Prime numbers between 71001 and 72,000
There are 95 prime numbers between 71001 and 72,000: 71011, 71023, 71039, 71059, 71069, 71081, 71089, 71119, 71129, 71143, 71147, 71153, 71161, 71167, 71171, 71191, 71209, 71233, 71237, 71249, 71257, 71261, 71263, 71287, 71293, 71317, 71327, 71329, 71333, 71339, 71341, 71347, 71353, 71359, 71363, 71387, 71389, 71399, 71411, 71413, 71419, 71429, 71437, 71443, 71453, 71471, 71473, 71479, 71483, 71503, 71527, 71537, 71549, 71551, 71563, 71569, 71593, 71597, 71633, 71647, 71663, 71671, 71693, 71699, 71707, 71711, 71713, 71719, 71741, 71761, 71777, 71789, 71807, 71809, 71821, 71837, 71843, 71849, 71861, 71867, 71879, 71881, 71887, 71899, 71909, 71917, 71933, 71941, 71947, 71963, 71971, 71983, 71987, 71993, 71999.
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 ā72000 ā 268.3 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 95 primes between 71001 and 72,000, with a total of 6,794,231.
- 3
The biggest gap between neighbouring primes in this range is 36, after 71597 (the next prime is 71633). There are 10 twin prime pairs (primes 2 apart): (71261, 71263), (71327, 71329), (71339, 71341), (71387, 71389), (71411, 71413), (71471, 71473), (71549, 71551), (71711, 71713), (71807, 71809), (71879, 71881).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 71,001 to 72,000 | 95 | 9.5% |
Questions
How many prime numbers are there between 71001 and 72,000?
95.
What is the biggest prime number below 72,000?
71999.
What is the first prime number after 71000?
71011.