Prime numbers between 4201 and 4,300
There are 16 prime numbers between 4201 and 4,300: 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297.
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 ā4300 ā 65.6 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 16 primes between 4201 and 4,300, with a total of 67,978.
- 3
The biggest gap between neighbouring primes in this range is 10, after 4201 (the next prime is 4211). There are 5 twin prime pairs (primes 2 apart): (4217, 4219), (4229, 4231), (4241, 4243), (4259, 4261), (4271, 4273).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 4,201 to 4,210 | 1 | 10% |
| 4,211 to 4,220 | 3 | 30% |
| 4,221 to 4,230 | 1 | 10% |
| 4,231 to 4,240 | 1 | 10% |
| 4,241 to 4,250 | 2 | 20% |
| 4,251 to 4,260 | 2 | 20% |
| 4,261 to 4,270 | 1 | 10% |
| 4,271 to 4,280 | 2 | 20% |
| 4,281 to 4,290 | 2 | 20% |
| 4,291 to 4,300 | 1 | 10% |
Questions
How many prime numbers are there between 4201 and 4,300?
16.
What is the biggest prime number below 4,300?
4297.
What is the first prime number after 4200?
4201.