Prime numbers between 3001 and 3,100
There are 12 prime numbers between 3001 and 3,100: 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089.
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 ā3100 ā 55.7 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 12 primes between 3001 and 3,100, with a total of 36,560.
- 3
The biggest gap between neighbouring primes in this range is 14, after 3023 (the next prime is 3037). There are no twin primes here.
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 3,001 to 3,010 | 1 | 10% |
| 3,011 to 3,020 | 2 | 20% |
| 3,021 to 3,030 | 1 | 10% |
| 3,031 to 3,040 | 1 | 10% |
| 3,041 to 3,050 | 2 | 20% |
| 3,051 to 3,060 | 0 | 0% |
| 3,061 to 3,070 | 2 | 20% |
| 3,071 to 3,080 | 1 | 10% |
| 3,081 to 3,090 | 2 | 20% |
| 3,091 to 3,100 | 0 | 0% |
Questions
How many prime numbers are there between 3001 and 3,100?
12.
What is the biggest prime number below 3,100?
3089.
What is the first prime number after 3000?
3001.