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11 is the only palindromic prime with an even number of digits due to the fact that all palindromes with an even number of digits are divisible by 11.
(1111 x 211 + 1)/(211 - 1) is prime. [Luhn]
There's a curious way to multiply a two digit number by the prime number 11. Add the two original digits and place this sum between them. E.g., 35 x 11. (3 + 5 = 8) and we get 385. Note that if the sum of the two digits exceeds 9 place the units digit of this sum between the two numbers, and add 1 to the hundreds digit. [Franco]
The smallest number with multiplicative persistence of 11 is 277777788888899. [Sloane]
An odd perfect number must have at least 11 prime factors if it's not divisible by 3.
The secret formula for Kentucky Fried Chicken includes 11 herbs and spices. [Sanders]
Sunspot activity seems to follow an 11-year cycle.
The smallest two-digit prime with no digit prime. [Gevisier]
2 + 35 x 711 is prime.
1111 contains two embedded elevens.
Also called a bar code, a Universal Product Code (UPC) consists of 11 numbers. [Bobick]
The 11th prime times (11) has a digit sum of 11.
Half of the first sixty-four partition numbers are divisible by 11. [Wilson]
Rotakas, spoken in the center of Bougainville Island in the South Pacific, uses only 11 letters (A, b, E, G, I, K, O, P, r, T and U).
The smallest anti-Yarborough prime, i.e., a prime containing any number of strictly 1s and zeros.
The Apollo 11 spacecraft reached Earth's parking orbit 11 minutes after takeoff. This was just 66 (6 x 11) years after Orville Wright flew two feet off the ground for over 11 seconds.
11 has the primitive root g = 2, meaning the remainders after dividing 2n by 11 assume all values 1, 2, ... 10, exactly once as n goes from 1 to 10.
There's a test for divisibility by 11. Combine the digits of a number in order, taking them with signs first + then -. If the result is 0 or a multiple of 11, the prime number 11 divides it. For example, is 21329 divisible by 11? Yes, since + 2 - 1 + 3 - 2 + 9 = 11.
Five consecutive powers of 11 produce palindromes:
110 = 1
69696 divided by 6336.
Below is the "smallest" doubly-true English alphametic with unique solution, where "smallest" means having the smallest sum word (11).
THREE THREE TWO TWO + ONE ------ ELEVEN [Keith]
The number of cards (including the Significator) typically used in a Tarot reading. [Haga]
The 1st prime repunit.
The smallest two digit Additive prime (a prime whose sum of digits is prime). [Russo]
There are 11 stars in Vincent van Gogh's Starry Night. [Easterling]
11 + 2n2 gives primes over the first 11 whole numbers.
Austrian composer Wolfgang Amadeus Mozart (1756-91) once wrote a waltz in which he specified 11 variations.
( ) = 11. [Kulsha]
11 divides its previous consecutive concatenated observed that 3*4 is 11).
According to Palestinian folklore, 11 is distinctly unlucky.
Giant Sequoia Trees have 11 pair of chromosomes. [Kaskel]
The repunit 11111111111 (11 ones) has only two prime factors.
Caldwell, New Jersey, is in Congressional District 11.
The number of letters in PRIME NUMBER . It is also equal to the number of letters in PRIME CURIOS! [Tarun Kumar]
11 is the (1+1)nd odd prime that cannot be expressed as the sum of two prime numbers. [Astle]
10! - 11 and 10! + 11 are two consecutive primes. [Firoozbakht]
11 is the only non-Nivenmorphic integer. [Boscaro]
The only known example where p divides (p - 1)# - 1. [Luhn]
Today only 11 lines of Sodades the Obscene of Maronea's works still remain.
The minimum prime p such that p + 1 each has exactly 2 distinct prime factors. [Das]
The No. 11 London Bus runs from Fulham Broadway to Liverpool Street Station. [Croll]
The only prime comprising an even number of identical digits. [Murthy]
The only prime p such that p + 8 and p + 6 are all prime. [Murthy]
A letter to the editor of "The Times" newspaper on the partially palindromic date of 22 February 2002 contained the 11 character palindrome "Madam I'm Adam" (excluding spaces and punctuation). [Croll]
The smallest prime with persistence (multiplicative as well as additive) of 1. [Gupta]
The palindrome 1234321 = 112 x 1012. Note the factors are palindromic primes. [Nelson]
The smallest prime (the fifth) which is greater than the corresponding (the fifth) composite, which is 10. [Murthy]
The smallest prime for which the sum of digits equals the number of digits. [Murthy]
11 is the smallest prime p such that 2^p-1 is composite. See page 11 of The STORY of MATHEMATICS by Motz and Weaver. [Russo]
11 is the smallest prime of the form n n's followed by 1. Note that eleven 11's followed by 1 is also prime. [Poo Sung]
The smallest odd prime which can be represented as sum of a triangular number and its reverse, i.e., 10 + 01 = 11. [Gupta]
11 is the smallest prime that is equal to the product plus sum of two primes (2*3 + (2+3) = 11). [Wagler]
The largest known example such that p# ± 1 are both primes. p# is primorial p. [Gupta]
The smallest multi-digit Lucasian prime: p is congruent to 3 (mod 4) with 2p+1 prime. [Russo]
The smallest prime p such that 6*p-1 is composite. [Russo]
No factorials can terminate with 11 zeros. [Dobb]
The smallest palprime p such that 2^p-1 has at most 2 prime factors. [Russo]
The smallest odd prime which can be represented as the sum of a number and its reverse, i.e., 10 + 01 = 11. [Gupta]
11 is the smallest Strong prime: p(n) > (p(n-1)+p(n+1))/2. [Russo]
11 = 3! + 5. Note that 3 and 5 are the first Twin primes. [Avrutin]
According to the FBI, a burglary occurs once every 11 seconds in the United States.
11 is the smallest prime p such that sigma(x) = 2^p has no solution. [Gupta]
Mod 11 was taken from each prime in "Visualizing Primes in 3D," enabling the program to move it's plotter in the z axis as well.
11=1+2+8 and the only known values of n for which (p(n)^p(n)-1)/(p(n)-1) is prime are n=1,2,8, and 11. [Rupinski]
The largest number (coincidentally prime) which is not expressible as sum of two composite numbers. [Gupta]
Dr. Michael Hartley discovered that the 120-cell has exactly 11 quotients.
The smallest prime p such that 6p + 1 do not form a twin prime pair. [Rupinski]
The budding computer knowledge of an 11-year-old middle school student from Florida resulted in a felony charge after he tapped into a teacher's computer and changed his grades.
11^2 = 37 + 41 + 43 (i.e., the sum of three consecutive primes). [La Haye]
2^^n-9 = 2^(2^(2^...(2^2)..))-9 is divisible by 11 for all sufficiently large n. 11 is the largest prime less than a million of which this is true. [Hartley]
No book in the Bible has exactly 11 chapters. [Hartley]
11 is the earliest prime p such that p^3 is the sum of 3 consecutive primes: 11^3 = 439 + 443 + 449. [Rivera]
ElevenSmooth is a distributed computing project searching for prime factors of M3326400.
In any given 12 hour period, on an analog clock, the minute hand resides in the same position as the hour hand exactly eleven times. [Patterson]
In "Western" music's 12-tone scale, ratios of fractions between 2 and 1 with a one-digit denominator that involve 11 are not used. The ratios 11/6, 11/7, 11/8, and 11/9 are not used in "Western" music. Neither are fractions with 11 as the denominator. These notes are not found in the "Western" twelve-tone scale, but might be found in the music of other cultures that use different tuning systems. [Max Obeidin]
A multiverse has been envisaged within the 11-dimensional extension of string theory known as M-theory.
Uri Geller (1946- ), who claims to possess supernatural powers, has always been fascinated by the prime number 11.
The largest non-McNugget number. [Patterson]
N = 11 is the largest prime with the following property: N# is written with n-1 distinct digits, where N is the nth prime. [Necula]
Elevenses is a British and colonial meal that is similar to afternoon tea, but eaten around 11 o'clock in the morning.
11^11+11^11*11-1 is prime. Note that 11 ones are used in the previous expression. [Patterson]
Visually, 11 is the first two positive Fibonacci numbers. [McAlee]
If T(A,B) = (A-B^2)^2-B with B < A, then 11 is the smallest value of A such that [A, A+2], [B, B+2], and [T(A,B), T(A,B)+2] are all twin prime pairs (in this case, B=5). All twin primes will exhibit this property if it is allowed that B > A. [Opao]
A hendecasyllabic is a verse or poem consisting of exactly 11 syllables. [Patterson]
11 is the smallest prime equal to the product of Twin primes minus their arithmetic mean (3*5 - 4 = 11). [Teofilatto]
11 is the smallest prime of the form 2^p + p. [Teofilatto]
11 is the only prime of the form 3^p + p. [Patterson]
There are exactly 11 positive odd integers N that cannot be expressed as the sum of two coprime composite integers, both of which are less than N. [Rupinski]
If you subtract the last digit of a number from the number formed from the remaining digits, and that number is divisible by eleven, then the original number is divisible by 11. E.g., the number 45771 is divisible by 11 because (4577 - 1) is divisible by 11. [Beedle]
Take a number (n) that is divisible by 11, and subtract the last digit from the remaining digits to get a new number (x). If (n) / 11 = (a), then (x) divided by 11 will equal the integer value of (a) divided by ten. [Beedle]
11 is the smallest prime which, when turned upside down, remains unchanged. [Astle]
11 is the smallest number of sides of a regular polygon that cannot be packed about a point with other regular polygons. E.g., a 7-sided polygon packs with a 42-sided polygon and a triangle. [Astle]
11 is the first multidigit number whose digital sum is prime. [Losnak]
"The Works of Charles Babbage" published in London contained 11 volumes. [McAlee]
11 is the smallest prime and the only prime of the form 2(p+q) + 1 which is not sum of two square. [Teofilatto]
World War I ended at 11AM on the 11th day of the 11th month of the year. Now the date is celebrated as Veteran's Day. [McCranie]
There is no number of the form n^2+n+1 that can be evenly divided by 11. [Schuler]
The badge number of Napoleon Solo in the TV show "The Man From U.N.C.L.E." is 11. [McCranie]
The name for the planet Pluto was proposed by 11-year-oldVenetia Burney of Oxford, England. For her it was the nameof a favorite Disney character. [Paddy]
Joseph-Louis Lagrange (1736-1813) is widely regarded as thefinest mathematician of the eighteenth century. He was bornthe youngest of 11 children but was the only child tosurvive beyond infancy.
11 is the largest integer that cannot be expressed as a sum of distinct primes. [Capelle]
A hendecagon is an eleven-sided polygon. [Patterson]
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