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 a quadratic polynomial that (for integer arguments) is prime infinitely often. Euler's proof that there are infinitely many primes considers the sums of reciprocals of primes, Euler showed that, for any arbitrary real number formula_22, there exists a prime formula_20 for which this sum is bigger than formula_22. This shows that there are infinitely many primes, because if there were finitely many primes the sum would reach its maximum value at the biggest prime rather than growing past every formula_22. The growth rate of this sum is described more precisely by Mertens' second theorem. For comparison, the sum does not