77 (number)

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← 76 77 78 →
Cardinal seventy-seven
Ordinal 77th
Factorization 7 × 11
Divisors 1, 7, 11, 77
Greek numeral ΟΖ´
Roman numeral LXXVII
Binary 10011012
Ternary 22123
Quaternary 10314
Quinary 3025
Senary 2056
Octal 1158
Duodecimal 6512
Hexadecimal 4D16
Vigesimal 3H20
Base 36 2536

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[edit]

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.[1]
  • 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.[2]
  • the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1.[3]
  • the number of digits of the 12th perfect number.[4]

It is possible for a sudoku puzzle to have as many as 77 givens, yet lack a unique solution.[5]

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

In science[edit]

In history[edit]

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.[6]

In religion[edit]

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.[7] Some have gone so far as to delineate these branches.[8]

The Gospel of Luke lists 77 generations from Adam to Jesus.[9]

In religious numerology[edit]

In certain numerological systems based on the English alphabet, the number 77 is associated with Jesus Christ. CHRIST is C = 3, H = 8, R = 18, I = 9, S = 19, T = 20, which added together equal 77.

'Liber 77' is the gematrian name for Liber OZ- a brief but popular publication by Aliester Crowley. The word 'oz', which means 'strength', is composed of two hebrew letters- ayin and zayin, which have gematrian values of 70 and 7 respectively, thus adding up to 77.

In other fields[edit]

Seventy-seven is also:


External links[edit]

Media related to 77 (number) at Wikimedia Commons