11 (number) "ùndici" (but in Spanish and Portuguese, 16, and in French, 17 is the first compound number), Chinese 十一 "shí yī", Korean 열한 "yeol han". 11 is a prime number. It is the smallest two-digit prime number in the decimal base. The next prime is 13, with which it comprises a twin prime. If a number is divisible by 11, reversing its digits will result in another multiple of 11. As long as no two adjacent digits of a number added together exceed 9, then multiplying the number by 11, reversing the digits of the product, and dividing that new number
Prime number theorem on primes in arithmetic progressions as a special case. In the theory of finite groups the Sylow theorems imply that, if a power of a prime number formula_195 divides the order of a group, then it has a subgroup of order formula_195. By Lagrange's theorem, any group of prime order is a cyclic group, and by the Burnside theorem any group whose order is divisible by only two primes is solvable. For a long time, number theory in general, and the study of prime numbers in particular, was seen as the canonical example of pure mathematics, with no applications