11 (number) is divisible by eleven. This also works by adding a trailing zero instead of a leading one: 65 + 63 + 70 = 198, which is divisible by 11. This also works with larger groups of digits, providing that each group has an even number of digits (not all groups have to have the same number of digits). An easy way of multiplying numbers by 11 in base 10 is: If the number has: In base 13 and higher bases (such as hexadecimal), 11 is represented as B, where ten is A. In duodecimal, however, 11 is sometimes represented as
Prime number theorem limit of the "difference" of the two functions as increases without bound. Instead, the theorem states that approximates in the sense that the relative error of this approximation approaches 0 as increases without bound. The prime number theorem is equivalent to the statement that the th prime number satisfies the asymptotic notation meaning, again, that the relative error of this approximation approaches 0 as increases without bound. For example, the th prime number is , and ()log() rounds to , a relative error of about 6.4%. The prime number theorem is also equivalent to where and are the first and