Massive dense cores (MDCs) are the high-mass equivalent of the so-called dense cores in nearby star-forming regions. With typical sizes of 0.1 pc, they could form either a few high-mass stars, or a cluster of low-mass stars. We present high-angular resolution continuum observations obtained with the IRAM Plateau de Bure interferometer at 1.3 and 3.5 mm towards the six most massive and youngest (IR-quiet) dense cores in the Cygnus X complex. Located at only 1.7 kpc, the Cygnus X region offers the opportunity of reaching small enough scales (of the order of 1700 AU at 1.3 mm) to separate individual collapsing objects, and thus to observe and constrain the result of the fragmentation process. The cores are sub-fragmented with a total of 23 fragments inside 5 cores. Only the most compact MDC, CygX-N63, may host a single proto-stellar object with an envelope as massive as ∼60 M . The fragments in the other cores have sizes and separations similar to low-mass pre-stellar condensations and Class 0 young stellar objects in nearby protoclusters, and are most probably self-gravitating objects (M > M vir ). In addition to CygX-N63, a total of 8 objects are found to be probable precursors of OB stars with their envelope masses ranging from 8.4 to 30 M inside a FWHM of 4000 AU. The level of fragmentation is globally higher than in the turbulence regulated, monolithic collapse scenario, but it is also not as high as expected in a pure gravo-turbulent scenario where the distribution of mass is dominated by low-mass protostars/stars. Here, the fractions of the total MDC masses in the high-mass proto-stellar fragments are found to be as high as 37, 58, and 100% in CygX-N12, CygX-N53, and CygX-N63, respectively. These high fractions of mass in the proto-stellar fragments are also indicative of a high efficiency of core formation in the MDCs. The increase in the core formation efficiency as a function of average density in the MDCs is proposed to be caused by the increasing importance of self-gravity leading to gravitational collapse on the scale of the MDCs. At the same time, the observed MDCs tend to fragment into a few proto-stellar objects within their central regions. We are therefore probably witnessing the primordial mass segregation of clusters. The physical origin of the fragmentation into a few high-mass objects is not yet clear, and will be investigated in the future by studying the kinematics of the MDCs.