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 the notion that the "density" of primes around should be . This function is related to the logarithm by the asymptotic expansion So, the prime number theorem can also be written as . In fact, in another paper in 1899 de la Vallée Poussin proved that for some positive constant , where is the big notation. This has been improved to Because of the connection between the Riemann zeta function and , the Riemann hypothesis has considerable importance in number theory: if established, it would yield a far better estimate of the error involved in the prime number theorem than