77 (number)

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← 76 77 78 →
Cardinalseventy-seven
Ordinal77th
(seventy-seventh)
Factorization7 × 11
Divisors1, 7, 11, 77
Greek numeralΟΖ´
Roman numeralLXXVII
Binary10011012
Ternary22123
Quaternary10314
Quinary3025
Senary2056
Octal1158
Duodecimal6512
Hexadecimal4D16
Vigesimal3H20
Base 362536

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 the Gospel of Matthew Peter asks "How many times shall i forgive my brother". Jesus replies "Seventy-seven times"

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:

References[edit]

  1. ^ Sloane, N. J. A. (ed.). "Sequence A016105 (Blum integers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A000041". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ "What's Special About This Number?".
  4. ^ Caldwell, Chris K. "Mersenne Primes: History, Theorems and Lists".
  5. ^ The Science behind Sudoku, J.P. Delahaye
  6. ^ Buchan, Jamie (2010), Easy as Pi: The Countless Ways We Use Numbers Every Day, Penguin, ISBN 9781606522783.
  7. ^ "A Verdict of Mufti Muhammad Hassan". Archived from the original on 2008-12-04. Retrieved 2008-05-29.
  8. ^ "Imam al-Tahanawi on the Seventy-Seven Branches". Archived from the original on 2009-06-20. Retrieved 2008-05-29.
  9. ^ "The genealogy of Jesus".
  10. ^ "10 Codes".

External links[edit]

Media related to 77 (number) at Wikimedia Commons