Prime numbers between 51001 and 52,000
There are 97 prime numbers between 51001 and 52,000: 51001, 51031, 51043, 51047, 51059, 51061, 51071, 51109, 51131, 51133, 51137, 51151, 51157, 51169, 51193, 51197, 51199, 51203, 51217, 51229, 51239, 51241, 51257, 51263, 51283, 51287, 51307, 51329, 51341, 51343, 51347, 51349, 51361, 51383, 51407, 51413, 51419, 51421, 51427, 51431, 51437, 51439, 51449, 51461, 51473, 51479, 51481, 51487, 51503, 51511, 51517, 51521, 51539, 51551, 51563, 51577, 51581, 51593, 51599, 51607, 51613, 51631, 51637, 51647, 51659, 51673, 51679, 51683, 51691, 51713, 51719, 51721, 51749, 51767, 51769, 51787, 51797, 51803, 51817, 51827, 51829, 51839, 51853, 51859, 51869, 51871, 51893, 51899, 51907, 51913, 51929, 51941, 51949, 51971, 51973, 51977, 51991.
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 ā52000 ā 228.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 97 primes between 51001 and 52,000, with a total of 4,996,599.
- 3
The biggest gap between neighbouring primes in this range is 38, after 51071 (the next prime is 51109). There are 14 twin prime pairs (primes 2 apart), the first ones (51059, 51061), (51131, 51133), (51197, 51199), (51239, 51241), (51341, 51343), (51347, 51349), (51419, 51421), (51437, 51439).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 51,001 to 52,000 | 97 | 9.7% |
Questions
How many prime numbers are there between 51001 and 52,000?
97.
What is the biggest prime number below 52,000?
51991.
What is the first prime number after 51000?
51001.