Prime numbers between 1 and 1,000
There are 168 prime numbers between 1 and 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 to work it out
- 1
A prime has exactly two factors, 1 and itself. To list them, cross out multiples of 2, then 3, then 5, and so on up to ā1000 ā 31.6 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 168 primes between 1 and 1,000, with a total of 76,127.
- 3
The biggest gap between neighbouring primes in this range is 20, after 887 (the next prime is 907). There are 35 twin prime pairs (primes 2 apart), the first ones (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 1 to 1,000 | 168 | 16.8% |
Questions
How many prime numbers are there between 1 and 1,000?
168.
What is the biggest prime number below 1,000?
997.
What is the first prime number after 0?
2.