# 109

This number is a prime. 103# + 107 is divisible by 109. Note the use of consecutive primes. [Rupinski] If 109 is written in Roman notation (CIX), then it becomes reflectable along the line it is written on. The pipe organ at the Cathedral of Notre Dame in Paris has 109 stops. When chilled below minus 109°F, CO2 becomes a solid, called dry ice. 109 equals the square root of 11881 or 118 - 8 - 1. 109 = 1*2+3*4+5*6+7*8+9. [Silva] Shibuya 109 is a trend setting fashion complex for young women in Tokyo, Japan. One of the buildings there is called "The Prime." [Anansi] The registry number of the famous patrol boat PT-109, commanded by John F. Kennedy. 109 can be expressed as 22 * 33 + 1. [Patterson] The Caldwell Catalog contains 109 deep-sky delights for backyard stargazers. Vatican City covers an area less than 109 acres. The period of the reciprocal of 109 ends with 853211 (the beginning of the Fibonacci sequence reversed). [Toews] The Sun is just over 109 times the diameter of the Earth. [Friedman] 109 = prime(prime (1+0+9)). Note that 109 is the only number with this property. [Firoozbakht] The smallest prime formed from reverse concatenation of two consecutive composite numbers. [Gupta] 109 = (7^3-5^3)/2 is the smallest prime which equals to one half of the difference of cubes of primes. [Simon] There are exactly 109 autobiographical numbers. [Wasserman] The smallest prime number which is sum of primeval primes. [Capelle] There are 109 letters in the following quotation: "Given the millennia that people have contemplated prime numbers, our continuing ignorance concerning the primes is stultifying." R. Crandall and C. Pomerance, from Prime Numbers: A Computational Perspective, Springer-Verlag, 2001. [Post] 109 can be expressed in the palindromic form 12*3^2+1. [Rupinski] The smallest invertible prime whose reversal is an invertible semiprime. [Capelle] In the movie "Escape From Alcatraz," 109 is the number of the cell assigned to Frank L. Morris (Clint Eastwood). 109 along with 601 are the only invertible primes that appear on a digital clock. [Punches] The difference of the sum of the squares of the composite digits and the sum of the squares of the non-composite digits. [Silva] Sustained body temperatures of over 109 degrees Fahrenheit are normally incompatible with life. The smallest invertible Cyclops prime. It yields the smallest invertible Cyclops semiprime when reversed-then-turned upside down. [Capelle] The smallest number (coincidentally prime) that has more distinct digits than its square. [Capelle] The smallest prime of the form 10^(2k)+10^k-1. Those primes consist of 1 followed by k 0's and k 9's. [Silva] The smallest non-trivial prime that is the sum of the reversal of two consecutive primes (109 = R(47) + R(53) = 74 + 35). [Meller] Smallest multidigit prime which is a partial sum of digital reversals of n: 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 1 + 11 + 21 + 31 = 109 is prime. [Post] The sum of the reversals of any two double-digit numbers summed to a hundred. [Loungrides] The smallest distinct-digit positive integer whose square has no unique digits. [Gaydos] 109 is as easy as 1^1 + 2^2 * 3^3. [Meyers] The Messerschmitt Bf 109 was the most-produced fighter aircraft in history. [Gaydos] 109 = (10*9) + (10+9). [Bui Quang Tuan] Convert 109 to binary to get 1101101 and treat it as a decimal number; 1101101 = 109*10101 = 92 and 10101 itself is a binary number. [Bergot] The smallest prime concatenated from two successive numbers, (9, 10), that are sides in an equable triangle. (A shape is called equable if its area equals its perimeter). The triangle is (9, 10, 17). [Loungrides] Consider the cubic equation x^3-15x-4=0, which has real coefficients, and three real roots for its answers. If we apply Cardano's formula to this problem, using a=1, b=0, c=-15, d=-4, we find taking the square root of negative 109 in the resulting computation is required! The magic sum for the hexagonal tortoise problem (지수귀문도) is maximal at 109. 109 has a partition whose parts concatenate to its cube: 109 = 1 + 29 + 50 + 29 -> 1295029 = 1093. [Beedassy] None of the 109 consecutive integers from 6498130362 to 6498130470 are semiprimes. [Gaydos] A new species of butterfly was discovered in Israel for the first time in 109 years. [Homewood] "Prime 109" is a classic yet innovative wood-fired steakhouse in Charlottesville, Virginia. [Homewood]

(There are 15 curios for this number that have not yet been approved by an editor.)