11 (number) to be a Mersenne prime, the converse is not true: 2 − 1 = 2047 which is 23 × 89. 11 raised to the nth power is the nth row of Pascal's Triangle. (This works for any base, but the number eleven must be changed to the number represented as 11 in that base; for example, in duodecimal this must be done using thirteen.) 11 is a Heegner number, meaning that the ring of integers of the field formula_1 has the property of unique factorization. One consequence of this is that there exists at most one point on the elliptic
Prime number theorem Dusart proved: The proof by de la Vallée Poussin implies the following. For every , there is an such that for all , As a consequence of the prime number theorem, one gets an asymptotic expression for the th prime number, denoted by : A better approximation is Again considering the th prime number , this gives an estimate of ; the first 5 digits match and relative error is about 0.00005%. Rosser's theorem states that This can be improved by the following pair of bounds: The table compares exact values of to the two approximations and . The last