Herschel extragalactic surveys offer a unique opportunity to efficiently select a significant number of rare and massive dusty objects, and thus gain insight into the prodigious star-forming activity that takes place in the very distant Universe. To search for z≥4 dusty star-forming galaxies, in this work we consider red SPIRE objects with fluxes rising from 250 μm to 500 μm (so-called "500 μm-risers"). We aim to implement a novel method to obtain a statistical sample of "500 μm-risers" and

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... y evaluate our selection inspecting different models of galaxy evolution. We consider one of the largest and deepest Herschel surveys, the Herschel Virgo Cluster Survey. We develop a novel selection algorithm which links the source extraction and spectral energy distribution fitting. We select 133 "500 μm-risers" over 55 deg^2, imposing the criteria: S_500>S_350>S_250, S_250>13.2 mJy and S_500>30 mJy. Differential number counts are in a fairly good agreement with models, displaying better match than other existing samples. In order to interpret the statistical properties of selected sources, which has been proven as a very challenging task due the complexity of observed artefacts, we make end-to-end simulations including physical clustering and lensing. The estimated fraction of strongly lensed sources is 24^+6_-5% based on models. We present the faintest known statistical sample of "500 μm-risers" and show that noise and strong lensing have crucial impact on measured counts and redshift distribution of selected sources. We estimate the flux-corrected star formation rate density at 44 sources.