Prime numbers between 3401 and 3,500
There are 11 prime numbers between 3401 and 3,500: 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499.
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 ā3500 ā 59.2 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 11 primes between 3401 and 3,500, with a total of 38,009.
- 3
The biggest gap between neighbouring primes in this range is 22, after 3469 (the next prime is 3491). There are 2 twin prime pairs (primes 2 apart): (3461, 3463), (3467, 3469).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 3,401 to 3,410 | 1 | 10% |
| 3,411 to 3,420 | 1 | 10% |
| 3,421 to 3,430 | 0 | 0% |
| 3,431 to 3,440 | 1 | 10% |
| 3,441 to 3,450 | 1 | 10% |
| 3,451 to 3,460 | 1 | 10% |
| 3,461 to 3,470 | 4 | 40% |
| 3,471 to 3,480 | 0 | 0% |
| 3,481 to 3,490 | 0 | 0% |
| 3,491 to 3,500 | 2 | 20% |
Questions
How many prime numbers are there between 3401 and 3,500?
11.
What is the biggest prime number below 3,500?
3499.
What is the first prime number after 3400?
3407.