kidzsearch.com > wiki Explore:web images videos games
Origins and definition
Ramanujan's result at the end of the paper was:
- [math]\pi(x) - \pi(x/2)[/math] ≥ 1, 2, 3, 4, 5, ... for all x ≥ 2, 11, 17, 29, 41, ... (sequence A104272 in OEIS)
where [math]\pi[/math](x) is the prime counting function. The prime counting function is the number of primes less than or equal to x.
The numbers 2, 11, 17, 29, 41 are first few Ramanujan primes. In other words:
Ramanujan primes are the integers Rn that are the smallest to satisfy the condition
- [math]\pi(x) - \pi(x/2)[/math] ≥ n, for all x ≥ Rn