List of prime numbers

The prime numbers from 1 to 100§

There are 25 primes below 100:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

The number 1 is not on the list: a prime must have exactly two divisors, and 1 has only one (Prime numbers). 2 is the only even prime, since every other even number is divisible by 2. Every number from 2 to 100 that is not listed is composite, and has a prime factor of 2, 3, 5 or 7 (the primes up to √100 = 10).

The 168 primes below 1000§

The count of primes in each hundred falls from 25 (1 to 100) to 21, 16, 16, 17, 14, 16, 14, 15 and 14 (901 to 1000). Primes thin out slowly as numbers grow: near x, about one number in ln x is prime^[1].

How the list is made§

The tool uses a segmented sieve of Eratosthenes^[1]. To list the primes from a to b, it first finds every prime up to √b (at most one million, since b is at most 10¹²), then crosses out their multiples inside the window, starting each prime p at the first multiple that is at least a and at least p². Whatever is left in the window is prime. Every whole number in the window is examined, so the list is exact and complete. The window is limited to 10,000 numbers so that the table stays readable and the page stays quick; the arithmetic itself is exact well beyond that.

Two checks you can make: there are exactly 168 primes below 1000 and 78,498 below one million^[2]. The ranges just above a million and just below a trillion show how much sparser primes are up there: about one number in 14 near a million, and one in 28 near a trillion.

Sources

1. Victor Shoup (2008). A Computational Introduction to Number Theory and Algebra, 2nd edition (Version 2, free PDF). Cambridge University Press. ISBN 9780521516440. textbook
2. The OEIS Foundation (2025). A006880: Number of primes < 10^n (π(10^n)). The On-Line Encyclopedia of Integer Sequences. database