Prime numbers between 3301 and 3,400
There are 15 prime numbers between 3301 and 3,400: 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391.
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 ā3400 ā 58.3 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 15 primes between 3301 and 3,400, with a total of 50,157.
- 3
The biggest gap between neighbouring primes in this range is 16, after 3373 (the next prime is 3389). There are 4 twin prime pairs (primes 2 apart): (3329, 3331), (3359, 3361), (3371, 3373), (3389, 3391).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 3,301 to 3,310 | 2 | 20% |
| 3,311 to 3,320 | 2 | 20% |
| 3,321 to 3,330 | 2 | 20% |
| 3,331 to 3,340 | 1 | 10% |
| 3,341 to 3,350 | 2 | 20% |
| 3,351 to 3,360 | 1 | 10% |
| 3,361 to 3,370 | 1 | 10% |
| 3,371 to 3,380 | 2 | 20% |
| 3,381 to 3,390 | 1 | 10% |
| 3,391 to 3,400 | 1 | 10% |
Questions
How many prime numbers are there between 3301 and 3,400?
15.
What is the biggest prime number below 3,400?
3391.
What is the first prime number after 3300?
3301.