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 factorizations are based on Euclid's lemma: If formula_20 is a prime number and formula_20 divides a product formula_33 of integers formula_34 and formula_35, then formula_20 divides formula_34 or formula_20 divides formula_35 (or both). Conversely, if a number formula_20 has the property that when it divides a product it always divides at least one factor of the product, then formula_20 must be prime. There are infinitely many prime numbers. Another way of saying this is that the sequence of prime numbers never ends. This statement is referred to as "Euclid's theorem" in honor of the ancient Greek mathematician Euclid, since the