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Photon correlations from the Mollow tripletPhoton correlations between the photoluminescence peaks of the Mollow triplet have been known for a long time, and recently hailed as a resource for heralded single-photon sources. Here, we provide the full picture of photon-correlations at all orders (we deal explicitly with up to four photons) and with no restriction to the peculiar frequency windows that enclose the peaks. We show that a rich multi-photon physics lies between the peaks, due to transitions involving virtual photons, and thereby much more strongly correlated than those transiting through the real states. Specifically, we show that such emissions occur in bundles of photons rather than as successive, albeit correlated, photons. We provide the recipe to frequency-filter the emission of the Mollow triplet to turn it into a versatile and tunable photon source, allowing in principle all scenarios of photon emission, with advantages already at the one-photon level, i.e., providing more strongly correlated heralded single-photon sources than those already known.