Considering that the Large Eddington Number has correctly predicted the number of atoms in the Universe, the properties of the Eddington electric number 137 are studied. This number shows abnormal arithmetic properties, in liaison with the 5th harmonic number 137/60. It seems that Egyptians was aware of this, as the architecture of the Hypostyle Karnak room reveals, as well as the Ptolemaic approximation p ≈ 2 + 137/120, together with a specific mention in the Bible, and overhelming connexions with musical canonic numbers. The SO(32) characteristic superstring number 496, the third perfect number, connects directly with the three main interaction parameters, and is very close to the square root of the Higgs boson-electron mass ratio, so the Higgs boson discovery excludes the Multiverse, favoring rather a unique Cosmos being a finite computer using 137 and its extension 137.036 as calculation basis. The direct liaison between the mean value of the two main cosmic radiuses and the Bohr radius through the simplest harmonic series excludes any role of chance. Precise symmetric relations involving the Kotov non-Doppler period permit to propose precise (100 ppb) values for the weak and strong interaction constants, as well as G ≈ 6.675464346 × 10^-11 kg-1 m3 s-2, at 2 sigmas higher than the tabulated value. This value is confirmed by a direct connection with the Superspeed ratio C/c ≈ 6.945480 × 10^60.