Context :

Aims : The detection of very hot plasma in the quiescent corona is important for diagnosing heating mechanisms .
The presence and the amount of such hot plasma is currently debated .
The SphinX instrument on-board CORONAS-PHOTON mission is sensitive to X-ray emission well above 1 keV and provides the opportunity to detect the hot plasma component .

Methods : We analyzed the X-ray spectra of the solar corona collected by the SphinX spectrometer in May 2009 ( when two active regions were present ) .
We modelled the spectrum extracted from the whole Sun over a time window of 17 days in the 1.34 - 7 keV energy band by adopting the latest release of the APED database .

Results : The SphinX broadband spectrum can not be modelled by a single isothermal component of optically thin plasma and two components are necessary .
In particular , the high statistics and the accurate calibration of the spectrometer allowed us to detect a very hot component at \sim 7 million K with an emission measure of \sim 2.7 \times 10 ^ { 44 } cm ^ { -3 } .
The X-ray emission from the hot plasma dominates the solar X-ray spectrum above 4 keV .
We checked that this hot component is invariably present both at high and low emission regimes , i.e .
even excluding resolvable microflares .
We also present and discuss a possible non-thermal origin ( compatible with a weak contribution from thick-target bremsstrahlung ) for this hard emission component .

Conclusions : Our results support the nanoflare scenario and might confirm that a minor flaring activity is ever-present in the quiescent corona , as also inferred for the coronae of other stars .