Prime numbers between 401 and 500
There are 17 prime numbers between 401 and 500: 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499.
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 ā500 ā 22.4 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 17 primes between 401 and 500, with a total of 7,649.
- 3
The biggest gap between neighbouring primes in this range is 12, after 467 (the next prime is 479). There are 3 twin prime pairs (primes 2 apart): (419, 421), (431, 433), (461, 463).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 401 to 410 | 2 | 20% |
| 411 to 420 | 1 | 10% |
| 421 to 430 | 1 | 10% |
| 431 to 440 | 3 | 30% |
| 441 to 450 | 2 | 20% |
| 451 to 460 | 1 | 10% |
| 461 to 470 | 3 | 30% |
| 471 to 480 | 1 | 10% |
| 481 to 490 | 1 | 10% |
| 491 to 500 | 2 | 20% |
Questions
How many prime numbers are there between 401 and 500?
17.
What is the biggest prime number below 500?
499.
What is the first prime number after 400?
401.