77 (seventy-seven) is the natural number following 76 and preceding 78. Seventy-seven is the smallest positive integer requiring five syllables in English.

In mathematics

77 is:

the 22nd discrete biprime and the first of the (7.q) family.
a Blum integer since both 7 and 11 are Gaussian primes.
the sum of three consecutive squares, 42 + 52 + 62.
the sum of the first eight prime numbers.
the number of integer partitions of the number 12.
the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1.
the number of digits of the 12th perfect number.

It is possible for a sudoku puzzle to have as many as 77 givens, yet lack a unique solution.

It and its sibling 49 are the only 2-digit numbers whose home primes (in base 10) have not been calculated.

In science

The atomic number of iridium
The boiling point of nitrogen

In history

During World War II in Sweden at the border with Norway, "77" was used as a shibboleth (password), because the tricky pronunciation in Swedish made it easy to instantly discern whether the speaker was native Swedish, Norwegian, or German.

In religion

In the Islamic tradition, "77" figures prominently. Muhammad is reported to have explained, "Faith has sixty-odd, or seventy-odd branches, the highest and best of which is to declare that there is no god but God, and the lowest of which is to remove something harmful from a road. Shyness, too, is a branch of faith." While some scholars refrain from clarifying "sixty-odd or seventy-odd", various numbers have been suggested, 77 being the most common. Some have gone so far as to delineate these branches.

The Gospel of Luke lists 77 generations from Adam to Jesus.