32nd in the world in rapid chess with an ELO rating of 2667.

In the 2017 edition, he defeated Vishy Anand in one of the games of their match, which ended in a draw. The former world champion was only able to prevail in the final tiebreaker.

Last year, he drew with the Spanish number 1, GM Francisco Vallejo, also losing in the tiebreaker, demonstrating constant progress that positions him as the most promising talent in Spanish chess.

In 2020, in an online edition of the tournament due to Covid-19, Jaime reached the Magistral final for the first time after defeating Alexey Shirov. In his match with Leinier Dominguez, the Cuban-American grandmaster won by a narrow margin after a hard-fought battle. Santos was crowned co-champion of Spain in 2020 alongside GM David Antón. In the 2020 Magistral tournament, Jaime eliminated chess legend Alexey Shirov, and in 2021 he again finished second in the Spanish Championship, finally breaking the 2600 ELO rating barrier. In 2022, he broke into the top 100 players in the world and reached second place in the Spanish ranking, behind Paco Vallejo.

2023 was a great year for the GM from León; he became European Rapid Champion and finally added his name to the historic record of the León Magistral, winning the 36th edition of the event.

In 2024, he defeated Arjun Erigaisi, the world's fourth-ranked player, in León.

In 2025 he became the Spanish Rapid Champion and runner-up in Blitz.

In León, he lost in a tiebreaker to the eventual winner of the Magistral tournament, Le Quang Liem.

In the world rapid chess ranking, he is ranked 31st, which makes him the best Spanish player in this format and one of the strongest in the world.