1,271. Chalakim

Hilchos Kiddush HaChodesh 6:2

Day and night always equal 24 hours combined, 12 hours of day and 12 of night. An hour is divided into 1,080 parts (chalakim). This number was chosen because it can be divided by 2, 4, 8, 3, 6, 9 and 10. Each of these divisions will contain many of these chalakim.

Hilchos Kiddush HaChodesh 6:3

The time from one conjunction of the moon and sun until the next based on their average rate of motion is 29 full days, 12 hours on the 30th day, and 793 chalakim from the 13th hour. The interval from one molad to the next is the length of a lunar month.