Prime numbers between 37001 and 38,000
There are 94 prime numbers between 37001 and 38,000: 37003, 37013, 37019, 37021, 37039, 37049, 37057, 37061, 37087, 37097, 37117, 37123, 37139, 37159, 37171, 37181, 37189, 37199, 37201, 37217, 37223, 37243, 37253, 37273, 37277, 37307, 37309, 37313, 37321, 37337, 37339, 37357, 37361, 37363, 37369, 37379, 37397, 37409, 37423, 37441, 37447, 37463, 37483, 37489, 37493, 37501, 37507, 37511, 37517, 37529, 37537, 37547, 37549, 37561, 37567, 37571, 37573, 37579, 37589, 37591, 37607, 37619, 37633, 37643, 37649, 37657, 37663, 37691, 37693, 37699, 37717, 37747, 37781, 37783, 37799, 37811, 37813, 37831, 37847, 37853, 37861, 37871, 37879, 37889, 37897, 37907, 37951, 37957, 37963, 37967, 37987, 37991, 37993, 37997.
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 ā38000 ā 194.9 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 94 primes between 37001 and 38,000, with a total of 3,525,086.
- 3
The biggest gap between neighbouring primes in this range is 44, after 37907 (the next prime is 37951). There are 12 twin prime pairs (primes 2 apart): (37019, 37021), (37199, 37201), (37307, 37309), (37337, 37339), (37361, 37363), (37547, 37549), (37571, 37573), (37589, 37591), (37691, 37693), (37781, 37783), (37811, 37813), (37991, 37993).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 37,001 to 38,000 | 94 | 9.4% |
Questions
How many prime numbers are there between 37001 and 38,000?
94.
What is the biggest prime number below 38,000?
37997.
What is the first prime number after 37000?
37003.