Prime numbers between 76001 and 77,000
There are 83 prime numbers between 76001 and 77,000: 76001, 76003, 76031, 76039, 76079, 76081, 76091, 76099, 76103, 76123, 76129, 76147, 76157, 76159, 76163, 76207, 76213, 76231, 76243, 76249, 76253, 76259, 76261, 76283, 76289, 76303, 76333, 76343, 76367, 76369, 76379, 76387, 76403, 76421, 76423, 76441, 76463, 76471, 76481, 76487, 76493, 76507, 76511, 76519, 76537, 76541, 76543, 76561, 76579, 76597, 76603, 76607, 76631, 76649, 76651, 76667, 76673, 76679, 76697, 76717, 76733, 76753, 76757, 76771, 76777, 76781, 76801, 76819, 76829, 76831, 76837, 76847, 76871, 76873, 76883, 76907, 76913, 76919, 76943, 76949, 76961, 76963, 76991.
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 ā77000 ā 277.5 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 83 primes between 76001 and 77,000, with a total of 6,349,635.
- 3
The biggest gap between neighbouring primes in this range is 44, after 76163 (the next prime is 76207). There are 11 twin prime pairs (primes 2 apart): (76001, 76003), (76079, 76081), (76157, 76159), (76259, 76261), (76367, 76369), (76421, 76423), (76541, 76543), (76649, 76651), (76829, 76831), (76871, 76873), (76961, 76963).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 76,001 to 77,000 | 83 | 8.3% |
Questions
How many prime numbers are there between 76001 and 77,000?
83.
What is the biggest prime number below 77,000?
76991.
What is the first prime number after 76000?
76001.