Prime numbers between 1401 and 1,500
There are 17 prime numbers between 1401 and 1,500: 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499.
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 ā1500 ā 38.7 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 17 primes between 1401 and 1,500, with a total of 24,773.
- 3
The biggest gap between neighbouring primes in this range is 14, after 1409 (the next prime is 1423). There are 4 twin prime pairs (primes 2 apart): (1427, 1429), (1451, 1453), (1481, 1483), (1487, 1489).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 1,401 to 1,410 | 1 | 10% |
| 1,411 to 1,420 | 0 | 0% |
| 1,421 to 1,430 | 3 | 30% |
| 1,431 to 1,440 | 2 | 20% |
| 1,441 to 1,450 | 1 | 10% |
| 1,451 to 1,460 | 3 | 30% |
| 1,461 to 1,470 | 0 | 0% |
| 1,471 to 1,480 | 1 | 10% |
| 1,481 to 1,490 | 4 | 40% |
| 1,491 to 1,500 | 2 | 20% |
Questions
How many prime numbers are there between 1401 and 1,500?
17.
What is the biggest prime number below 1,500?
1499.
What is the first prime number after 1400?
1409.