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.
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.
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.