Fact / Proposition : There are infinitely many more positive integers than there are prime numbers, or prime numbers have a zero density relative to the positive integers, and prime numbers generate the positive even integers efficiently so that gaps between two consecutive prime numbers increase without bound.
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A physically more realistic modeling of "'p "'( "'r "') would have the dipole moment density drop off rapidly, but smoothly to zero at the boundary of the confining region, rather than making a sudden step to zero density.
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More precisely, showed that for any positive ?, all but an infinitely small proportion of zeros lie within a distance ? of the critical line . gives several more precise versions of this result, called " zero density estimates ", which bound the number of zeros in regions with imaginary part at most " T " and real part at least 1 / 2 + ?.
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