Prime numbers between 85001 and 86,000
There are 85 prime numbers between 85001 and 86,000: 85009, 85021, 85027, 85037, 85049, 85061, 85081, 85087, 85091, 85093, 85103, 85109, 85121, 85133, 85147, 85159, 85193, 85199, 85201, 85213, 85223, 85229, 85237, 85243, 85247, 85259, 85297, 85303, 85313, 85331, 85333, 85361, 85363, 85369, 85381, 85411, 85427, 85429, 85439, 85447, 85451, 85453, 85469, 85487, 85513, 85517, 85523, 85531, 85549, 85571, 85577, 85597, 85601, 85607, 85619, 85621, 85627, 85639, 85643, 85661, 85667, 85669, 85691, 85703, 85711, 85717, 85733, 85751, 85781, 85793, 85817, 85819, 85829, 85831, 85837, 85843, 85847, 85853, 85889, 85903, 85909, 85931, 85933, 85991, 85999.
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 ā86000 ā 293.3 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 85 primes between 85001 and 86,000, with a total of 7,265,479.
- 3
The biggest gap between neighbouring primes in this range is 58, after 85933 (the next prime is 85991). There are 11 twin prime pairs (primes 2 apart): (85091, 85093), (85199, 85201), (85331, 85333), (85361, 85363), (85427, 85429), (85451, 85453), (85619, 85621), (85667, 85669), (85817, 85819), (85829, 85831), (85931, 85933).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 85,001 to 86,000 | 85 | 8.5% |
Questions
How many prime numbers are there between 85001 and 86,000?
85.
What is the biggest prime number below 86,000?
85999.
What is the first prime number after 85000?
85009.