77 (number)

77 (seventy-seven) is the natural number following 76 and preceding 78. Seventy-seven is the smallest positive integer requiring five syllables in English.

← 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
Greek numeral	ΟΖ´
Roman numeral	LXXVII, lxxvii
Binary	10011012
Ternary	22123
Senary	2056
Octal	1158
Duodecimal	6512
Hexadecimal	4D16

In mathematics

77 is:

• the 22nd discrete semiprime^[1] and the first of the (7.q) family, where q is a higher prime.
• with a prime aliquot sum of 19 within an aliquot sequence (77, 19, 1, 0) to the Prime in the 19-aliquot tree. 77 is the second composite member of the 19-aliquot tree with 65
• a Blum integer since both 7 and 11 are Gaussian primes.^[2]
• 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.^[3]
• the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1.^[4]
• the number of digits of the 12th perfect number.^[5]

It is possible for a sudoku puzzle to have as many as 77 givens, yet lack a unique solution.^[6]

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

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.^[7]

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 and believe that there is no god but Allah without any equals or highers and anyone worthy of worship, 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.^[8] Some have gone so far as to delineate these branches.^[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.^{[citation needed]}

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^[10]

References

1. Sloane, N. J. A. (ed.). "Sequence A001358". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. Sloane, N. J. A. (ed.). "Sequence A016105 (Blum integers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
3. Sloane, N. J. A. (ed.). "Sequence A000041". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
4. Sloane, N. J. A. (ed.). "Sequence A051882 (numbers that are not strict-sense Egyptian)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-08-29.
5. Caldwell, Chris K. "Mersenne Primes: History, Theorems and Lists".
6. "The Science behind Sudoku, J.P. Delahaye" (PDF). Archived from the original (PDF) on 2016-03-04. Retrieved 2008-10-07.
7. Buchan, Jamie (2010), Easy as Pi: The Countless Ways We Use Numbers Every Day, Penguin, ISBN 9781606522783.
8. "A Verdict of Mufti Muhammad Hassan". Archived from the original on 2008-12-04. Retrieved 2008-05-29.
9. "Imam al-Tahanawi on the Seventy-Seven Branches". Archived from the original on 2009-06-20. Retrieved 2008-05-29.
10. "10 Codes".

External links

Media related to 77 (number) at Wikimedia Commons