Prime numbers between 3901 and 4,000
There are 11 prime numbers between 3901 and 4,000: 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989.
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 ā4000 ā 63.2 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 11 primes between 3901 and 4,000, with a total of 43,283.
- 3
The biggest gap between neighbouring primes in this range is 22, after 3967 (the next prime is 3989). There are 2 twin prime pairs (primes 2 apart): (3917, 3919), (3929, 3931).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 3,901 to 3,910 | 1 | 10% |
| 3,911 to 3,920 | 3 | 30% |
| 3,921 to 3,930 | 2 | 20% |
| 3,931 to 3,940 | 1 | 10% |
| 3,941 to 3,950 | 2 | 20% |
| 3,951 to 3,960 | 0 | 0% |
| 3,961 to 3,970 | 1 | 10% |
| 3,971 to 3,980 | 0 | 0% |
| 3,981 to 3,990 | 1 | 10% |
| 3,991 to 4,000 | 0 | 0% |
Questions
How many prime numbers are there between 3901 and 4,000?
11.
What is the biggest prime number below 4,000?
3989.
What is the first prime number after 3900?
3907.