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.
Zeta5Irrational
.
Table
.
U02
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LeanPool.Zeta5Irrational.Table.UpperCertificate
Imported by
Zeta5Irrational
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U_24_1
Zeta5Irrational
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U_24_2
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U_24_3
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U_24_4
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U_24_5
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U_24_6
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U_24_7
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U_24_8
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U_24_9
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U_24_10
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U_24_11
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U_24_12
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U_24_13
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U_24_14
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U_24_15
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U_24_16
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U_24
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U_25_1
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U_25_2
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U_25_3
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U_25_4
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U_25_5
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U_25_6
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U_25_7
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U_25_8
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U_25_9
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U_25_10
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U_25_11
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U_25_12
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U_25_13
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U_25_14
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U_25_15
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U_25_16
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U_25
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U_26_1
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U_26_2
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U_26_3
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U_26_4
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U_26_5
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U_26_6
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U_26_7
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U_26_8
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U_26_9
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U_26_10
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U_26_11
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U_26_12
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U_26_13
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U_26_14
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U_26_15
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U_26_16
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U_26
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U_27_1
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U_27_2
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U_27_3
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U_27_4
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U_27_9
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U_27_10
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U_27_14
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U_27_16
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U_27
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U_28_1
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U_28_2
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U_28_3
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U_28_4
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U_28_6
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U_28_12
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U_28_14
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U_28
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U_29_1
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U_29_2
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U_29_3
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U_29_4
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U_29_6
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U_29_7
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U_29_13
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U_29_14
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U_29_15
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U_29_16
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U_29
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U_30_1
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U_30_2
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U_30_3
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U_30_7
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U_30_10
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U_30_12
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U_30_13
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U_30_14
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U_30_15
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U_30_16
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U_30
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U_35_1
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U_35_2
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U_35_3
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U_35_4
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U_35_6
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U_35_7
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U_35_9
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U_35_10
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U_35_11
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U_35_12
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U_35_13
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U_35_14
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U_35_15
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U_35_16
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U_35
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U_36_1
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U_36_2
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U_36_3
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U_36_8
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U_36_12
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U_36_13
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U_36_14
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U_36_15
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U_36_16
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U_36
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U_37_1
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U_37_2
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U_37_3
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U_37_4
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U_37_5
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U_37_14
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U_37
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U_38_1
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U_38_2
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U_38_3
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U_38_4
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U_38_5
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U_38_6
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U_38_7
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U_38_8
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U_38_13
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U_38_14
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U_38_15
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U_38_16
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U_38
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U_39_1
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U_39_2
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U_39_3
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U_39_4
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U_39_6
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U_39_7
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U_39_16
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U_39
Certified arcsine potential bounds (U02)
#
source
theorem
Zeta5Irrational
.
U_24_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
280457333
/
200000000000
)
≤
-
(
53593986196108414589993
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_24_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
280457333
/
200000000000
)
≤
-
(
52043031588685060884247
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_24_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
280457333
/
200000000000
)
≤
-
(
25512130211755314637529
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_24_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
280457333
/
200000000000
)
≤
-
(
11449496158609380585237
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_24_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
280457333
/
200000000000
)
≤
-
(
20577364119368339121527
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_24_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
280457333
/
200000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_24_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
280457333
/
200000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_24_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
280457333
/
200000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_24_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
280457333
/
200000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_24_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
280457333
/
200000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_24_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
280457333
/
200000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_24_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
280457333
/
200000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_24_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
280457333
/
200000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_24_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
280457333
/
200000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_24_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
280457333
/
200000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_24_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
280457333
/
200000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_24
:
Uρ
(
280457333
/
200000000000
)
≤
-
(
28391530796819438246561
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_25_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
6519108259
/
4000000000000
)
≤
-
(
27066132270492516043287
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_25_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
6519108259
/
4000000000000
)
≤
-
(
52730540587954460599153
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_25_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
6519108259
/
4000000000000
)
≤
-
(
25512130211755314637529
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_25_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
6519108259
/
4000000000000
)
≤
-
(
11449496158609380585237
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_25_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
6519108259
/
4000000000000
)
≤
-
(
20577364119368339121527
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_25_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
6519108259
/
4000000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_25_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
6519108259
/
4000000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_25_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
6519108259
/
4000000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_25_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
6519108259
/
4000000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_25_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
6519108259
/
4000000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_25_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
6519108259
/
4000000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_25_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
6519108259
/
4000000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_25_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
6519108259
/
4000000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_25_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
6519108259
/
4000000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_25_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
6519108259
/
4000000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_25_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
6519108259
/
4000000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_25
:
Uρ
(
6519108259
/
4000000000000
)
≤
-
(
14208726599741697552523
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_26_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
3714534929
/
2000000000000
)
≤
-
(
13676747820096012817053
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_26_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
3714534929
/
2000000000000
)
≤
-
(
26776440993766361792693
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_26_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
3714534929
/
2000000000000
)
≤
-
(
25512130211755314637529
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_26_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
3714534929
/
2000000000000
)
≤
-
(
11449496158609380585237
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_26_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
3714534929
/
2000000000000
)
≤
-
(
20577364119368339121527
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_26_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
3714534929
/
2000000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_26_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
3714534929
/
2000000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_26_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
3714534929
/
2000000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_26_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
3714534929
/
2000000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_26_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
3714534929
/
2000000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_26_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
3714534929
/
2000000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_26_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
3714534929
/
2000000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_26_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
3714534929
/
2000000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_26_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
3714534929
/
2000000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_26_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
3714534929
/
2000000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_26_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
3714534929
/
2000000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_26
:
Uρ
(
3714534929
/
2000000000000
)
≤
-
(
28447732623893462494161
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_27_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
8339031457
/
4000000000000
)
≤
-
(
55324376016046487597617
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_27_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
8339031457
/
4000000000000
)
≤
-
(
10926753652502540317131
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_27_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
8339031457
/
4000000000000
)
≤
-
(
25512130211755314637529
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_27_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
8339031457
/
4000000000000
)
≤
-
(
11449496158609380585237
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_27_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
8339031457
/
4000000000000
)
≤
-
(
20577364119368339121527
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_27_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
8339031457
/
4000000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_27_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
8339031457
/
4000000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_27_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
8339031457
/
4000000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_27_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
8339031457
/
4000000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_27_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
8339031457
/
4000000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_27_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
8339031457
/
4000000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_27_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
8339031457
/
4000000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_27_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
8339031457
/
4000000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_27_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
8339031457
/
4000000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_27_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
8339031457
/
4000000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_27_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
8339031457
/
4000000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_27
:
Uρ
(
8339031457
/
4000000000000
)
≤
-
(
5697216077868329425469
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_28_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
289031033
/
125000000000
)
≤
-
(
27996295164352877284557
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_28_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
289031033
/
125000000000
)
≤
-
(
57268912150832389796717
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_28_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
289031033
/
125000000000
)
≤
-
(
25512130211755314637529
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_28_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
289031033
/
125000000000
)
≤
-
(
11449496158609380585237
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_28_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
289031033
/
125000000000
)
≤
-
(
20577364119368339121527
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_28_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
289031033
/
125000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_28_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
289031033
/
125000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_28_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
289031033
/
125000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_28_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
289031033
/
125000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_28_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
289031033
/
125000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_28_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
289031033
/
125000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_28_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
289031033
/
125000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_28_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
289031033
/
125000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_28_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
289031033
/
125000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_28_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
289031033
/
125000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_28_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
289031033
/
125000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_28
:
Uρ
(
289031033
/
125000000000
)
≤
-
(
7142692332734663141767
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_29_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
124379927
/
40000000000
)
≤
-
(
14737682003414632220873
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_29_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
124379927
/
40000000000
)
≤
-
(
57268912150832389796717
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_29_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
124379927
/
40000000000
)
≤
-
(
25512130211755314637529
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_29_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
124379927
/
40000000000
)
≤
-
(
11449496158609380585237
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_29_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
124379927
/
40000000000
)
≤
-
(
20577364119368339121527
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_29_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
124379927
/
40000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_29_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
124379927
/
40000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_29_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
124379927
/
40000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_29_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
124379927
/
40000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_29_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
124379927
/
40000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_29_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
124379927
/
40000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_29_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
124379927
/
40000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_29_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
124379927
/
40000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_29_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
124379927
/
40000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_29_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
124379927
/
40000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_29_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
124379927
/
40000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_29
:
Uρ
(
124379927
/
40000000000
)
≤
-
(
893808622258701750129
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_30_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
7016246261
/
2000000000000
)
≤
-
(
1910848611840935650757
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_30_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
7016246261
/
2000000000000
)
≤
-
(
57268912150832389796717
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_30_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
7016246261
/
2000000000000
)
≤
-
(
25512130211755314637529
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_30_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
7016246261
/
2000000000000
)
≤
-
(
11449496158609380585237
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_30_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
7016246261
/
2000000000000
)
≤
-
(
20577364119368339121527
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_30_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
7016246261
/
2000000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_30_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
7016246261
/
2000000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_30_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
7016246261
/
2000000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_30_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
7016246261
/
2000000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_30_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
7016246261
/
2000000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_30_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
7016246261
/
2000000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_30_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
7016246261
/
2000000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_30_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
7016246261
/
2000000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_30_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
7016246261
/
2000000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_30_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
7016246261
/
2000000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_30_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
7016246261
/
2000000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_30
:
Uρ
(
7016246261
/
2000000000000
)
≤
-
(
1789060791099578778267
/
625000000000000000000
)
source
theorem
Zeta5Irrational
.
U_35_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
19572466643
/
2000000000000
)
≤
-
(
5896789100911232295581
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_35_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
19572466643
/
2000000000000
)
≤
-
(
57268912150832389796717
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_35_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
19572466643
/
2000000000000
)
≤
-
(
25512130211755314637529
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_35_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
19572466643
/
2000000000000
)
≤
-
(
11449496158609380585237
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_35_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
19572466643
/
2000000000000
)
≤
-
(
20577364119368339121527
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_35_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
19572466643
/
2000000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_35_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
19572466643
/
2000000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_35_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
19572466643
/
2000000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_35_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
19572466643
/
2000000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_35_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
19572466643
/
2000000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_35_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
19572466643
/
2000000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_35_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
19572466643
/
2000000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_35_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
19572466643
/
2000000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_35_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
19572466643
/
2000000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_35_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
19572466643
/
2000000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_35_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
19572466643
/
2000000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_35
:
Uρ
(
19572466643
/
2000000000000
)
≤
-
(
14301028195703943639221
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_36_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
40732008867
/
4000000000000
)
≤
-
(
28671312100952179027439
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_36_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
40732008867
/
4000000000000
)
≤
-
(
57268912150832389796717
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_36_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
40732008867
/
4000000000000
)
≤
-
(
25512130211755314637529
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_36_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
40732008867
/
4000000000000
)
≤
-
(
11449496158609380585237
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_36_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
40732008867
/
4000000000000
)
≤
-
(
20577364119368339121527
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_36_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
40732008867
/
4000000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_36_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
40732008867
/
4000000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_36_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
40732008867
/
4000000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_36_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
40732008867
/
4000000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_36_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
40732008867
/
4000000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_36_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
40732008867
/
4000000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_36_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
40732008867
/
4000000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_36_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
40732008867
/
4000000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_36_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
40732008867
/
4000000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_36_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
40732008867
/
4000000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_36_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
40732008867
/
4000000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_36
:
Uρ
(
40732008867
/
4000000000000
)
≤
-
(
3573120717747316300783
/
1250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_37_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
1322471389
/
125000000000
)
≤
-
(
437620085001547802181
/
78125000000000000000
)
source
theorem
Zeta5Irrational
.
U_37_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
1322471389
/
125000000000
)
≤
-
(
57268912150832389796717
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_37_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
1322471389
/
125000000000
)
≤
-
(
25512130211755314637529
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_37_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
1322471389
/
125000000000
)
≤
-
(
11449496158609380585237
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_37_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
1322471389
/
125000000000
)
≤
-
(
20577364119368339121527
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_37_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
1322471389
/
125000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_37_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
1322471389
/
125000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_37_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
1322471389
/
125000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_37_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
1322471389
/
125000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_37_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
1322471389
/
125000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_37_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
1322471389
/
125000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_37_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
1322471389
/
125000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_37_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
1322471389
/
125000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_37_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
1322471389
/
125000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_37_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
1322471389
/
125000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_37_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
1322471389
/
125000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_37
:
Uρ
(
1322471389
/
125000000000
)
≤
-
(
28571008882018903964403
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_38_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
4549323561
/
400000000000
)
≤
-
(
53882828561175423362757
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_38_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
4549323561
/
400000000000
)
≤
-
(
57268912150832389796717
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_38_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
4549323561
/
400000000000
)
≤
-
(
25512130211755314637529
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_38_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
4549323561
/
400000000000
)
≤
-
(
11449496158609380585237
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_38_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
4549323561
/
400000000000
)
≤
-
(
20577364119368339121527
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_38_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
4549323561
/
400000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_38_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
4549323561
/
400000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_38_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
4549323561
/
400000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_38_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
4549323561
/
400000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_38_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
4549323561
/
400000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_38_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
4549323561
/
400000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_38_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
4549323561
/
400000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_38_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
4549323561
/
400000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_38_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
4549323561
/
400000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_38_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
4549323561
/
400000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_38_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
4549323561
/
400000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_38
:
Uρ
(
4549323561
/
400000000000
)
≤
-
(
142742919640776502841
/
50000000000000000000
)
source
theorem
Zeta5Irrational
.
U_39_1
:
Uω
(
aρ
1
)
(
bρ
1
)
(
12166846693
/
1000000000000
)
≤
-
(
52178850672124585216629
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_39_2
:
Uω
(
aρ
2
)
(
bρ
2
)
(
12166846693
/
1000000000000
)
≤
-
(
57268912150832389796717
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_39_3
:
Uω
(
aρ
3
)
(
bρ
3
)
(
12166846693
/
1000000000000
)
≤
-
(
25512130211755314637529
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_39_4
:
Uω
(
aρ
4
)
(
bρ
4
)
(
12166846693
/
1000000000000
)
≤
-
(
11449496158609380585237
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_39_5
:
Uω
(
aρ
5
)
(
bρ
5
)
(
12166846693
/
1000000000000
)
≤
-
(
20577364119368339121527
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_39_6
:
Uω
(
aρ
6
)
(
bρ
6
)
(
12166846693
/
1000000000000
)
≤
-
(
3698074464695343529243
/
1000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_39_7
:
Uω
(
aρ
7
)
(
bρ
7
)
(
12166846693
/
1000000000000
)
≤
-
(
33239459906384759787341
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_39_8
:
Uω
(
aρ
8
)
(
bρ
8
)
(
12166846693
/
1000000000000
)
≤
-
(
14956372202312055299661
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_39_9
:
Uω
(
aρ
9
)
(
bρ
9
)
(
12166846693
/
1000000000000
)
≤
-
(
26986659976834617141369
/
10000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_39_10
:
Uω
(
aρ
10
)
(
bρ
10
)
(
12166846693
/
1000000000000
)
≤
-
(
12224255358108186379559
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_39_11
:
Uω
(
aρ
11
)
(
bρ
11
)
(
12166846693
/
1000000000000
)
≤
-
(
4457298065613116122159
/
2000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_39_12
:
Uω
(
aρ
12
)
(
bρ
12
)
(
12166846693
/
1000000000000
)
≤
-
(
640305991230515290559
/
312500000000000000000
)
source
theorem
Zeta5Irrational
.
U_39_13
:
Uω
(
aρ
13
)
(
bρ
13
)
(
12166846693
/
1000000000000
)
≤
-
(
4762195995179309567439
/
2500000000000000000000
)
source
theorem
Zeta5Irrational
.
U_39_14
:
Uω
(
aρ
14
)
(
bρ
14
)
(
12166846693
/
1000000000000
)
≤
-
(
8977612329965299982791
/
5000000000000000000000
)
source
theorem
Zeta5Irrational
.
U_39_15
:
Uω
(
aρ
15
)
(
bρ
15
)
(
12166846693
/
1000000000000
)
≤
-
(
268788866070650094343
/
156250000000000000000
)
source
theorem
Zeta5Irrational
.
U_39_16
:
Uω
(
aρ
16
)
(
bρ
16
)
(
12166846693
/
1000000000000
)
≤
-
(
419641552645073499393
/
250000000000000000000
)
source
theorem
Zeta5Irrational
.
U_39
:
Uρ
(
12166846693
/
1000000000000
)
≤
-
(
5706133116954878622153
/
2000000000000000000000
)