Prime numbers between 4001 and 4,100
There are 15 prime numbers between 4001 and 4,100: 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099.
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 ā4100 ā 64.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 15 primes between 4001 and 4,100, with a total of 60,683.
- 3
The biggest gap between neighbouring primes in this range is 22, after 4027 (the next prime is 4049). There are 4 twin prime pairs (primes 2 apart): (4001, 4003), (4019, 4021), (4049, 4051), (4091, 4093).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 4,001 to 4,010 | 3 | 30% |
| 4,011 to 4,020 | 2 | 20% |
| 4,021 to 4,030 | 2 | 20% |
| 4,031 to 4,040 | 0 | 0% |
| 4,041 to 4,050 | 1 | 10% |
| 4,051 to 4,060 | 2 | 20% |
| 4,061 to 4,070 | 0 | 0% |
| 4,071 to 4,080 | 2 | 20% |
| 4,081 to 4,090 | 0 | 0% |
| 4,091 to 4,100 | 3 | 30% |
Questions
How many prime numbers are there between 4001 and 4,100?
15.
What is the biggest prime number below 4,100?
4099.
What is the first prime number after 4000?
4001.