The Doomsday rule was devised by John Conway in 1973 to compute the day of week in your head (https://en.wikipedia.org/wiki/Doomsday_rule). Others have made improvements for easier mental calculation.
Currently, the simplest one is published in 2023 in the paper "A Simple Formula for Doomsday" by Hirofumi Nakai (https://thatsmaths.com/2023/06/22/a-simple-formula-for-the-weekday/).
- split the year into century part and the remaining 2-digit part:
Y = 100c + y - compute the modulo 4 of these 2 parts:
c₄ = c % 4,y₄ = y % 4 - the Doomsday would be
(5(c₄ + y₄ - 1) + 10y) % 7