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 first known proof for this statement is attributed to him. Many more proofs of the infinitude of primes are known, including an analytical proof by Euler, Goldbach's proof based on Fermat numbers, Furstenberg's proof using general topology, and Kummer's elegant proof. Euclid's proof shows that every finite list of primes is incomplete. The key idea is to multiply together the primes in any given list and add formula_42. If the list consists of the primes formula_43, this gives the number By the fundamental theorem, formula_45 has a prime factorization with one or more prime factors. formula_45 is evenly divisible by