Context. Understanding the conditions that lead to the formation of planetesimals – the building blocks of planets - and their initial size distribution is a central problem of modern planetology. While most of these original planetesimals were accreted onto the terrestrial planets and the cores of the giant planets, some were also stranded in the main belt, where 4.5 Gyr of collisional evolution broke most of them into families of collisional asteroid fragments. However, some planetesimals survived, and are still hidden amongst asteroid fragments in the main belt. Aims. We make use of astronomical data to identify these leftover planetesimals amongst all other asteroids. Our search is based on separating planetesimal survivors from families of asteroids generated by collisions. Namely, we aim to identify and “clean” the main belt of collisional family members: by doing so, we would be left with the surviving members of the original planetesimals. Methods. We focus here on the inner portion of the main belt for asteroids with intermediate to high albedo. It is known that current asteroid family catalogs are not suitable for the aforementioned cleaning; they are conservative and only one-quarter of the known asteroids are associated with the approximately 120 distinct asteroid families. We therefore developed methods to inclusively link asteroids to known collisional families in order to better capture their extent. Namely, we apply a hierarchical clustering method (HCM) on asteroids filtered according to the V-shape of the Yarkovsky drift of each family in order to reassess family membership (V-shape-constrained HCM). The identified families were removed and the remaining background population was searched for previously undetected collisional families. Results. We succeed in using our V-shape-constrained HCM to link family “halos” to their cores. After removing these reassessed families from the asteroid population, our V-shape search reveals a previously unknown collisional family of S-type asteroids in the inner main belt with an age of 4.3 ± 1.7 Gyr and a significance level of 3.4 σ . When this ancient collisional family is removed, 34 planetesimals are identified and their size-frequency distribution is presented. Conclusions. The asteroid belt has two components: planetesimals and collisional fragments. The cumulative size-frequency distribution of planetesimals has a steep power-law index for bodies larger than 100 km in diameter and a much smaller power-law index for planetesimals smaller than 100 km.