Near any large N, a random integer: The average gap between consecutive prime numbers increases as N gets larger … thus, the probability decreases that N is prime: 1/ln(x), where ln is the natural logarithm. Let pi(x) ~ x/ln(x) be an asymtotic function. example: How many primes are there from 1,000 to 1,000,000? (10^6)/(6ln(10) – (10^3)/(3ln(10) = 72,238 prime numbers per 100,000, or about 7.2% For more details see www.math.columbia.edu/~goldfeld/ErdosSelbergDispute.pdf Dorian Goldfeld Columbia University New York, NY 10027. Image: The Sombrero Galaxy (M104), located in the constellation Virgo, 28 million light years distant. M104b_peris2048.jpg apod.nasa.gov

the density of primes