Ramanujan primes
As the integers get larger, the spacing between prime numbers slowly lengthens, but the spacing between primes increases at a slower rate than the numbers themselves increase. A consequence of this difference in rates of increase is the existence of special primes, called Ramanujan primes.
Ramanujan primes is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
The `n`th Ramanujan prime is defined to be the least integer for which there are at least n primes between x and x/2 for all x greater or equal to n.
- Task
- Generate and show the first 100 Ramanujan prime numbers.
- Find and show the 1000th Ramanujan prime number.
- Stretch task
Find and show the 10,000th Ramanujan prime number.
- See also
- The pi prime function, not to be confused with the trancendental number π
- The OEIS entry: OEIS entry
- The Wikipedia entry: Ramanujan_prime.