Ramanujan primes/twins: Difference between revisions
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<pre>
There are 74973 twins in the first million Ramanujan primes
</pre>
=={{header|Go}}==
{{trans|Wren}}
{{libheader|Go-rcu}}
<lang go>package main
import (
"fmt"
"math"
"rcu"
"time"
)
var count []int
func primeCounter(limit int) {
count = make([]int, limit)
for i := 0; i < limit; i++ {
count[i] = 1
}
if limit > 0 {
count[0] = 0
}
if limit > 1 {
count[1] = 0
}
for i := 4; i < limit; i += 2 {
count[i] = 0
}
for p, sq := 3, 9; sq < limit; p += 2 {
if count[p] != 0 {
for q := sq; q < limit; q += p << 1 {
count[q] = 0
}
}
sq += (p + 1) << 2
}
sum := 0
for i := 0; i < limit; i++ {
sum += count[i]
count[i] = sum
}
}
func primeCount(n int) int {
if n < 1 {
return 0
}
return count[n]
}
func ramanujanMax(n int) int {
fn := float64(n)
return int(math.Ceil(4 * fn * math.Log(4*fn)))
}
func ramanujanPrime(n int) int {
if n == 1 {
return 2
}
for i := ramanujanMax(n); i >= 2*n; i-- {
if i%2 == 1 {
continue
}
if primeCount(i)-primeCount(i/2) < n {
return i + 1
}
}
return 0
}
func rpc(p int) int { return primeCount(p) - primeCount(p/2) }
func main() {
for _, limit := range []int{1e5, 1e6} {
start := time.Now()
primeCounter(1 + ramanujanMax(limit))
rplim := ramanujanPrime(limit)
climit := rcu.Commatize(limit)
fmt.Printf("The %sth Ramanujan prime is %s\n", climit, rcu.Commatize(rplim))
r := rcu.Primes(rplim)
c := make([]int, len(r))
for i := 0; i < len(c); i++ {
c[i] = rpc(r[i])
}
ok := c[len(c)-1]
for i := len(c) - 2; i >= 0; i-- {
if c[i] < ok {
ok = c[i]
} else {
c[i] = 0
}
}
var fr []int
for i, r := range r {
if c[i] != 0 {
fr = append(fr, r)
}
}
twins := 0
for i := 0; i < len(fr)-1; i++ {
if fr[i]+2 == fr[i+1] {
twins++
}
}
fmt.Printf("There are %s twins in the first %s Ramanujan primes.\n", rcu.Commatize(twins), climit)
fmt.Println("Took", time.Since(start))
fmt.Println()
}
}</lang>
{{out}}
<pre>
The 100,000th Ramanujan prime is 2,916,539
There are 8,732 twins in the first 100,000 Ramanujan primes.
Took 50.745239ms
The 1,000,000th Ramanujan prime is 34,072,993
There are 74,973 twins in the first 1,000,000 Ramanujan primes.
Took 699.967994ms
</pre>
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