Before the 20th century, definitions of primality were inconsistent, and significant mathematicians such as Goldbach, Lambert, Legendre, Cayley, and Kronecker wrote that 1 was prime.[10] The modern definition of "prime number" is "positive integer with exactly 2 factors", so 1 is not prime. This definition can be rationalized by observing that it more naturally suits mathematical theorems that concern the primes. For example, the fundamental theorem of arithmetic is easier to state when 1 is not considered prime.[11]