Prime numbers between 1301 and 1,400
There are 11 prime numbers between 1301 and 1,400: 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399.
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 ā1400 ā 37.4 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 11 primes between 1301 and 1,400, with a total of 14,759.
- 3
The biggest gap between neighbouring primes in this range is 34, after 1327 (the next prime is 1361). There are 2 twin prime pairs (primes 2 apart): (1301, 1303), (1319, 1321).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 1,301 to 1,310 | 3 | 30% |
| 1,311 to 1,320 | 1 | 10% |
| 1,321 to 1,330 | 2 | 20% |
| 1,331 to 1,340 | 0 | 0% |
| 1,341 to 1,350 | 0 | 0% |
| 1,351 to 1,360 | 0 | 0% |
| 1,361 to 1,370 | 2 | 20% |
| 1,371 to 1,380 | 1 | 10% |
| 1,381 to 1,390 | 1 | 10% |
| 1,391 to 1,400 | 1 | 10% |
Questions
How many prime numbers are there between 1301 and 1,400?
11.
What is the biggest prime number below 1,400?
1399.
What is the first prime number after 1300?
1301.