It is not known whether the double-Mersenne number MM(61) is prime or composite. It contains 694,127,911,065,419,642 digits and is currently far too large for the usual Lucas-Lehmer test.
The number of digits in M(61) is 61 turned upside down.
In 1657, Fermat challenged the mathematicians of Europe and England, "We await these solutions, which, if England or Belgic or Celtic Gaul do not produce, then Narbonese Gaul (Fermat's region) will." Among the challenges was this 500-year-old example from Bhaskara II: x2 - 61y2 = 1 (x, y > 0). [Balazs]
(261 - 1)/(2 - 1) and (261 + 1)/(2 + 1) are both primes. [Luhn]
The letter 'A' occurs 61 times among the U.S. state names. It is the most common letter used in this manner. [Blanchette]
The 61st book in the KJV Bible has 61 verses. [Desrosiers]
61 is the (6 - 1)th repfigit number: 61, 6 + 1 = 7, 1 + 7 = 8, 7 + 8 = 15, 8 + 15 = 23, 15 + 23 = 38, 23 + 38 = 61. [Mirizzi]
Ten consecutive distinct digits begin at position 61 after the decimal point of . [Wu]
(61+1)^61-61 is prime. [Luhn]
The smallest multidigit prime such that 61*16 + 1 is prime. [Gupta]
The smallest multidigit prime p such that the sum of first 2p primes is prime. [Russo]
The smallest multidigit prime p such that the sum of digits of pp is a square. [Russo]
The least prime such that its square can be expressed as the sum of one, two, three, or four distinct squares: 612 = 602 + 112 = 522 + 242 + 212 = 562 + 222 + 102 + 12. [Rupinski]
The smallest prime for which the decimal expansion of the reciprocal 1/61 contains all 10 digits in equal proportions. [Hartley]
The largest known prime of the form Ack(m, m), where Ack is the Ackermann function (which grows faster than an exponential function). Ack(3, 3) = 61. [Hartley]
The average life expectancy for an American male in 1960. Note the same year it was 73 (also prime) for American females. [Fearon]
61 is the sum of two consecutive squares: 52 + 62. [Schlesinger]
61 is the smallest number m and only two-digit number m such that the reversal of concatenation of the first m natural numbers is prime. [Firoozbakht]
Promethium (atomic number 61) may be missing from our solar system, but it has been detected in the spectrum of a variable star in the constellation Andromeda.
(61!/16!)+1 is prime with prime digital sum and length. [Patterson]
The smallest prime p such that p# is pandigital. [Patterson]
Cyclist Lance Armstrong defeated Jan Ullrich by 61 seconds in the 2003 Tour de France. [Hartley]
61 codons specify individual amino acids. [Necula]
61!*16! - 1 is prime with prime sum of digits. [Firoozbakht]
61 is the 7th prime of the form 3k+1 and 61 = (77+777)/(7+7). Note that seven 7's are used. [Firoozbakht]
61 67 71 67 71 73 71 73 79.[Silva]
61 is the sum of the first three primes ending with seven. [Sladcik]
Adding all the Roman numerals in Yugoslavia (i.e., yUgosLaVIa = 5+50+5+1 = 61) is prime. [Opao]
When numbering the sixty vertices of the fullerine buckyball in ordered pairs of ascending and descending numbers, the sum of the opposite pairs will equal 61. [McGown]
In 1838, astronomer Friedrich Wilhelm Bessel calculated the large proper motion of 61 Cygni using trigonometric parallax. This was the first star (other than the Sun) to have its distance known from the Earth. [McGown]
61 (sixty-one) is the largest prime whose name spelled out in English has no repeated letters. [Brahinsky]
61 is the smallest base b for which the generalized repunit ((b^37)-1)/(b-1) is prime.
The Monument, a memorial to the Great Fire of London in 1666, is the world's highest (at 61 meters) stone column marking the distance to Pudding Lane, where the fire started. Note that the reversal of 1666 is a beastly prime ending with 61. [Capelle]
The smallest prime repfigit number equal to the sum of the first n repfigit numbers. [Loungrides]
In "The Local Galaxy Group & Galactic Neighborhood Observing Guide" (Astronomical League, 2008) by Robert McGown and Dareth Murray, the authors dedicate the Virgo galaxy M61 (Prime Curio Galaxy) to the research of Chris K. Caldwell, G. L. Honaker, Jr., and others whose prime number research brings together some of the unique mathematical relationships in the universe.
The number of "questions and answers" in a complete TV game show of Jeopardy! [Davidson]
The first Self-Belgian number of type 2. [Angelini]
The great Topologist John Milnor had his conjecture disproved by M. Mahowald, who found S(61), the set of all oriented diffeomorphism classes of closed smooth homotopy 61-spheres is the trivial group. Reference: "Differential Toplogy Forty-Six Years Later", John Milnor, Notice of the AMS, June/July 2011, pp.804-809. [Post]
A leap second on Saturday (6/30/2012) will cause a 61-second minute.
The Focke-Wulf Fw 61 is often considered the first practical, functional helicopter.
Astronomers have discovered a large asteroid containing abundant amounts of water orbiting a white dwarf star, designated GD 61.
The reversal of 61 is a fourth power, and the reversal of its fourth power is a prime. Are there any more primes with both of these properties? [Gaydos]
The 61 1st-move pairs in chess yielding the minimum 19 2nd-move options for White are the symmetrical double advances of King-Bishop Pawns and all 20 responses with either that pawn's or either Rook Pawn's single advance. [Merickel]
The sum of the lowest digit in each of the powers of two (2 + 4 + 8 + 1 + 2 + 4 + 1 + 2 + 1 + 0 + 0 + 0 + 1 + 1 + 2 + 3 + 0 ...) is 61 unless there are some large power of two that has no zero. [Gaydos]
If we sum the last digits of the numbers up to 61 raised to the power of zerro or bigger, we always yield primes (61, 271 or 199). 61 is the smallest number with this property. If we sum the last digits of the first 61 numbers n raised to the power of n, the result is prime again (283). [Petrov]
61 and its prime index (18) are both reverse fourth powers. There are no more examples of this property in the first billion primes. Are there any more at all? [Gaydos]
(There are 20 curios for this number that have not yet been approved by an editor.)