Top: Close encounter distances vs. time computed for 3710 NEOs larger than ~420 m and their clones (due to the Yarkovsky drift). The total number of bodies was 37100. The number of encounters closer than the 2029 Apophis encounter was 21; the corresponding frequency is approximately once per 4800 y. Middle: Cumulative histogram of distances, N(<r). The dependence is parabolic (as πr²). Bottom: Differential histogram of encounters N_enc per NEO. Only 20% of NEOs underwent encounters closer than 0.01 au in the course of 10⁴ y. Specifically, Apophis clones underwent from 11 to 53 encounters and Apophis-like bodies were responsible for half of all encounters.