Prime numbers between 301 and 400
There are 16 prime numbers between 301 and 400: 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397.
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 ā400 ā 20.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 16 primes between 301 and 400, with a total of 5,612.
- 3
The biggest gap between neighbouring primes in this range is 14, after 317 (the next prime is 331). There are 2 twin prime pairs (primes 2 apart): (311, 313), (347, 349).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 301 to 310 | 1 | 10% |
| 311 to 320 | 3 | 30% |
| 321 to 330 | 0 | 0% |
| 331 to 340 | 2 | 20% |
| 341 to 350 | 2 | 20% |
| 351 to 360 | 2 | 20% |
| 361 to 370 | 1 | 10% |
| 371 to 380 | 2 | 20% |
| 381 to 390 | 2 | 20% |
| 391 to 400 | 1 | 10% |
Questions
How many prime numbers are there between 301 and 400?
16.
What is the biggest prime number below 400?
397.
What is the first prime number after 300?
307.