Prime numbers between 70001 and 71,000
There are 98 prime numbers between 70001 and 71,000: 70001, 70003, 70009, 70019, 70039, 70051, 70061, 70067, 70079, 70099, 70111, 70117, 70121, 70123, 70139, 70141, 70157, 70163, 70177, 70181, 70183, 70199, 70201, 70207, 70223, 70229, 70237, 70241, 70249, 70271, 70289, 70297, 70309, 70313, 70321, 70327, 70351, 70373, 70379, 70381, 70393, 70423, 70429, 70439, 70451, 70457, 70459, 70481, 70487, 70489, 70501, 70507, 70529, 70537, 70549, 70571, 70573, 70583, 70589, 70607, 70619, 70621, 70627, 70639, 70657, 70663, 70667, 70687, 70709, 70717, 70729, 70753, 70769, 70783, 70793, 70823, 70841, 70843, 70849, 70853, 70867, 70877, 70879, 70891, 70901, 70913, 70919, 70921, 70937, 70949, 70951, 70957, 70969, 70979, 70981, 70991, 70997, 70999.
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 ā71000 ā 266.5 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 98 primes between 70001 and 71,000, with a total of 6,909,012.
- 3
The biggest gap between neighbouring primes in this range is 30, after 70393 (the next prime is 70423). There are 16 twin prime pairs (primes 2 apart), the first ones (70001, 70003), (70121, 70123), (70139, 70141), (70181, 70183), (70199, 70201), (70379, 70381), (70457, 70459), (70487, 70489).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 70,001 to 71,000 | 98 | 9.8% |
Questions
How many prime numbers are there between 70001 and 71,000?
98.
What is the biggest prime number below 71,000?
70999.
What is the first prime number after 70000?
70001.