Prime Numbers up to 1,000

There are 168 prime numbers between 1 and 1,000.

What is a prime?

A prime number is a whole number greater than 1 whose only divisors are 1 and itself. 2 is the only even prime. 1 is not prime, because a prime must have exactly two divisors. Every whole number greater than 1 can be written as a product of primes in exactly one way — the fundamental theorem of arithmetic.

Primes by hundred

1–100 (25 primes)

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

101–200 (21 primes)

101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199

201–300 (16 primes)

211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293

301–400 (16 primes)

307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397

401–500 (17 primes)

401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499

501–600 (14 primes)

503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599

601–700 (16 primes)

601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691

701–800 (14 primes)

701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797

801–900 (15 primes)

809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887

901–1000 (14 primes)

907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997

Quick divisibility tests

  • By 2: the last digit is even.
  • By 3: the digit sum is divisible by 3.
  • By 5: the last digit is 0 or 5.
  • By 11: the alternating digit sum (e.g. 9 − 1 + 3 for 913) is divisible by 11.
  • To test n for primality you only need to try primes up to √n.