Ramanujan primes: Difference between revisions

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Stretch goal takes a while - just over 6 minutes on my machine compared to Julia's 36 seconds - but that's not too bad for the Wren interpreter.

Stretch goal takes a while - just over 2 minutes on my machine compared to Julia's 36 seconds - but that's not too bad for the Wren interpreter.

<lang ecmascript>import "/math" for Int

import "/~~trait~~" for ~~Indexed~~

import "/seq" for Lst

import "/fmt" for Fmt

import "/sort" for Find

var primes = Int.primeSieve(~~1e6~~) // say

var primes = Int.primeSieve(700000) // say

var ramanujan = Fn.new { |n|

var i = (4 * n * (4 * n).log / 2.log).floor

var max = (4 * n * (4 * n).log / 2.log).floor

var pi = 0

var pi = Find.all(primes, max)[2].from // binary search

for (se in Indexed.new(primes)) {

if (se.value > i) {

pi = se.index - 1

break

}

while (true) {

var delta = ~~Int.primeCount(primes[~~pi]) - Int.primeCount((primes[pi]/2).floor)

var delta = pi + 1 - Int.primeCount((primes[pi]/2).floor)

if (delta <= n) return primes[pi]

pi = pi - 1

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<pre>

The first 100 Ramanujan primes are:

2 11 17 29 41 47 59 67 71 97

101 107 127 149 151 167 179 181 227 229

233 239 241 263 269 281 307 311 347 349

367 373 401 409 419 431 433 439 461 487

491 503 569 571 587 593 599 601 607 641

643 647 653 659 677 719 727 739 751 769

809 821 823 827 853 857 881 937 941 947

967 983 1,009 1,019 1,021 1,031 1,049 1,051 1,061 1,063

1,087 1,091 1,097 1,103 1,151 1,163 1,187 1,217 1,229 1,249

1,277 1,289 1,297 1,301 1,367 1,373 1,423 1,427 1,429 1,439

The 1,000th Ramanujan prime is 19,403