Since the discovery of pulsars, dozens of surveys have already been conducted with their searches. In the course of surveys in the sky, areas from thousands to tens of thousands of square degrees are explored. Despite repeated observations of the same areas, new pulsars are constantly being discovered. We present Pushchino Multibeam Pulsar Search (PUMPS), having a sensitivity that is an order of magnitude higher than the sensitivity of all previously made surveys on pulsar search. In PUMPS daily round-the-clock observations are carried out of the area located on declinations $-9^o < \delta < +42^o$. The survey is carried out on 96 beams of a Large Phased Array (LPA) at a frequency of 111 MHz. During the observation period of August 2014 – August 2022, the survey was repeated approximately 3 000 times. The expected sensitivity in the survey reaches up to 0.1 mJy. The paper considers some tasks that can be solved when processing the received data.