List of Prime Numbers

See every prime number in any range, plus the first 168 primes and how many exist below each power of ten.

List all the prime numbers between two values.

From

The first 1,000 prime numbers and how they are counted

A prime number is a whole number greater than 1 whose only divisors are 1 and itself. The first primes are 2, 3, 5, 7, 11 and 13; 2 is the only even prime. There are 25 primes below 100, 168 below 1,000 and 1,229 below 10,000. The 100th prime is 541 and the 1,000th prime is 7,919.

All 168 primes up to 1,000

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, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997

How many primes are there?

There are infinitely many primes, as Euclid proved around 300 BC, but they get rarer as numbers grow. The table shows the count of primes up to each power of ten.

Up to	Primes	Share of numbers
10	4	40.00%
100	25	25.00%
1,000	168	16.80%
10,000	1,229	12.29%
100,000	9,592	9.59%
1,000,000	78,498	7.85%
10,000,000	664,579	6.65%
100,000,000	5,761,455	5.76%
1,000,000,000	50,847,534	5.08%

How the list is generated

The calculator uses the sieve of Eratosthenes: it writes every number up to your end value, then repeatedly crosses out the multiples of each prime, starting with 2. The numbers left standing are the primes. To check one specific number, use the prime number checker, and to split a number into primes use the factor calculator.

How to use the prime number list tool

Enter the start of your range (use 0 or 1 to begin at the first prime).
Enter the end of your range, up to 10,000,000.
Read the count of primes and the full list for that range.

Frequently asked questions

How many prime numbers are there between 1 and 100?

There are 25: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

What is the 100th prime number?

The 100th prime number is 541. The 1,000th prime is 7,919.

Is 1 a prime number?

No. A prime has exactly two divisors, and 1 has only one. Treating 1 as non-prime keeps the unique factorization of every number into primes.

Is 2 the only even prime number?

Yes. Every other even number is divisible by 2, so it has at least three divisors and cannot be prime.

What is the largest known prime number?

The largest known primes are Mersenne primes with tens of millions of digits, found by distributed computer searches. No largest prime exists, since there are infinitely many.

How do I check whether one number is prime?

Use the prime number checker: it tells you instantly whether a number is prime and shows its prime factorization and the nearest primes.

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