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 such as the Meissel–Lehmer algorithm can compute exact values of formula_88 faster than it would be possible to list each prime up to formula_1. The prime number theorem states that formula_88 is asymptotic to formula_94, which is denoted as and means that the ratio of formula_88 to the right-hand fraction approaches 1 as formula_1 grows to infinity. This implies that the likelihood that a randomly chosen number less than formula_1 is prime is (approximately) inversely proportional to the number of digits in formula_1. It also implies that the formula_1th prime number is proportional to formula_101 and therefore that the average