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# 11 (number)

11 (eleven) is the natural number following 10 and preceding 12. Eleven is the smallest positive integer requiring three syllables in English.

 List of numbers — Integers << 10 11 12 13 14 15 16 17 18 19 >>
Cardinal eleven
Ordinal eleventh
Numeral system
Factorization prime
Roman numeral XI
Binary 1011

## In mathematics

Eleven is the 5th smallest prime number, and also a repunit prime. Although it is necessary for n to be prime for 2n-1 to be a Mersenne prime, the converse is not true: 211 - 1 = 2047 which is 23 × 89. The next prime is thirteen, with which it comprises a twin prime.

Because it has a reciprocal of unique period length among primes, 11 is a unique prime. 11 goes into 99 exactly 9 times, so fractions with 11 in the denominator have two digit repeating sequences in their decimal expansions. Multiples of eleven by one-digit numbers all have double digits: 00 (=0), 11, 22, 33, 44 . . .

In base 10, there is a simple test to determine if an integer is divisible by 11: take every other digit and add them up, then take the remaining digits and add them up. If the difference between the two sums is a multiple of 11, including 0, then the number is divisible by 11.

An eleven-sided polygon is a hendecagon.

In base thirteen and higher bases (such as hexadecimal), eleven is represented as B, where ten is A. In duodecimal, however, eleven is sometimes represented as E and ten as T.

Multiplied by -1, eleven is a Heegner number.

## In other fields

There are eleven players in a soccer as well as in a cricket team.

The number eleven is important in numerology, as it is the first of the master numbers.

Being only one hour before 12:00 -- midnight -- the eleventh hour means the last possible moment to take care of something, and often implies a situation of urgent danger or emergency (see Doomsday clock).

Uri Geller has always been fascinated by the number eleven. After the September 11 World Trade Center attack, he published an open list of connections to the number eleven involved in that attack.

In the film This Is Spinal Tap, guitarist Nigel Tufnel proudly shows off an amplifier with top settings of 11, higher than the traditional 10.

Eleven is:

• The atomic number of sodium.
• The number of guns in a gun salute to U.S. Army, Air Force and Marine Corps Brigadier Generals, and to Navy and Coast Guard Rear Admirals Lower Half.
• The number of General Orders for Sentries in the Marine Corps.
• The number of spacetime dimensions in M-theory.
• A page in the Service Record Book of an enlisted Marine for writing down disciplinary actions.
• In rugby union the left wing wears the 11 shirt.
• Historical years: 11 A.D., 11 B.C, or 1911