  The CoVid-19 is spreading pandemically all over the world. A rapid defeat of
the pandemic requires carrying out on the population a mass screening, able to
separate positive from negative cases. Such a cleaning will free a flow of
productive population. The current rate and cost of testing, performed with the
common PCR (polymerase chain reaction) method and with the available resources,
is forcing a selection of the subjects to be tested. Indeed, each one must be
examined individually at the cost of precious time. Moreover, the exclusion of
potentially positive individuals from screening induces health risks, a broad
slowdown in the effort to curb the viral spread, and the consequent mortality
rates. We present a new procedure, the Purified by Unified Resampling of
Infected Multitudes, in short Purim, able to untangle any massive candidate
sample with inexpensive screening, through the cross-correlated analysis of the
joint speciments. This procedure can reveal and detect most negative patients
and in most cases discover the identity of the few positives already in the
first or few secondary tests. We investigate the the two-dimensional
correlation case in function of the infection probability. The
multi-dimensional topology, the scaled Purim procedure are also considered.
Extensive Purim tests may measure and weight the degree of epidemic: their
outcome may identify focal regions in the early stages. Assuming hundreds or
thousand subjects, the saving both in time and in cost will be remarkable.
Purim may be able to filter scheduled flights, scholar acceptance, popular
international event participants. The optimal extension of Purim outcome is
growing as the inverse of the epidemia expansion. Therefore, the earlier, the
better.
