Although there are no known distribution patterns of prime numbers, the asymptotic distribution of primes is described by the prime number theorem:
where π(x) is the number of prime numbers less than or equal to x > 1. Note that the prime number theorem describes only the asymptotic distribution of primes. In other words, the bigger x is, the more accurate x/ln(x) estimates π(x) relatively.
According to the prime number theorem, the number of prime numbers between 2000 and 2100, is estimated to be:
2100/ln(2100) - 2000/ln(2000),
which is approximately 11.4, a rough estimate knowing that
π(2100) - π(2000) = 14.