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 we have in particular empirically the primes congruent to 3 are more numerous and are nearly always ahead in this "prime number race"; the first reversal occurs at . However Littlewood showed in 1914 that there are infinitely many sign changes for the function so the lead in the race switches back and forth infinitely many times. The phenomenon that is ahead most of the time is called Chebyshev's bias. The prime number race generalizes to other moduli and is the subject of much research; Pál Turán asked whether it is always the case that and change places when and