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 is also a sufficient condition for formula_20 to be prime. Wilson's theorem says that an integer formula_145 is prime if and only if the factorial formula_146 is congruent to formula_147 mod formula_20. For a composite this cannot hold, since one of its factors divides both and formula_149, and so formula_150 is impossible. The formula_20-adic order formula_152 of an integer formula_1 is the number of copies of formula_20 in the prime factorization of formula_1. The same concept can be extended from integers to rational numbers by defining the formula_20-adic order of a fraction formula_157 to be formula_158. The formula_20-adic absolute value