77 (number)

← 76 77 78 →
← 70 71 72 73 74 75 76 77 78 79 → List of numbers — Integers ← 0 10 20 30 40 50 60 70 80 90 →
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

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.
• a Harshad number in bases 3, 6, 8, 11, 12 and 15
• 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]

77 and 78 form a Ruth–Aaron pair.

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 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

• The atomic number of iridium
• The boiling point of nitrogen

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 sports

• Portland Trail Blazers coach Jack Ramsay led his team to their only NBA title in his first season. #77 was retired in honor of the 1977 NBA title.
• The number posthumously retired by the Minnesota Vikings of the NFL for offensive lineman Korey Stringer.
• The number worn by Ray Bourque in the NHL from 1987 to 2001. This number has been retired by the Boston Bruins, with whom he played for 20 years, and the Colorado Avalanche, with whom he won the Stanley Cup in his last NHL game. He wore 77 after his previous number (7), which he wore for his first eight seasons, was retired for Phil Esposito.
• The number worn by football legend Red Grange. Retired by both the University of Illinois and the Chicago Bears.
• The number worn by NFL Hall of Famer Jim Parker.^[10] Retired by the Indianapolis Colts
• The number worn by NFL offensive tackle Stan Mauldin. Retired by the Arizona Cardinals.
• The number worn by NCAA football legend Dennis Byrd. Retired by NC State in 2001.^[11]
• The number worn by NCAA football legend John Schmitt. Retired by Hofstra University.^[12]
• The number worn by Alex Melvin of the Pickering Red Sox (PBA). Retired in 2009.
• The number worn by NCAA basketball legend Bill Spivey. Retired by the University of Kentucky.
• The number of the car Valtteri Bottas drives in F1.

In other fields

Seventy-seven is also:

• 10-77 – the New York City Fire Department's (FDNY) 10 code for high-rise, multiple-dwelling fire ^[13]
• Shortening of a 1950's-60's TV series, 77 Sunset Strip
• Group of 77, a group of developing nations at the United Nations
• 77 – Talking Heads's debut album (Talking Heads: 77) released in 1977
• The 77's, an American Rock band
• The temperature, in Fahrenheit, some characteristics of semiconductors are specifically given in a datasheet (77 °F = 25 °C).

References

1. "Sloane's A016105 : Blum integers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
2. The On-Line Encyclopedia of Integer Sequences
3. Erich Friedman, Stetson University
4. 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
8. Imam al-Tahanawi on the Seventy-Seven Branches
9. The genealogy of Jesus
10. Best Athletes by the numbers
11. NC State Football Legend Dennis Byrd Dies at Age of 63
12. http://www.gohofstra.com/ViewArticle.dbml?DB_OEM_ID=22200&ATCLID=3710342
13. http://www.fdnewyork.com/10code.asp