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

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

## In mathematics

61 is:

• the 18th prime number.
• a twin prime with 59.
• a cuban prime of the form p = x3y3/xy, where x = y + 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).: 166
• the exponent of the 9th Mersenne prime. (261 − 1 = 2,305,843,009,213,693,951)
• the sum of two squares, 52 + 62.
• a centered square number.
• a centered hexagonal number.
• a centered decagonal number.
• 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.
• 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...
• 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 (namely 6,469,693,291; 7,420,738,134,871; and 1,922,760,350,154,212,639,131).

Sixty-one is:

## In sports

• 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 – JOIN clause