Ramanujan primes: Difference between revisions

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 <lang julia>using Primes
+@time let
+        MASK = primesmask(625000)
+        PIVEC = accumulate(+, MASK)
+        PI(n) = n < 1 ? 0 : PIVEC[n]
+    function Ramanujan_prime(n)
-const PRIMES = [primes(625000)]
+        maxposs = Int(ceil(4n * (log(4n) / log(2))))
+        for i in maxposs:-1:1
-function PI(n)
+            PI(i) - PI(i ÷ 2) < n && return i + 1
-    if n > first(PRIMES)[end]
-        empty!(PRIMES)
+        end
-        push!(PRIMES, primes(2n))
+        return 0
     end
-    return n < 100000 ? findfirst(x -> x > n, first(PRIMES)) - 1 :
-        findlast(x -> x <= n, first(PRIMES))
-end
+    for i in 1:100
-function Ramanujan_prime(n)
+        print(lpad(Ramanujan_prime(i), 5), i % 20 == 0 ? "\n" :  "")
-    maxposs = Int(ceil(4n * (log(4n) / log(2))))
-    for i in maxposs:-1:1
-        PI(i) - PI(i ÷ 2) < n && return i + 1
     end
-    return 0
-end
+    println("\nThe 1000th Ramanujan prime is ", Ramanujan_prime(1000))
-for i in 1:100
+    println("\nThe 10,000th Ramanujan prime is ", Ramanujan_prime(10000))
-    print(lpad(Ramanujan_prime(i), 5), i % 20 == 0 ? "\n" :  "")
 end
-println("\nThe 1000th Ramanujan prime is ", Ramanujan_prime(1000))
-println("\nThe 10,000th Ramanujan prime is ", Ramanujan_prime(10000))
 </lang>{{out}}
 <pre>