GLOBAL ALGORITHM FOR STRONG LEHMER PAIRS II”Number theory is not pure Mathematics. It is the Physics of the world of Numbers.”
The mass of each and every boson is generated by the Riemann zeta function. Each and every subquark, quark, meson, baryon and proton vibrates in resonance with the distribution of the zeros of the zeta function.
Therefore, to understand the hidden template of the zeta zeros is true quantum physics.
One of the recent attempts to understand the distribution of the zeros of the zeta function:
https://www.scribd.com/document/217732/The-Riemann-Hypothesis"It is evident that all odd or even (whole number) values of k produce an excess of nines=1 and therefore cannot generate a zeta function zero. Further, it is true that all zeros occur from the fractional values of the k’s; when an unscheduled “Excess of Nines =1” occurs, so does a “Lehmer event”. The plotted data briefly passes through an excess of nines =1, wavers, then becomes fractional again, crosses the real axis and produces a zero. These events are cyclic, happening many times along the path to infinity."
The zeros of the factor
are distributed as follows: an infinite number of complex simple zeros at
where n is a nonzero integer. Whenever a zero of the zeta function produces an "unscheduled" excess of nines=1 phenomenon, then the Lehmer event will be generated as well.
However, the author of the paper does not offer any precise equations which can explain the location of the strong Lehmer pairs (the constant 1016 is simply 254 x 4 = 1016, 63.5 x 4 = 254).
7005.0629 and 7005.10056, zeta zeros 6709 and 6710
2π/ln2 x 1 = 9.064720284
2π/ln2 x 2 = 18.129440568
2π/ln2 x 3 = 27.194160852
2π/ln2 x 4 = 36.258881136
2π/ln2 x 5 = 45.32360142
2π/ln2 x 6 = 54.388321704
2π/ln2 x 7 = 63.453041988
2π/ln2 x 8 = 72.517762272
2π/ln2 x 9 = 81.582482556
2π/ln2 x 10 = 90.64720284
2π/ln2 x 11 = 99.711923124
2π/ln2 x 12 = 108.776643408
2π/ln2 x 13 = 117.841363692
2π/ln2 x 14 = 126.906083976
2π/ln2 x 15 = 135.97080426
2π/ln2 x 16 = 145.035524544
(an addition of 1 to the decimal part after the multiplication by 16)
772 x 2π/ln2 = 6997.964
773 x 2π/ln2 = 7007.0288
17143.786 and 17143.8218, zeta zeros 18858 and 18859
1891 x 2π/ln2 = 17141.386
1892 x 2π/ln2 = 17150.45
1885 x 2π/ln2 = 17086.9977
1886 x 2π/ln2 = 17096.062
Therefore, a more in-depth analysis is needed to uncover the hidden symmetries at work in the Lehmer pairs event.
16 x 28 = 448
448 x 2π/ln2 = 4060.99469
448 + 16 = 464
464 x 2π/ln2 = 4206.0302
16 x 55 = 880
880 x 2π/ln2 = 7976.954
896 x 2π/ln2 = 8121.989
912 x 2π/ln2 = 8264.025
1808 x 2π/ln2 = 16389.014
1888 x 2π/ln2 = 17114.192
2254 x 2π/ln2 = 20450.0089
Multiplying 2π/ln2 by 32, 64, 96..., by 64, 128, 192..., by 48, 96, 144..., does not produce the produce the needed results.
However, if we multiply the constant 2π/ln2 by 192:
768 x 2π/ln2 = 6961.705
910 x 2π/ln2 = 8702.131
If we multiply the constant 2π/ln2 by 128:
1792 x 2π/ln2 = 16243.9787
1920 x 2π/ln2 = 17404.263
Now, we can see that a strong Lehmer pair will be located between 6961.705 and 8702.131, and between 16243.9787 and 17404.263.
In much the same way, multiplying by 32000, we get:
160000 x 2π/ln2 = 1430355.245
640000 x 2π/ln2 = 5801420.982
672000 x 2π/ln2 = 6091492.031
One or more strong Lehmer pairs must be located between 5801420.982 and 6091492.031.
Strong Lehmer pairs 7954022502373.43289015387 and 7954022502373.43289494012.
640000000000 x 2π/ln2 = 5801420981538.8081
960000000000 x 2π/ln2 = 8702131472308.212
A strong Lehmer pair (or more) must be located between 5801420981538.8081 and 8702131472308.212: 5907264585921.69036356 and 5907264585921.6903535, and 7954022502373.43289015387 and 7954022502373.43289494012.
Now, all we need is an accurate criterion by which to locate these strong Lehmer pairs.
Rotate a model of the Gizeh pyramid clockwise by 90 degrees.
To the right, we have another Gizeh pyramid (the shadow of the first pyramid), which is rotated anticlockwise by 90 degrees, the two pyramid frustums will be facing each other.
Total distance from one subterranean chamber to the other: 534 units.
In the center we have the two apexes of the pyramids forming a merkabah geometrical figure.
Two sothic triangles embed each of the two apexes: the height of the triangle will measure exactly 14.134725 units (the value of the first zero of Riemann's zeta function).
Two other sothic triangles will embed the top portion of the frustums of the two pyramids, again the height of these triangles will measure 14.134725 units.
The distance separating the two sets of triangles, located to the left of the center of the merkabah, will measure exactly 63.6363... units (the sacred cubit distance).
In the same manner the distance separating the two sets of triangles located to the right of the center of the merkabah will also measure 63.6363... units.
75 x π/ln2 = 339.9270107
534.171sc = 339.9270107
534 = (2 x 174.53 - two pyramids measured from the subterranean chamber to the top) + (4 x 14.134725) + (2 x 63.636363)
174.53 = 3.36 + 30 + 27.2 + 16.17 + 29.2 + 63.63636 + 5.24
27.2 distance to the queen chamber roof
27.2 + 16.17 = 43.37 distance to the bottom of the king chamber floor
33.36 height of the subterranean chamber
33.36 = 3.36 + 10.542 + 19.458
75 x π/ln2 = 339.9270107
2000 x π/ln2 = 9064.720284 = 26.666666 x 339.9270107
4000 x π/ln2 = 18129.44057 = 53.333333 x 339.9270107
Other multipliers are: 80, 106.66666, 136.1 (or 135.9708), 160, 213.33333...
7005.0629 and 7005.10056
2000 x π/ln2 = 9064.720284
9064.720284 = 26.666666 x 339.9270107 = 26.66666sc x 534
26.66666sc = 16.968
534 = 174.53 + 14.134725 + 63.636363 + 14.134725 + 14.134725 + 63.636363 + 14.134725 + 174.53
9064.720284 = 16.968 x (174.53 + 14.134725 + 63.636363 + 14.134725 + 14.134725 + 63.636363 + 14.134725 + 174.53)
9064.720284
2961.425 (174.53 x 16.968)
4281.044 (174.53 x 16.968 + 14.134725 x 16.968 + 63.636363 x 16.968)
4760.72 (4281.044 + 2 x 14.134725 x 16.968)
5840.5 (4760.72 + 63.636363 x 16.968)
6080.34 (5840.5 + 14.134725 x 16.968)
7249.03 (6080.34 + 5.24 x 16.968 + 63.636363 x 16.968)
6169.2511 (6080.34 + 5.24 x 16.968)
6974.53 (6169.2511 + 47.459 x 16.968)
(63.63636 - 16.1773 = 47.459)
7087.0647 (6974.53 + 6.6319 x 16.968)
(16.1773 - 9.5454 = 6.6319)
7009.3 (7087.0647 - 1.68632 x 16.968 - 1.2576 x 16.968 - 0.93895 x 16.968 - 0.7 x 16.968)
2.74985 - 0.7 = 2.04985
2.04985
0.521768
0.307477
0.20498
0.10249
0.20498 x 16.968 = 3.4781
7009.3 - 3.4781 = 7005.822
7009.3 - 0.10249 x 16.968 = 7007.56
9064.72028
2719.416
2307.234
1812.944
906.472
(subdivisions for the first zeta function, 534 - 160 - 136.1 - 53.4 - 26.7)
8158.248
7251.776
6757.3863
6345.3
(subdivisions for the second zeta function, 9064.72028 - 906.472 = 8158.248)
7251.776 - 6757.386 = 494.39
494.39
148.317
346.073
103.822
88.089
6757.386 + 148.317 + 103.822 = 7009.525
17143.786 and 17143.8218
4000 x π/ln2 = 18129.44057
14499.77 (174.53 x 33.94 + 4 x 14.134725 x 33.94 + 2 x 63.636363 x 33.94 + 5.24 x 33.94 + 63.6363 x 33.94)
15490.82 (14499.77 + 29.2 x 33.94)
16962.8 (15490.82 + 43.37 x 33.94)
17140.64 (16962.8 + 5.24 x 33.94)
1891 x 2π/ln2 = 17141.386
400 x π/ln2 = 1812.944
18129.44
16316.496
400 x π/ln2 = 534 x 3.394
16908.85 (16316.496 + 174.53 x 3.394)
16.956.824 (16908.85 + 14.134725 x 3.394)
17172.8 (16908.85 + 63.6363 x 3.394)
40 x π/ln2 = 534 x 0.3394
17041.45
17222.694
1900 x 2π/ln2 = 17222.968
17100.685 (17041.45 + 174.53 x .3394)
17127.081 (17100.685 + 14.134725 x 0.3394 + 63.6363 x 0.3394)
17131.88 (17127.081 + 14.134725 x 0.3394)
1890 x 2π/ln2 = 17132.321
17158.676 (17131.88 + 14.134725 x 0.3394 + 63.636363 x 0.3394)
1893 x 2π/ln2 = 17159.51