Prime numbers between 61001 and 62,000
There are 87 prime numbers between 61001 and 62,000: 61001, 61007, 61027, 61031, 61043, 61051, 61057, 61091, 61099, 61121, 61129, 61141, 61151, 61153, 61169, 61211, 61223, 61231, 61253, 61261, 61283, 61291, 61297, 61331, 61333, 61339, 61343, 61357, 61363, 61379, 61381, 61403, 61409, 61417, 61441, 61463, 61469, 61471, 61483, 61487, 61493, 61507, 61511, 61519, 61543, 61547, 61553, 61559, 61561, 61583, 61603, 61609, 61613, 61627, 61631, 61637, 61643, 61651, 61657, 61667, 61673, 61681, 61687, 61703, 61717, 61723, 61729, 61751, 61757, 61781, 61813, 61819, 61837, 61843, 61861, 61871, 61879, 61909, 61927, 61933, 61949, 61961, 61967, 61979, 61981, 61987, 61991.
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 ā62000 ā 249.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 87 primes between 61001 and 62,000, with a total of 5,351,613.
- 3
The biggest gap between neighbouring primes in this range is 42, after 61169 (the next prime is 61211). There are 6 twin prime pairs (primes 2 apart): (61151, 61153), (61331, 61333), (61379, 61381), (61469, 61471), (61559, 61561), (61979, 61981).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 61,001 to 62,000 | 87 | 8.7% |
Questions
How many prime numbers are there between 61001 and 62,000?
87.
What is the biggest prime number below 62,000?
61991.
What is the first prime number after 61000?
61001.