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Concept
11 (number)
Summary
11 (eleven) is the natural number following 10 and preceding 12. It is the first repdigit. In English, it is the smallest positive integer whose name has three syllables.
"Eleven" derives from the Old English ęndleofon, which is first attested in Bede's late 9th-century Ecclesiastical History of the English People. It has cognates in every Germanic language (for example, German elf), whose Proto-Germanic ancestor has been reconstructed as *ainalifa-, from the prefix *aina- (adjectival "one") and suffix *-lifa-, of uncertain meaning. It is sometimes compared with the Lithuanian vienúolika, though -lika is used as the suffix for all numbers from 11 to 19 (analogously to "-teen").
The Old English form has closer cognates in Old Frisian, Saxon, and Norse, whose ancestor has been reconstructed as *ainlifun. This was formerly thought to be derived from Proto-Germanic *tehun ("ten"); it is now sometimes connected with *leikw- or *leip- ("left; remaining"), with the implicit meaning that "one is left" after counting to ten.
While 11 has its own name in Germanic languages such as English, German, or Swedish, and some Latin-based languages such as Spanish, Portuguese, and French, it is the first compound number in many other languages: Chinese 十一 shí yī, Korean 열하나 yeol hana or 십일 ship il.
Eleven is the fifth prime number, and the first two-digit numeric palindrome in decimal. It forms a twin prime with 13, and it is the first member of the second prime quadruplet (11, 13, 17, 19). The eleventh prime number is the first prime exponent that does not yield a Mersenne prime, where , which is composite. On the other hand, the eleventh prime number 31 is the third Mersenne prime, while the thirty-first prime number 127 is not only a Mersenne prime but also the second double Mersenne prime. 11 is also the fifth Heegner number, meaning that the ring of integers of the field has the property of unique factorization and class number 1. 11 is the first prime repunit in decimal (and simply, the first repunit), as well as the second unique prime in base ten.
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