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 large threshold, is described by the prime number theorem, but no efficient formula for the formula_1-th prime is known. Dirichlet's theorem on arithmetic progressions, in its basic form, asserts that linear polynomials with relatively prime integers formula_34 and formula_35 take infinitely many prime values. Stronger forms of the theorem state that the sum of the reciprocals of these prime values diverges, and that different linear polynomials with the same formula_35 have approximately the same proportions of primes. Although conjectures have been formulated about the proportions of primes in higher-degree polynomials, they remain unproven, and it is unknown whether there exists