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.
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.
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Zeta5Irrational
.
U_136_1
Zeta5Irrational
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U_136_2
Zeta5Irrational
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U_136_3
Zeta5Irrational
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U_136_4
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U_136_5
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U_136_6
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U_136_7
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U_136_8
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U_136_9
Zeta5Irrational
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U_136_10
Zeta5Irrational
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U_136_11
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U_136_12
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U_136_13
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U_136_14
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U_136_15
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U_136_16
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U_136
Zeta5Irrational
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U_137_1
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U_137_2
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U_137_3
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U_137_4
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U_137_5
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U_137_6
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U_137_7
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U_137_8
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U_137_9
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U_137_10
Zeta5Irrational
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U_137_11
Zeta5Irrational
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U_137_12
Zeta5Irrational
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U_137_13
Zeta5Irrational
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U_137_14
Zeta5Irrational
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U_137_15
Zeta5Irrational
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U_137_16
Zeta5Irrational
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U_137
Zeta5Irrational
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U_138_1
Zeta5Irrational
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U_138_2
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U_138_3
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U_138_4
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U_138_5
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U_138_6
Zeta5Irrational
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U_138_7
Zeta5Irrational
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U_138_8
Zeta5Irrational
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U_138_9
Zeta5Irrational
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U_138_10
Zeta5Irrational
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U_138_11
Zeta5Irrational
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U_138_12
Zeta5Irrational
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U_138_13
Zeta5Irrational
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U_138_14
Zeta5Irrational
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U_138_15
Zeta5Irrational
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U_138_16
Zeta5Irrational
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U_138
Zeta5Irrational
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U_139_1
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U_139_2
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U_139_3
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U_139_4
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U_139_5
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U_139_6
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U_139_7
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U_139_8
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U_139_9
Zeta5Irrational
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U_139_10
Zeta5Irrational
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U_139_11
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U_139_12
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U_139_13
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U_139_14
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U_139_15
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U_139_16
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U_139
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U_140_1
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U_140_2
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U_140_3
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U_140_4
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U_140_5
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U_140_6
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U_140_7
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U_140_8
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U_140_9
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U_140_10
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U_140_11
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U_140_12
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U_140_13
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U_140_14
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U_140_15
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U_140_16
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U_140
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U_141_1
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U_141_2
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U_141_3
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U_141_4
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U_141_5
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U_141_6
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U_141_7
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U_141_8
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U_141_9
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U_141_10
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U_141_11
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U_141_12
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U_141_13
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U_141_14
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U_141_15
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U_141_16
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U_141
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U_142_1
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U_142_2
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U_142_3
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U_142_4
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U_142_5
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U_142_6
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U_142_7
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U_142_8
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U_142_9
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U_142_10
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U_142_11
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U_142_12
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U_142_13
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U_142_14
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U_142
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U_143_1
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U_143_2
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U_143_3
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U_143_4
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U_143_5
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U_143_6
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U_143_7
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U_143_8
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U_143_9
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U_143_10
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U_143_11
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U_143_12
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U_143_13
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U_143_14
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U_143
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U_144_1
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U_144_2
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U_144_3
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U_144_4
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U_144_6
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U_144
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U_145_1
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U_145_2
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U_145_3
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U_145
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U_146_1
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U_146_2
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U_146
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U_147_1
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U_147_3
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U_147
Certified arcsine potential bounds (U11)
#
source
theorem
Zeta5Irrational
.
U_136_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
257805414251
/
3200000000000
)
≤
-
(
26024389347350076319563
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_136_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
257805414251
/
3200000000000
)
≤
-
(
26368086404189464320953
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_136_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
257805414251
/
3200000000000
)
≤
-
(
3389297048001651951123
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_136_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
257805414251
/
3200000000000
)
≤
-
(
7147172329350315520741
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_136_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
257805414251
/
3200000000000
)
≤
-
(
31984033130623965837531
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_136_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
257805414251
/
3200000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_136_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
257805414251
/
3200000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_136_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
257805414251
/
3200000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_136_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
257805414251
/
3200000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_136_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
257805414251
/
3200000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_136_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
257805414251
/
3200000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_136_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
257805414251
/
3200000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_136_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
257805414251
/
3200000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_136_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
257805414251
/
3200000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_136_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
257805414251
/
3200000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_136_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
257805414251
/
3200000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_136
:
Uρ
(
257805414251
/
3200000000000
)
≤
-
(
24683602313731326949681
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_137_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
2611684090831
/
32000000000000
)
≤
-
(
25883504479644690843899
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_137_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
2611684090831
/
32000000000000
)
≤
-
(
5244411439855569471477
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_137_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
2611684090831
/
32000000000000
)
≤
-
(
26956144140679057589663
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_137_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
2611684090831
/
32000000000000
)
≤
-
(
1136048455279144140469
/
400000000000000000000
)
source
theorem
Zeta5Irrational
.
U_137_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
2611684090831
/
32000000000000
)
≤
-
(
15841971990601673642843
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_137_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
2611684090831
/
32000000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_137_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
2611684090831
/
32000000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_137_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
2611684090831
/
32000000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_137_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
2611684090831
/
32000000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_137_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
2611684090831
/
32000000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_137_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
2611684090831
/
32000000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_137_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
2611684090831
/
32000000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_137_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
2611684090831
/
32000000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_137_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
2611684090831
/
32000000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_137_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
2611684090831
/
32000000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_137_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
2611684090831
/
32000000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_137
:
Uρ
(
2611684090831
/
32000000000000
)
≤
-
(
12319697019856429271619
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_138_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
165332127447
/
2000000000000
)
≤
-
(
25744578028657117086197
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_138_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
165332127447
/
2000000000000
)
≤
-
(
3259767267427656465799
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_138_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
165332127447
/
2000000000000
)
≤
-
(
3350052051316778232639
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_138_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
165332127447
/
2000000000000
)
≤
-
(
14108699468577326473109
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_138_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
165332127447
/
2000000000000
)
≤
-
(
627911566201869230741
/
200000000000000000000
)
source
theorem
Zeta5Irrational
.
U_138_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
165332127447
/
2000000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_138_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
165332127447
/
2000000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_138_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
165332127447
/
2000000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_138_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
165332127447
/
2000000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_138_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
165332127447
/
2000000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_138_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
165332127447
/
2000000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_138_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
165332127447
/
2000000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_138_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
165332127447
/
2000000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_138_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
165332127447
/
2000000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_138_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
165332127447
/
2000000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_138_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
165332127447
/
2000000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_138
:
Uρ
(
165332127447
/
2000000000000
)
≤
-
(
4919279757412061629749
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_139_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
2678943987473
/
32000000000000
)
≤
-
(
25607556263304084967409
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_139_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
2678943987473
/
32000000000000
)
≤
-
(
3242033609723343368109
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_139_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
2678943987473
/
32000000000000
)
≤
-
(
5329422790878437414709
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_139_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
2678943987473
/
32000000000000
)
≤
-
(
350463796210277297691
/
125000000000000000000
)
source
theorem
Zeta5Irrational
.
U_139_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
2678943987473
/
32000000000000
)
≤
-
(
15558937803900991527783
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_139_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
2678943987473
/
32000000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_139_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
2678943987473
/
32000000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_139_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
2678943987473
/
32000000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_139_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
2678943987473
/
32000000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_139_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
2678943987473
/
32000000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_139_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
2678943987473
/
32000000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_139_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
2678943987473
/
32000000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_139_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
2678943987473
/
32000000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_139_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
2678943987473
/
32000000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_139_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
2678943987473
/
32000000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_139_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
2678943987473
/
32000000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_139
:
Uρ
(
2678943987473
/
32000000000000
)
≤
-
(
3069316120527173883389
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_140_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
1356286967897
/
16000000000000
)
≤
-
(
25472387635023400139573
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_140_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
1356286967897
/
16000000000000
)
≤
-
(
12898195814616624135193
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_140_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
1356286967897
/
16000000000000
)
≤
-
(
26496161287310828503139
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_140_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
1356286967897
/
16000000000000
)
≤
-
(
217657707718408659519
/
78125000000000000000
)
source
theorem
Zeta5Irrational
.
U_140_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
1356286967897
/
16000000000000
)
≤
-
(
30849926669156202687773
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_140_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
1356286967897
/
16000000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_140_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
1356286967897
/
16000000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_140_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
1356286967897
/
16000000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_140_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
1356286967897
/
16000000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_140_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
1356286967897
/
16000000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_140_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
1356286967897
/
16000000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_140_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
1356286967897
/
16000000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_140_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
1356286967897
/
16000000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_140_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
1356286967897
/
16000000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_140_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
1356286967897
/
16000000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_140_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
1356286967897
/
16000000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_140
:
Uρ
(
1356286967897
/
16000000000000
)
≤
-
(
12256854110596322856331
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_141_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
694958458109
/
8000000000000
)
≤
-
(
1260370690780799325851
/
500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_141_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
694958458109
/
8000000000000
)
≤
-
(
3190299248545577399671
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_141_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
694958458109
/
8000000000000
)
≤
-
(
3275127593940399875157
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_141_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
694958458109
/
8000000000000
)
≤
-
(
13757985990762632792871
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_141_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
694958458109
/
8000000000000
)
≤
-
(
30340243654537166784837
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_141_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
694958458109
/
8000000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_141_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
694958458109
/
8000000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_141_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
694958458109
/
8000000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_141_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
694958458109
/
8000000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_141_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
694958458109
/
8000000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_141_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
694958458109
/
8000000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_141_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
694958458109
/
8000000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_141_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
694958458109
/
8000000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_141_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
694958458109
/
8000000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_141_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
694958458109
/
8000000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_141_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
694958458109
/
8000000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_141
:
Uρ
(
694958458109
/
8000000000000
)
≤
-
(
24434952955612677719747
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_142_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
1423546864539
/
16000000000000
)
≤
-
(
3118660448249061296987
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_142_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
1423546864539
/
16000000000000
)
≤
-
(
12627864479779576637511
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_142_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
1423546864539
/
16000000000000
)
≤
-
(
25914457472574753600061
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_142_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
1423546864539
/
16000000000000
)
≤
-
(
217470394859432947223
/
80000000000000000000
)
source
theorem
Zeta5Irrational
.
U_142_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
1423546864539
/
16000000000000
)
≤
-
(
7465335220405714049317
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_142_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
1423546864539
/
16000000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_142_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
1423546864539
/
16000000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_142_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
1423546864539
/
16000000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_142_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
1423546864539
/
16000000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_142_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
1423546864539
/
16000000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_142_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
1423546864539
/
16000000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_142_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
1423546864539
/
16000000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_142_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
1423546864539
/
16000000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_142_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
1423546864539
/
16000000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_142_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
1423546864539
/
16000000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_142_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
1423546864539
/
16000000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_142
:
Uρ
(
1423546864539
/
16000000000000
)
≤
-
(
12179839953679917785211
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_143_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
72858840643
/
800000000000
)
≤
-
(
4939530432806504756481
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_143_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
72858840643
/
800000000000
)
≤
-
(
12498006527585179078093
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_143_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
72858840643
/
800000000000
)
≤
-
(
25635980836800211611331
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_143_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
72858840643
/
800000000000
)
≤
-
(
26862818505948193076349
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_143_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
72858840643
/
800000000000
)
≤
-
(
3676145772901062746707
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_143_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
72858840643
/
800000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_143_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
72858840643
/
800000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_143_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
72858840643
/
800000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_143_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
72858840643
/
800000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_143_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
72858840643
/
800000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_143_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
72858840643
/
800000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_143_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
72858840643
/
800000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_143_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
72858840643
/
800000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_143_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
72858840643
/
800000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_143_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
72858840643
/
800000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_143_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
72858840643
/
800000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_143
:
Uρ
(
72858840643
/
800000000000
)
≤
-
(
189746280053298967991
/
78125000000000000000
)
source
theorem
Zeta5Irrational
.
U_144_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
762218354751
/
8000000000000
)
≤
-
(
24212631311087841507319
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_144_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
762218354751
/
8000000000000
)
≤
-
(
24496038767204679231087
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_144_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
762218354751
/
8000000000000
)
≤
-
(
25101527446924252214789
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_144_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
762218354751
/
8000000000000
)
≤
-
(
13125734602345873881497
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_144_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
762218354751
/
8000000000000
)
≤
-
(
28572647461235244444859
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_144_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
762218354751
/
8000000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_144_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
762218354751
/
8000000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_144_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
762218354751
/
8000000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_144_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
762218354751
/
8000000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_144_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
762218354751
/
8000000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_144_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
762218354751
/
8000000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_144_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
762218354751
/
8000000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_144_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
762218354751
/
8000000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_144_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
762218354751
/
8000000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_144_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
762218354751
/
8000000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_144_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
762218354751
/
8000000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_144
:
Uρ
(
762218354751
/
8000000000000
)
≤
-
(
6037851914004356594239
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_145_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
24870259471
/
250000000000
)
≤
-
(
5937514892280973947171
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_145_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
24870259471
/
250000000000
)
≤
-
(
24019940915667638914899
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_145_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
24870259471
/
250000000000
)
≤
-
(
12297242736766437788551
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_145_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
24870259471
/
250000000000
)
≤
-
(
25676711922883085692547
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_145_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
24870259471
/
250000000000
)
≤
-
(
13905575961864639085561
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_145_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
24870259471
/
250000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_145_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
24870259471
/
250000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_145_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
24870259471
/
250000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_145_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
24870259471
/
250000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_145_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
24870259471
/
250000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_145_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
24870259471
/
250000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_145_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
24870259471
/
250000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_145_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
24870259471
/
250000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_145_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
24870259471
/
250000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_145_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
24870259471
/
250000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_145_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
24870259471
/
250000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_145
:
Uρ
(
24870259471
/
250000000000
)
≤
-
(
6006179333855527615251
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_146_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
1614118950931
/
16000000000000
)
≤
-
(
23600490741746310132633
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_146_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
1614118950931
/
16000000000000
)
≤
-
(
23866145357694081674823
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_146_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
1614118950931
/
16000000000000
)
≤
-
(
4886213425407009894147
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_146_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
1614118950931
/
16000000000000
)
≤
-
(
25492478055288563125353
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_146_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
1614118950931
/
16000000000000
)
≤
-
(
27571482204858512832921
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_146_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
1614118950931
/
16000000000000
)
≤
-
(
17303896956176881585291
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_146_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
1614118950931
/
16000000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_146_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
1614118950931
/
16000000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_146_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
1614118950931
/
16000000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_146_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
1614118950931
/
16000000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_146_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
1614118950931
/
16000000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_146_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
1614118950931
/
16000000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_146_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
1614118950931
/
16000000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_146_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
1614118950931
/
16000000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_146_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
1614118950931
/
16000000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_146_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
1614118950931
/
16000000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_146
:
Uρ
(
1614118950931
/
16000000000000
)
≤
-
(
1189858212400226247237
/
500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_147_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
818270647859
/
8000000000000
)
≤
-
(
586328171474169128263
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_147_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
818270647859
/
8000000000000
)
≤
-
(
23714685092528748377319
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_147_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
818270647859
/
8000000000000
)
≤
-
(
3033787739285829484113
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_147_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
818270647859
/
8000000000000
)
≤
-
(
25311691807556838955743
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_147_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
818270647859
/
8000000000000
)
≤
-
(
13669097951678662512941
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_147_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
818270647859
/
8000000000000
)
≤
-
(
2102041636154490140537
/
625000000000000000000
)
source
theorem
Zeta5Irrational
.
U_147_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
818270647859
/
8000000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_147_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
818270647859
/
8000000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_147_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
818270647859
/
8000000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_147_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
818270647859
/
8000000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_147_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
818270647859
/
8000000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_147_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
818270647859
/
8000000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_147_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
818270647859
/
8000000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_147_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
818270647859
/
8000000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_147_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
818270647859
/
8000000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_147_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
818270647859
/
8000000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_147
:
Uρ
(
818270647859
/
8000000000000
)
≤
-
(
23680709076845825592017
/
10000000000000000000000
)