We present the serendipitous discovery of z=4.05 molecular gas CO emission lines with the IRAM Plateau de Bure interferometer coincident with GN20 and GN20.2, two luminous submillimeter galaxies (SMGs) in the Great Observatories Origins Deep Survey North field (GOODS-N). These are among the most distant submillimeter-selected galaxies reliably identified through CO emission and also some of the most luminous known. In terms of CO to bolometric luminosities, stellar mass and star formation rates (SFRs), these newly discovered z>4 SMGs are similar to z~1.5-3 SMGs studied to date. These z~4 SMGs have much higher specific SFRs than typical B-band dropout Lyman break galaxies at the same redshift. The stellar mass-SFR correlation for normal galaxies does not seem to evolve much further, between z~2 and z~4. A significant z=4.05 spectroscopic redshift spike is observed in GOODS-N, and a strong spatial overdensity of B-band dropouts and IRAC selected z>3.5 galaxies appears to be centered on the GN20 and GN20.2 galaxies. This suggests a proto-cluster structure with total mass ~10^14 Msun. Using photometry at mid-IR, submm and radio wavelengths, we show that reliable photometric redshifts (Dz/(1+z)~0.1) can be derived for SMGs over 1<z<4. This new photometric redshift technique has been used to provide a first estimate of the space density of 3.5<z<6 hyper-luminous starburst galaxies, and to show that they contribute substantially to the SFR density at early epochs. Many of these high-redshift starbursts will be within reach of Herschel. We find that the radio to mid-IR flux density ratio can be used to select z>3.5 starbursts, regardless of their submm/mm emission [abridged].
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