77 (number)

From Wikipedia, the free encyclopedia - View original article

767778
Cardinalseventy-seven
Ordinal77th
(seventy-seventh)
Factorization7 × 11
Divisors1, 7, 11, 77
Roman numeralLXXVII
Binary10011012
Ternary22123
Quaternary10314
Quinary3025
Senary2056
Octal1158
Duodecimal6512
Hexadecimal4D16
Vigesimal3H20
Base 362536
 
Jump to: navigation, search
767778
Cardinalseventy-seven
Ordinal77th
(seventy-seventh)
Factorization7 × 11
Divisors1, 7, 11, 77
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]

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