77 (number)

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76 77 78
Cardinal seventy-seven
Ordinal 77th
(seventy-seventh)
Factorization 7 × 11
Divisors 1, 7, 11, 77
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]

Seventy-seven is the 22nd discrete biprime and the first of the (7.q) family. Since both 7 and 11 are Gaussian primes, this means that 77 is a Blum integer.

77 has an aliquot sum of 19 and it is the second number to do so the first being 65; 77 is the 2nd member of the 19-aliquot tree.

It is the sum of three squares, 42 + 52 + 62, as well as the sum of the first eight prime numbers.

It also is the number of integer partitions of the number 12.[1]

It is the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1.[2]

77 and 78 form a Ruth–Aaron pair.

It is possible for a sudoku puzzle to have as many as 77 givens, yet lack a unique solution.[3]

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

It is the number of digits of the 12th perfect number.[4]

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.[5]

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

The genealogy of the bible lists 77 generations from Adam to Jesus.[8]

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 sports[edit]

In other fields[edit]

Seventy-seven is also:

References[edit]

  1. ^ The On-Line Encyclopedia of Integer Sequences
  2. ^ Erich Friedman, Stetson University
  3. ^ The Science behind Sudoku, J.P. Delahaye
  4. ^ Mersenne Primes: History, Theorems and Lists
  5. ^ Buchan, Jamie (2010), Easy as Pi: The Countless Ways We Use Numbers Every Day, Penguin, ISBN 9781606522783 .
  6. ^ A Verdict of Mufti Muhammad Hassan
  7. ^ Imam al-Tahanawi on the Seventy-Seven Branches
  8. ^ The genealogy of Jesus
  9. ^ Best Athletes by the numbers
  10. ^ NC State Football Legend Dennis Byrd Dies at Age of 63
  11. ^ http://www.gohofstra.com/ViewArticle.dbml?DB_OEM_ID=22200&ATCLID=3710342
  12. ^ http://www.fdnewyork.com/10code.asp