Context : Dark gamma-ray bursts ( GRBs ) are sources with a low optical-to-X-ray flux ratio .
Proposed explanations for this darkness are : i ) the GRB is at high redshift ii ) dust in the GRB host galaxy absorbs the optical/NIR flux iii ) GRBs have an intrinsically faint afterglow emission .

Aims : We study two dark GRBs discovered by Swift , namely , GRB 100614A and GRB 100615A .
These sources are bright in the X-rays , but no optical/NIR afterglow has been detected for either source , despite the efforts of several follow-up campaigns that have been performed since soon after the GRB explosion .

Methods : We analyze the X-ray data and collect all the optical/NIR upper limits in literature for these bursts .
We then build optical-to-X-ray spectral energy distributions ( SEDs ) at the times at which the reddest upper limits are available , and we model our SEDs with the attenuation curves of the Milky Way ( MW ) , Small Magellanic Cloud ( SMC ) , and one obtained for a sample of starburst galaxies .

Results : We find that to explain the deepest NIR upper limits assuming either a MW or SMC extinction law , the visual extinction towards GRB 100614A is A _ { V } > 47 mag , while for GRB 100615A we obtain A _ { V } > 58 mag using data taken within one day after the burst and A _ { V } > 22 mag even 9.2 days after the trigger .

Conclusions : A possible explanation to these unlikely values is that optical radiation and X-rays are not part of the same synchrotron spectrum .
An alternative , or complementary explanation of the previous possibility , involves greyer extinction laws .
A starburst attenuation curve gives A _ { V } > 11 ( A _ { V } > 15 ) for GRB 100614A ( GRB 100615A ) before 1 day after the burst , which is less extreme , despite still very high .
Assuming high redshift in addition to extinction , implies that A _ { V } > 10 at z = 2 and A _ { V } > 4 - 5 at z = 5 , regardless of the adopted extinction recipe .
These lower limits are well above the A _ { V } computed for previous GRBs at known redshift , but not unlikely .
A different , exotic possibility would be an extremely high redshift origin ( z > 17 given the missing K detections ) .
PopIII stars are expected to emerge at z \sim 20 and can produce GRBs with energies well above those inferred for our GRBs at these redshifts .
However , high N _ { H } values ( above the Galactic ones ) towards our GRBs challenge this scenario .
Mid- and far-IR late afterglow ( > 10 ^ { 5 } s after trigger ) observations of these extreme class of GRBs can help us to differentiate between the proposed scenarios .