61 (number)

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← 60 61 62 →
Cardinalsixty-one
Ordinal61st
(sixty-first)
Factorizationprime
Prime18th
Divisors1, 61
Greek numeralΞΑ´
Roman numeralLXI
Binary1111012
Ternary20213
Octal758
Duodecimal5112
Hexadecimal3D16

61 (sixty-one) is the natural number following 60 and preceding 62.

In mathematics[edit]

61 is:

  • the 18th prime number.
  • a twin prime with 59.
  • a cuban prime of the form p = x3y3/xy, where x = y + 1.[1]
  • the smallest proper prime, a prime p which ends in the digit 1 in base 10 and whose reciprocal in base 10 has a repeating sequence with length p − 1. In such primes, each digit 0, 1, ..., 9 appears in the repeating sequence the same number of times as does each other digit (namely, p − 1/10 times).[2]:166
  • the exponent of the 9th Mersenne prime.[3] (261 − 1 = 2,305,843,009,213,693,951)
  • the sum of two squares, 52 + 62.
  • a centered square number.[4]
  • a centered hexagonal number.[5]
  • a centered decagonal number.[6]
  • the sixth Euler zigzag number (or Up/down number).
  • a unique prime in base 14, since no other prime has a 6-digit period in base 14.
  • a Pillai prime since 8! + 1 is divisible by 61 but 61 is not one more than a multiple of 8.[7]
  • a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 6, 1, 7, 8, 15, 23, 38, 61...[8]
  • palindromic in bases 6 (1416) and 60 (1160)

In the list of Fortunate numbers, 61 occurs thrice, since adding 61 to either the tenth, twelfth or seventeenth primorial gives a prime number[9] (namely 6,469,693,291; 7,420,738,134,871; and 1,922,760,350,154,212,639,131).

In science[edit]

Astronomy[edit]

In other fields[edit]

Sixty-one is:

In sports[edit]

References[edit]

  • R. Crandall and C. Pomerance (2005). Prime Numbers: A Computational Perspective. Springer, NY, 2005, p. 79.
  1. ^ "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  2. ^ Dickson, L. E., History of the Theory of Numbers, Volume 1, Chelsea Publishing Co., 1952.
  3. ^ "Sloane's A000043 : Mersenne exponents". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  4. ^ "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  5. ^ "Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  6. ^ "Sloane's A062786 : Centered 10-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  7. ^ "Sloane's A063980 : Pillai primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  8. ^ "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  9. ^ "Sloane's A005235 : Fortunate numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  10. ^ Hoyle, Edmund Hoyle's Official Rules of Card Games pub. Gary Allen Pty Ltd, (2004) p. 470
  11. ^ MySQL Reference Manual – Limits of Joins

External links[edit]