Prime numbers between 36001 and 37,000
There are 99 prime numbers between 36001 and 37,000: 36007, 36011, 36013, 36017, 36037, 36061, 36067, 36073, 36083, 36097, 36107, 36109, 36131, 36137, 36151, 36161, 36187, 36191, 36209, 36217, 36229, 36241, 36251, 36263, 36269, 36277, 36293, 36299, 36307, 36313, 36319, 36341, 36343, 36353, 36373, 36383, 36389, 36433, 36451, 36457, 36467, 36469, 36473, 36479, 36493, 36497, 36523, 36527, 36529, 36541, 36551, 36559, 36563, 36571, 36583, 36587, 36599, 36607, 36629, 36637, 36643, 36653, 36671, 36677, 36683, 36691, 36697, 36709, 36713, 36721, 36739, 36749, 36761, 36767, 36779, 36781, 36787, 36791, 36793, 36809, 36821, 36833, 36847, 36857, 36871, 36877, 36887, 36899, 36901, 36913, 36919, 36923, 36929, 36931, 36943, 36947, 36973, 36979, 36997.
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 ā37000 ā 192.4 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 99 primes between 36001 and 37,000, with a total of 3,615,395.
- 3
The biggest gap between neighbouring primes in this range is 44, after 36389 (the next prime is 36433). There are 9 twin prime pairs (primes 2 apart): (36011, 36013), (36107, 36109), (36341, 36343), (36467, 36469), (36527, 36529), (36779, 36781), (36791, 36793), (36899, 36901), (36929, 36931).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 36,001 to 37,000 | 99 | 9.9% |
Questions
How many prime numbers are there between 36001 and 37,000?
99.
What is the biggest prime number below 37,000?
36997.
What is the first prime number after 36000?
36007.