77 (number)

← 76 77 78 →
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Cardinal seventy-seven
Ordinal 77th
(seventy-seventh)
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

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

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.[6]

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.[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

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

Seventy-seven is also:

References

  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".

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