
1250000000000000000000
source
theorem
Zeta5Irrational
.
U_683_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
6746637295669
/
4000000000000
)
≤
646873916084388180027
/
1250000000000000000000
source
theorem
Zeta5Irrational
.
U_683_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
6746637295669
/
4000000000000
)
≤
5146608484439031249377
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_683_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
6746637295669
/
4000000000000
)
≤
637431915769893316069
/
1250000000000000000000
source
theorem
Zeta5Irrational
.
U_683_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
6746637295669
/
4000000000000
)
≤
15711355649568528379
/
31250000000000000000
source
theorem
Zeta5Irrational
.
U_683_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
6746637295669
/
4000000000000
)
≤
1231163739354149495203
/
2500000000000000000000
source
theorem
Zeta5Irrational
.
U_683_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
6746637295669
/
4000000000000
)
≤
4784372414919632677529
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_683_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
6746637295669
/
4000000000000
)
≤
1150527614874777660297
/
2500000000000000000000
source
theorem
Zeta5Irrational
.
U_683_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
6746637295669
/
4000000000000
)
≤
4375967434278497798067
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_683_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
6746637295669
/
4000000000000
)
≤
4108233282580037516371
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_683_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
6746637295669
/
4000000000000
)
≤
761357075335845670987
/
2000000000000000000000
source
theorem
Zeta5Irrational
.
U_683_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
6746637295669
/
4000000000000
)
≤
139448290184602758597
/
400000000000000000000
source
theorem
Zeta5Irrational
.
U_683_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
6746637295669
/
4000000000000
)
≤
3168189274869361871549
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_683_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
6746637295669
/
4000000000000
)
≤
288054402101994101473
/
1000000000000000000000
source
theorem
Zeta5Irrational
.
U_683_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
6746637295669
/
4000000000000
)
≤
1327044432574458074269
/
5000000000000000000000
source
theorem
Zeta5Irrational
.
U_683_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
6746637295669
/
4000000000000
)
≤
2517089256916817378273
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_683
:
Uρ
(
6746637295669
/
4000000000000
)
≤
991641173695049392639
/
2500000000000000000000
source
theorem
Zeta5Irrational
.
U_684_1
:
Uω
(
aρ
1
)
(
bρ
1
)
2
≤
431197938622519678389
/
625000000000000000000
source
theorem
Zeta5Irrational
.
U_684_2
:
Uω
(
aρ
2
)
(
bρ
2
)
2
≤
1721803564318625397281
/
2500000000000000000000
source
theorem
Zeta5Irrational
.
U_684_3
:
Uω
(
aρ
3
)
(
bρ
3
)
2
≤
3431657896680287743107
/
5000000000000000000000
source
theorem
Zeta5Irrational
.
U_684_4
:
Uω
(
aρ
4
)
(
bρ
4
)
2
≤
6823648472170288821807
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_684_5
:
Uω
(
aρ
5
)
(
bρ
5
)
2
≤
6763315653946060878467
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_684_6
:
Uω
(
aρ
6
)
(
bρ
6
)
2
≤
333849709093393011791
/
500000000000000000000
source
theorem
Zeta5Irrational
.
U_684_7
:
Uω
(
aρ
7
)
(
bρ
7
)
2
≤
3279879678491493456121
/
5000000000000000000000
source
theorem
Zeta5Irrational
.
U_684_8
:
Uω
(
aρ
8
)
(
bρ
8
)
2
≤
6408070500101273547501
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_684_9
:
Uω
(
aρ
9
)
(
bρ
9
)
2
≤
3110439556119279087301
/
5000000000000000000000
source
theorem
Zeta5Irrational
.
U_684_10
:
Uω
(
aρ
10
)
(
bρ
10
)
2
≤
6000773764786687711391
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_684_11
:
Uω
(
aρ
11
)
(
bρ
11
)
2
≤
5755005827102536483859
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_684_12
:
Uω
(
aρ
12
)
(
bρ
12
)
2
≤
1099230232572658765387
/
2000000000000000000000
source
theorem
Zeta5Irrational
.
U_684_13
:
Uω
(
aρ
13
)
(
bρ
13
)
2
≤
2621030225880535406049
/
5000000000000000000000
source
theorem
Zeta5Irrational
.
U_684_14
:
Uω
(
aρ
14
)
(
bρ
14
)
2
≤
250733810854960598567
/
500000000000000000000
source
theorem
Zeta5Irrational
.
U_684_15
:
Uω
(
aρ
15
)
(
bρ
15
)
2
≤
2418686312017971573191
/
5000000000000000000000
source
theorem
Zeta5Irrational
.
U_684_16
:
Uω
(
aρ
16
)
(
bρ
16
)
2
≤
4730867613563951102639
/
10000000000000000000000
source
theorem
Zeta5Irrational
.
U_684
:
Uρ
2
≤
1138744120442109294651
/
2000000000000000000000