Prime numbers between 3101 and 3,200
There are 10 prime numbers between 3101 and 3,200: 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191.
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 ā3200 ā 56.6 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 10 primes between 3101 and 3,200, with a total of 31,544.
- 3
The biggest gap between neighbouring primes in this range is 26, after 3137 (the next prime is 3163). There are 2 twin prime pairs (primes 2 apart): (3119, 3121), (3167, 3169).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 3,101 to 3,110 | 1 | 10% |
| 3,111 to 3,120 | 1 | 10% |
| 3,121 to 3,130 | 1 | 10% |
| 3,131 to 3,140 | 1 | 10% |
| 3,141 to 3,150 | 0 | 0% |
| 3,151 to 3,160 | 0 | 0% |
| 3,161 to 3,170 | 3 | 30% |
| 3,171 to 3,180 | 0 | 0% |
| 3,181 to 3,190 | 2 | 20% |
| 3,191 to 3,200 | 1 | 10% |
Questions
How many prime numbers are there between 3101 and 3,200?
10.
What is the biggest prime number below 3,200?
3191.
What is the first prime number after 3100?
3109.