Ramanujan primes: Difference between revisions
Added completed solution in python
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{{draft task|Prime Numbers}}
As the integers get larger, the spacing between prime numbers slowly lengthens, but the spacing
Line 25:
=={{header|
<syntaxhighlight lang="algol68">
BEGIN # find some Ramanujan primes: the nth Ramanujan prime is the least n #
# such that there are at least n primes between x and x/2 for all x>=n #
PR read "primes.incl.a68" PR # include the prime utilities #
[]BOOL p = PRIMESIEVE 1 000 000; # generate a sieve of primes #
# find the highest numbers where the number of primes between x and x/2 #
# is at most n, store the list in hpx #
[ 0 : UPB p ]INT hpx;
BEGIN
# count the primes up to n #
[ 0 : UPB p ]INT pc; # pc[ n ]: count of primes up to n #
FOR i FROM LWB pc TO UPB pc DO pc[ i ] := 0 OD;
INT p count := 0;
FOR i TO UPB pc DO
IF p[ i ] THEN p count +:= 1 FI;
pc[ i ] := p count
OD;
# count the pimes between x and x/2 #
[ 0 : UPB p ]INT pc2; # pc2[ n ]: count of primes between n and n/2 #
FOR i FROM LWB pc2 TO UPB pc2 DO
pc2[ i ] := pc[ i ] - pc[ i OVER 2 ]
OD;
# find the highest x where the prime count between x and x/2 is x #
FOR i FROM LWB hpx TO UPB hpx DO hpx[ i ] := 0 OD;
FOR i FROM LWB hpx TO UPB hpx DO
hpx[ pc2[ i ] ] := i
OD
END;
# show the Ramanjan primes #
INT r count := 0;
INT power of 10 := 1 000;
FOR n FROM LWB hpx TO UPB hpx WHILE r count < 10 000 DO
# hpx[ n ] contains the highest number where the number of primes #
# between x and x/2 is at most n, so we need to find the next #
# prime >= n #
INT rp := hpx[ n ];
WHILE NOT p[ rp ] DO rp +:= 1 OD;
IF ( r count +:= 1 ) <= 100 THEN
print( ( " ", whole( rp, -4 ) ) );
IF r count MOD 20 = 0 THEN print( ( newline ) ) FI
ELIF r count = power of 10 THEN
print( ( "The ", whole( r count, -8 ), "th Ramanujan prime is: ", whole( rp, 0 ), newline ) );
power of 10 *:= 10
FI
OD
END
</syntaxhighlight>
{{out}}
<pre>
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 1009 1019 1021 1031 1049 1051 1061 1063
1087 1091 1097 1103 1151 1163 1187 1217 1229 1249 1277 1289 1297 1301 1367 1373 1423 1427 1429 1439
The 1000th Ramanujan prime is: 19403
The 10000th Ramanujan prime is: 242057
</pre>
=={{header|BASIC}}==
==={{header|FreeBASIC}}===
{{trans|Phix}}
<syntaxhighlight lang="vbnet">#define floor(x) ((x*2.0-0.5) Shr 1)
Dim Shared As Integer pi()
Sub primeCounter(limit As Integer)
Dim As Integer i, q, p, sq, total
pi(0) = 0
pi(1) = 0
For i = 2 To limit
pi(i) = 1
Next
If limit > 2 Then
For i = 4 To limit Step 2
pi(i) = 0
Next i
p = 3
sq = 9
While sq <= limit
If pi(p) <> 0 Then
For q = sq To limit Step p*2
pi(q) = 0
Next q
End If
sq += (p + 1) * 4
p += 2
Wend
total = 0
For i = 2 To limit
total += pi(i)
pi(i) = total
Next i
End If
End Sub
Function ramanujanMax(n As Integer) As Integer
Return floor(4 * n * Log(4*n))
End Function
Function ramanujanPrime(n As Integer) As Integer
Dim As Integer i, maxposs
If n = 1 Then Return 2
maxposs = ramanujanMax(n)
For i = maxposs - (maxposs Mod 2) To 1 Step -2
If pi(i) - pi(i\2) < n Then Return i + 1
Next i
Return 0
End Function
Dim As Integer p, n, limit = 1e6
Dim As Double t0 = Timer
primeCounter(ramanujanMax(limit))
Print "The first 100 Ramanujan primes are:"
For p = 1 To 100
Print Using " ####"; ramanujanPrime(p);
If p Mod 20 = 0 Then Print
Next p
Print
For p = 3 To 6
n = 10 ^ p
Print Using "The &th Ramanujan prime is &"; n; ramanujanPrime(n)
Next p
Print Using "##.##sec."; Timer - t0
Sleep</syntaxhighlight>
{{out}}
<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 1009 1019 1021 1031 1049 1051 1061 1063
1087 1091 1097 1103 1151 1163 1187 1217 1229 1249 1277 1289 1297 1301 1367 1373 1423 1427 1429 1439
The 1000th Ramanujan prime is 19403
The 10000th Ramanujan prime is 242057
The 100000th Ramanujan prime is 2916539
The 1000000th Ramanujan prime is 34072993
1.53sec.</pre>
==={{header|Yabasic}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="vbnet">dim cnt(1e6)
primeCounter(ramanujanMax((1e6)))
print "The first 100 Ramanujan primes are:"
for p = 1 to 100
print ramanujanPrime(p) using ("#####");
if mod(p, 20) = 0 print
next p
print
for p = 3 to 6
n = 10 ^ p
print "The ", n, "th Ramanujan prime is ", ramanujanPrime(n)
next p
print peek("millisrunning") / 1000, "sec."
end
sub primeCounter(limit)
local i, q, p, sq, total
redim cnt(limit)
cnt(0) = 0
for i = 2 to limit
cnt(i) = 1
next
if limit > 2 then
for i = 4 to limit step 2
cnt(i) = 0
next i
p = 3
sq = 9
while sq <= limit
if cnt(p) <> 0 then
for q = sq to limit step p*2
cnt(q) = 0
next q
fi
sq = sq + (p + 1) * 4
p = p + 2
wend
total = 0
for i = 2 to limit
total = total + cnt(i)
cnt(i) = total
next i
fi
end sub
sub ramanujanMax(n)
return floor(4 * n * log(4*n))
end sub
sub ramanujanPrime(n)
local i, maxposs
if n = 1 return 2
maxposs = ramanujanMax(n)
for i = maxposs - mod(maxposs, 2) to 1 step -2
if cnt(i) - cnt(floor(i/2)) < n return i + 1
next i
return 0
end sub</syntaxhighlight>
{{out}}
<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 1009 1019 1021 1031 1049 1051 1061 1063
1087 1091 1097 1103 1151 1163 1187 1217 1229 1249 1277 1289 1297 1301 1367 1373 1423 1427 1429 1439
The 1000th Ramanujan prime is 19403
The 10000th Ramanujan prime is 242057
The 100000th Ramanujan prime is 2916539
The 1000000th Ramanujan prime is 34072993
35.14sec.</pre>
=={{header|C++}}==
{{trans|Julia}}
<syntaxhighlight lang="cpp">#include <chrono>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <numeric>
#include <vector>
class prime_counter {
public:
explicit prime_counter(int limit);
int prime_count(int n) const { return n < 1 ? 0 : count_.at(n); }
private:
std::vector<int> count_;
};
prime_counter::prime_counter(int limit) : count_(limit, 1) {
if (limit > 0)
count_[0] = 0;
if (limit > 1)
count_[1] = 0;
for (int i = 4; i < limit; i += 2)
count_[i] = 0;
for (int p = 3, sq = 9; sq < limit; p += 2) {
if (count_[p]) {
for (int q = sq; q < limit; q += p << 1)
count_[q] = 0;
}
sq += (p + 1) << 2;
}
std::partial_sum(count_.begin(), count_.end(), count_.begin());
}
int ramanujan_max(int n) {
return static_cast<int>(std::ceil(4 * n * std::log(4 * n)));
}
int ramanujan_prime(const prime_counter& pc, int n) {
int max = ramanujan_max(n);
for (int i = max; i >= 0; --i) {
if (pc.prime_count(i) - pc.prime_count(i / 2) < n)
return i + 1;
}
return 0;
}
int main() {
std::cout.imbue(std::locale(""));
auto start = std::chrono::high_resolution_clock::now();
prime_counter pc(1 + ramanujan_max(100000));
for (int i = 1; i <= 100; ++i) {
std::cout << std::setw(5) << ramanujan_prime(pc, i)
<< (i % 10 == 0 ? '\n' : ' ');
}
std::cout << '\n';
for (int n = 1000; n <= 100000; n *= 10) {
std::cout << "The " << n << "th Ramanujan prime is " << ramanujan_prime(pc, n)
<< ".\n";
}
auto end = std::chrono::high_resolution_clock::now();
std::cout << "\nElapsed time: "
<< std::chrono::duration<double>(end - start).count() * 1000
<< " milliseconds\n";
}</syntaxhighlight>
{{out}}
<pre>
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.
The 10,000th Ramanujan prime is 242,057.
The 100,000th Ramanujan prime is 2,916,539.
Elapsed time: 46.0828 milliseconds
</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
Uses the [[Extensible_prime_generator#Delphi|Delphi Prime-Generator Object]]
<syntaxhighlight lang="Delphi">
procedure ShowRamanujanPrimes(Memo: TMemo);
var S: string;
var PrimeCounts: array of Integer;
var Sieve: TPrimeSieve;
var I,Cnt,P: integer;
const Size = 1000000;
function GetRamanujanMax(N: integer): integer;
{Get maximum possible Ramanujan for a particular N}
begin
Result:=Ceil(4 * N * (log(4 * N) / log(2)));
end;
function RamanujanPrime(N: integer): integer;
{Find largest I for Pi[I]-Pi[I/2]<N, Pi[I] is count primes less than I}
var I: integer;
begin
for I:=GetRamanujanMax(N) downto 0 do
if (PrimeCounts[I] - PrimeCounts[I div 2]) < N then
begin
Result:=I+1;
exit;
end;
Result:=0;
end;
begin
Sieve:=TPrimeSieve.Create;
try
{Get primes up to 1 million}
Sieve.Intialize(Size);
{Count total number of primes up to a specific number}
SetLength(PrimeCounts,Size);
Cnt:=0;
for I:=0 to Sieve.Count-1 do
begin
if Sieve.Flags[I] then Inc(Cnt);
PrimeCounts[I]:=Cnt;
end;
{display first 100 Ramanujan Prime}
S:='';
for I:=1 to 100 do
begin
P:=RamanujanPrime(I);
S:=S+Format('%5d',[P]);
if (I mod 10)=0 then S:=S+CRLF;
end;
Memo.Lines.Add(S);
P:=RamanujanPrime(1000);
Memo.Lines.Add('1,000th Prime: '+IntToStr(P));
P:=RamanujanPrime(10000);
Memo.Lines.Add('10,000th Prime: '+IntToStr(P));
finally Sieve.Free; end;
end;
</syntaxhighlight>
{{out}}
<pre>
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 1009 1019 1021 1031 1049 1051 1061 1063
1087 1091 1097 1103 1151 1163 1187 1217 1229 1249
1277 1289 1297 1301 1367 1373 1423 1427 1429 1439
1,000th Prime: 19403
10,000th Prime: 242057
Elapsed Time: 19.269 ms.
</pre>
=={{header|EasyLang}}==
{{trans|Go}}
<syntaxhighlight>
global cnt[] .
proc primcnt limit . .
cnt[] = [ 0 1 1 ]
for i = 4 step 2 to limit
cnt[] &= 0
cnt[] &= 1
.
p = 3
sq = 9
while sq <= limit
if cnt[p] <> 0
for q = sq step p * 2 to limit
cnt[q] = 0
.
.
sq += (p + 1) * 4
p += 2
.
for i = 2 to limit
sum += cnt[i]
cnt[i] = sum
.
.
func log n .
e = 2.7182818284590452354
return log10 n / log10 e
.
func ramamax n .
return floor (4 * n * log (4 * n))
.
func ramaprim n .
if n = 1
return 2
.
for i = ramamax n downto 2 * n
if i mod 2 = 0
if cnt[i] - cnt[i / 2] < n
return i + 1
.
.
.
return 0
.
primcnt (1 + ramamax 1000)
print "The first 100 Ramanujan primes are:"
for i = 1 to 100
write ramaprim i & " "
.
print ""
print ""
print "The 1000th Ramanujan prime is " & ramaprim 1000
</syntaxhighlight>
=={{header|F_Sharp|F#}}==
This task uses [http://www.rosettacode.org/wiki/Extensible_prime_generator#The_functions Extensible Prime Generator (F#)]
<syntaxhighlight lang="fsharp">
// Ramanujan primes. Nigel Galloway: September 7th., 2021
let fN g=if isPrime g then 1 else if g%2=1 then 0 else if isPrime(g/2) then -1 else 0
let rP p=let N,G=Array.create p 0,(Seq.item(3*p-2)(primes32()))+1 in let rec fG n g=if g=G then N else(if n<p then N.[n]<-g); fG(n+(fN g))(g+1) in fG 0 1
let n=rP 100000
n.[0..99]|>Array.iter(printf "%d "); printfn ""
[1000;10000;100000]|>List.iter(fun g->printf $"The %d{g}th Ramanujan prime is %d{n.[g-1]}\n" )
</syntaxhighlight>
{{out}}
<pre>
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 1009 1019 1021 1031 1049 1051 1061 1063 1087 1091 1097 1103 1151 1163 1187 1217 1229 1249 1277 1289 1297 1301 1367 1373 1423 1427 1429 1439
The 1000th Ramanujan prime is 19403
The 10000th Ramanujan prime is 242057
The 100000th Ramanujan prime is 2916539
</pre>
=={{header|Go}}==
{{trans|C++}}
{{libheader|Go-rcu}}
<br>
This takes about 40 ms to find the 100,000th Ramanujan prime on my machine. The millionth takes about 520 ms.
<syntaxhighlight 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 main() {
start := time.Now()
primeCounter(1 + ramanujanMax(1e6))
fmt.Println("The first 100 Ramanujan primes are:")
rams := make([]int, 100)
for n := 0; n < 100; n++ {
rams[n] = ramanujanPrime(n + 1)
}
for i, r := range rams {
fmt.Printf("%5s ", rcu.Commatize(r))
if (i+1)%10 == 0 {
fmt.Println()
}
}
fmt.Printf("\nThe 1,000th Ramanujan prime is %6s\n", rcu.Commatize(ramanujanPrime(1000)))
fmt.Printf("\nThe 10,000th Ramanujan prime is %7s\n", rcu.Commatize(ramanujanPrime(10000)))
fmt.Printf("\nThe 100,000th Ramanujan prime is %6s\n", rcu.Commatize(ramanujanPrime(100000)))
fmt.Printf("\nThe 1,000,000th Ramanujan prime is %7s\n", rcu.Commatize(ramanujanPrime(1000000)))
fmt.Println("\nTook", time.Since(start))
}</syntaxhighlight>
{{out}}
<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
The 10,000th Ramanujan prime is 242,057
The 100,000th Ramanujan prime is 2,916,539
The 1,000,000th Ramanujan prime is 34,072,993
Took 519.655163ms
</pre>
=={{header|Java}}==
{{trans|C++}}
<syntaxhighlight lang="java">import java.util.Arrays;
public class RamanujanPrimes {
public static void main(String[] args) {
long start = System.nanoTime();
System.out.println("First 100 Ramanujan primes:");
PrimeCounter pc = new PrimeCounter(1 + ramanujanMax(100000));
for (int i = 1; i <= 100; ++i) {
int p = ramanujanPrime(pc, i);
System.out.printf("%,5d%c", p, i % 10 == 0 ? '\n' : ' ');
}
System.out.println();
for (int i = 1000; i <= 100000; i *= 10) {
int p = ramanujanPrime(pc, i);
System.out.printf("The %,dth Ramanujan prime is %,d.\n", i, p);
}
long end = System.nanoTime();
System.out.printf("\nElapsed time: %.1f milliseconds\n", (end - start) / 1e6);
}
private static int ramanujanMax(int n) {
return (int)Math.ceil(4 * n * Math.log(4 * n));
}
private static int ramanujanPrime(PrimeCounter pc, int n) {
for (int i = ramanujanMax(n); i >= 0; --i) {
if (pc.primeCount(i) - pc.primeCount(i / 2) < n)
return i + 1;
}
return 0;
}
private static class PrimeCounter {
private PrimeCounter(int limit) {
count = new int[limit];
Arrays.fill(count, 1);
if (limit > 0)
count[0] = 0;
if (limit > 1)
count[1] = 0;
for (int i = 4; i < limit; i += 2)
count[i] = 0;
for (int p = 3, sq = 9; sq < limit; p += 2) {
if (count[p] != 0) {
for (int q = sq; q < limit; q += p << 1)
count[q] = 0;
}
sq += (p + 1) << 2;
}
Arrays.parallelPrefix(count, (x, y) -> x + y);
}
private int primeCount(int n) {
return n < 1 ? 0 : count[n];
}
private int[] count;
}
}</syntaxhighlight>
{{out}}
<pre>
First 100 Ramanujan primes:
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.
The 10,000th Ramanujan prime is 242,057.
The 100,000th Ramanujan prime is 2,916,539.
Elapsed time: 187.2 milliseconds
</pre>
=={{header|J}}==
<syntaxhighlight lang=j> result=. (((] - _1&(33 b.)@:>:@[ { ]) _1&p:) i. 3e6) i: i. 1e5
_10 ]\ 100 {. result
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 1009 1019 1021 1031 1049 1051 1061 1063
1087 1091 1097 1103 1151 1163 1187 1217 1229 1249
1277 1289 1297 1301 1367 1373 1423 1427 1429 1439
(10 <:@^ 3 4 5) { result
19403 242057 2916539</syntaxhighlight>
=={{header|jq}}==
'''Adapted from [[#Wren|Wren]]'''
{{works with|jq}}
<syntaxhighlight lang=jq>
def lpad($len): tostring | ($len - length) as $l | (" " * $l) + .;
# tabular print
def tprint(columns; wide):
reduce _nwise(columns) as $row ("";
. + ($row|map(lpad(wide)) | join(" ")) + "\n" );
# output: {count}
def primeCounter($limit):
{count: [range(0; $limit) | 1] }
| if ($limit > 0) then .count[0] = 0 else . end
| if ($limit > 1) then .count[1] = 0 else . end
| .count |= reduce range(4; $limit; 2) as $i (.; .[$i] = 0)
| .p = 3
| .sq = 9
| until(.sq >= $limit;
if (.count[.p] != 0)
then .q = .sq
| until (.q >= $limit;
.count[.q] = 0
| .q += (.p * 2) )
else .
end
| .sq += ((.p + 1) * 4)
| .p += 2 )
| .sum = 0
| reduce range(0; $limit) as $i (.;
.sum += .count[$i]
| .count[$i] = .sum ) ;
# input: {count}
def primeCount($n): if $n < 1 then 0 else .count[$n] end;
# 2n ln 2n < Rn < 4n ln 4n
def ramanujanMax(n): (4 * n * ((4*n)|log))|ceil;
# input: {count}
def ramanujanPrime($n):
if ($n == 1) then 2
else first( foreach range(ramanujanMax($n); 1+2*$n; -1) as $i (.emit=null;
if ($i % 2 == 1) then .
elif (primeCount($i) - primeCount(($i/2)|floor) < $n) then .emit=$i + 1
else .
end)
| select(.emit).emit ) // 0
end ;
# The tasks
primeCounter(1 + ramanujanMax(1e6))
| "The first 100 Ramanujan primes are:",
( [range(1;101) as $i | ramanujanPrime($i) ]
| tprint(10; 5) ),
"\nThe 1,000th Ramanujan prime is \(ramanujanPrime(1000))",
"\nThe 10,000th Ramanujan prime is \(ramanujanPrime(10000))",
"\nThe 100,000th Ramanujan prime is \(ramanujanPrime(100000))",
"\nThe 1,000,000th Ramanujan prime is \(ramanujanPrime(1000000))"
</syntaxhighlight>
{{output}}
<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 1009 1019 1021 1031 1049 1051 1061 1063
1087 1091 1097 1103 1151 1163 1187 1217 1229 1249
1277 1289 1297 1301 1367 1373 1423 1427 1429 1439
The 1,000th Ramanujan prime is 19403
The 10,000th Ramanujan prime is 242057
The 100,000th Ramanujan prime is 2916539
The 1,000,000th Ramanujan prime is 34072993
</pre>
=={{header|Julia}}==
<syntaxhighlight lang="julia">using Primes
@time let
MASK = primesmask(625000)
PIVEC = accumulate(+, MASK)
PI(n) = n < 1 ? 0 : PIVEC[n]
function Ramanujan_prime(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
for i in 1:100
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))
end
</syntaxhighlight>{{out}}
<pre>
2 11 17 29 41 47 59 67 71 97 101 107 127 149 151 167 179 181 227 229
Line 64 ⟶ 841:
The 10,000th Ramanujan prime is 242057
0.272471 seconds (625.44 k allocations: 38.734 MiB, 33.07% compilation time)
</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">l = PrimePi[Range[10^6]] - PrimePi[Range[10^6]/2];
Multicolumn[1 + Position[l, #][[-1, 1]] & /@ Range[0, 99], {Automatic, 10}, Appearance -> "Horizontal"]
1 + Position[l, 999][[-1, 1]]
1 + Position[l, 9999][[-1, 1]]</syntaxhighlight>
{{out}}
<pre>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 1009 1019 1021 1031 1049 1051 1061 1063
1087 1091 1097 1103 1151 1163 1187 1217 1229 1249
1277 1289 1297 1301 1367 1373 1423 1427 1429 1439
19403
242057</pre>
=={{header|Nim}}==
{{trans|C++}}
I compiled using command <code>nim c -d:release -d:lto --gc:arc ramanujan_primes.nim</code>, i.e. with runtime checks on, link time optimization and using Arc garbage collector. To find the 100_000th Ramanujan prime, the program runs in about 100 ms on my laptop (i5-8250U CPU @ 1.60GHz, 8 GB Ram, Linux Manjaro).
<syntaxhighlight lang="nim">import math, sequtils, strutils, times
let t0 = now()
type PrimeCounter = seq[int]
proc initPrimeCounter(limit: Positive): PrimeCounter =
doAssert limit > 1
result = repeat(1, limit)
result[0] = 0
result[1] = 0
for i in countup(4, limit - 1, 2): result[i] = 0
var p = 3
var p2 = 9
while p2 < limit:
if result[p] != 0:
for q in countup(p2, limit - 1, p shl 1):
result[q] = 0
p2 += (p + 1) shl 2
if p2 >= limit: break
inc p, 2
# Compute partial sums in place.
var sum = 0
for item in result.mitems:
sum += item
item = sum
func ramanujanMax(n: int): int {.inline.} = int(ceil(4 * n.toFloat * ln(4 * n.toFloat)))
proc ramanujanPrime(pi: PrimeCounter; n: int): int =
if n == 1: return 2
var max = ramanujanMax(n)
if (max and 1) == 1: dec max
for i in countdown(max, 2, 2):
if pi[i] - pi[i div 2] < n:
return i + 1
let pi = initPrimeCounter(1 + ramanujanMax(100_000))
for n in 1..100:
stdout.write ($ramanujanPrime(pi, n)).align(4), if n mod 20 == 0: '\n' else: ' '
echo "\nThe 1000th Ramanujan prime is ", ramanujanPrime(pi, 1_000)
echo "The 10_000th Ramanujan prime is ", ramanujanPrime(pi, 10_000)
echo "The 100_000th Ramanujan prime is ", ramanujanPrime(pi, 100_000)
echo "\nElapsed time: ", (now() - t0).inMilliseconds, " ms"</syntaxhighlight>
{{out}}
<pre> 2 11 17 29 41 47 59 67 71 97 101 107 127 149 151 167 179 181 227 229
233 239 241 263 269 281 307 311 347 349 367 373 401 409 419 431 433 439 461 487
491 503 569 571 587 593 599 601 607 641 643 647 653 659 677 719 727 739 751 769
809 821 823 827 853 857 881 937 941 947 967 983 1009 1019 1021 1031 1049 1051 1061 1063
1087 1091 1097 1103 1151 1163 1187 1217 1229 1249 1277 1289 1297 1301 1367 1373 1423 1427 1429 1439
The 1000th Ramanujan prime is 19403
The 10_000th Ramanujan prime is 242057
The 100_000th Ramanujan prime is 2916539
Elapsed time: 99 ms</pre>
=={{header|Perl}}==
{{trans|Raku}}
{{libheader|ntheory}}
<syntaxhighlight lang="perl">use strict;
use warnings;
use ntheory 'primes';
sub count {
my($n,$p) = @_;
my $c = -1;
do { $c++ } until $$p[$c] > $n;
return $c;
}
my(@rp,@mem);
my $primes = primes( 100_000_000 );
sub r_prime {
my $n = shift;
for my $x ( reverse 1 .. int 4*$n * log(4*$n) / log 2 ) {
my $y = int $x / 2;
return 1 + $x if ($mem[$x] //= count($x,$primes)) - ($mem[$y] //= count($y,$primes)) < $n
}
}
push @rp, r_prime($_) for 1..100;
print "First 100:\n" . (sprintf "@{['%5d' x 100]}", @rp) =~ s/(.{100})/$1\n/gr;
print "\n\n 1000th: " . r_prime( 1000) . "\n";
print "\n10000th: " . r_prime(10000) . "\n"; # faster with 'ntheory' function 'ramanujan_primes'</syntaxhighlight>
{{out}}
<pre>First 100:
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 1009 1019 1021 1031 1049 1051 1061 1063
1087 1091 1097 1103 1151 1163 1187 1217 1229 1249 1277 1289 1297 1301 1367 1373 1423 1427 1429 1439
1000th: 19403
10000th: 242057</pre>
=={{header|Phix}}==
{{trans|
{{libheader|Phix/online}}
You can run this online [http://phix.x10.mx/p2js/Ramanujan_primes.htm here].
<!--<
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">
<span style="color: #008080;">
<span style="color: #
<span style="color: #008080;">if</span> <span style="color: #000000;">
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">
<span style="color: #008080;">while</span> <span style="color: #000000;">sq</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">limit</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">pi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">p</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">q</span><span style="color: #0000FF;">=</span><span style="color: #000000;">sq</span> <span style="color: #008080;">to</span> <span style="color: #000000;">limit</span> <span style="color: #008080;">by</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">*</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">pi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">q</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">sq</span> <span style="color: #0000FF;">+=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">p</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">4</span>
<span style="color: #000000;">p</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">2</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">total</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">limit</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">total</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">pi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">pi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">total</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">ramanujanMax</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">4</span><span style="color: #0000FF;">*</span><span style="color: #000000;">n</span><span style="color: #0000FF;">*</span><span style="color: #7060A8;">log</span><span style="color: #0000FF;">(</span><span style="color: #000000;">4</span><span style="color: #0000FF;">*</span><span style="color: #000000;">n</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">
<span style="color: #
<span style="color: #
<span style="color: #008080;">if</span> <span style="color: #000000;">pi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]-</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">[</span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)]</span> <span style="color: #0000FF;"><</span> <span style="color: #000000;">n</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
Line 97 ⟶ 1,019:
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">
<span style="color: #004080;">integer</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()=</span><span style="color: #004600;">JS</span><span style="color: #0000FF;">?</span><span style="color: #000000;">5</span><span style="color: #0000FF;">:</span><span style="color: #000000;">6</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">primeCounter</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ramanujanMax</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lim</span><span style="color: #0000FF;">)))</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">100</span><span style="color: #0000FF;">),</span><span style="color: #000000;">ramanujanPrime</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">,{{</span><span style="color: #008000;">"%5d"</span><span style="color: #0000FF;">},</span><span style="color: #000000;">r</span><span style="color: #0000FF;">}),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">))</span>
<span style="color: #
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Line 111 ⟶ 1,037:
1087 1091 1097 1103 1151 1163 1187 1217 1229 1249 1277 1289 1297 1301 1367 1373 1423 1427 1429 1439
The
The 10,000th Ramanujan prime is
The 100,000th Ramanujan prime is 2,916,539
The 1,000,000th Ramanujan prime is 34,072,993
"2.7s"
</pre>
<small>The last line is omitted under pwa/p2js since the primeCounter array is too much for Javascript to handle.</small>
=={{header|Python}}==
{{trans|Java}}
<syntaxhighlight lang="python">
import time
import math
class PrimeCounter:
"""Generate a list 'count' where count[n] is the number of primes less than or equal to n"""
def __init__(self, limit):
self.count = [1] * limit
count = self.count
if limit > 0:
count[0] = 0
if limit > 1:
count[1] = 0
for i in range(4, limit, 2):
count[i] = 0
p = 3
while p**2 < limit:
if count[p] != 0:
q = p**2
while q < limit:
count[q] = 0
q += p * 2
p += 2
for i, j in enumerate(count):
if i == 0:
continue
count[i] += count[i - 1]
def prime_count(self, n):
"""Get the number of primes less than or equal to n"""
if n > 0:
return self.count[n]
return 0
def ramanujan_prime_upper_bound(n):
"""Calculate the largest number the nth Ramanujan number could possibly be"""
return math.ceil(4 * n * math.log(4 * n))
def ramanujan_prime(prime_counter_in, n):
"""Generate the nth Ramanujan prime by finding the largest number 'i' where less than n primes are in the
range i//2 and i - the Ramanujan prime is one more than i"""
pci = prime_counter_in
for i in range(ramanujan_prime_upper_bound(n), -1, -1):
pi_n = pci.prime_count(i)
pi_half_n = pci.prime_count(i // 2)
if pi_n - pi_half_n < n:
return i + 1
return 0
def print_ramanujan_primes_in_range(start_number, end_number, prime_counter_in):
"""Print all Ramanujan primes between start_number (inclusive) and end_number (exclusive)"""
for i in range(start_number, end_number):
p = ramanujan_prime(prime_counter_in, i)
print(f"{p : <4}", end=" ")
if i % 10 == 0:
print()
def solve():
"""Return the first 100 Ramanujan primes and the 1000th, 10000th & 100000th Ramanujan primes"""
print("First 100 Ramanujan primes:\n")
largest_number_to_calculate = ramanujan_prime_upper_bound(100000) + 1
prime_counter = PrimeCounter(largest_number_to_calculate)
print_ramanujan_primes_in_range(1, 101, prime_counter)
print()
for number in (1_000, 10_000, 100_000):
answer = ramanujan_prime(prime_counter, number)
print(
f"The {number : >6}th ramanujan prime is {answer : >7}"
)
start = time.perf_counter()
solve()
end = time.perf_counter()
time_taken_ms = int((end - start) * 1000)
print(f"\nElapsed time: {time_taken_ms}ms")</syntaxhighlight>
{{out}}
<pre>
First 100 Ramanujan primes:
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 1009 1019 1021 1031 1049 1051 1061 1063
1087 1091 1097 1103 1151 1163 1187 1217 1229 1249
1277 1289 1297 1301 1367 1373 1423 1427 1429 1439
The 1000th ramanujan prime is 19403
The 10000th ramanujan prime is 242057
The 100000th ramanujan prime is 2916539
Elapsed time: 1460ms
</pre>
=={{header|Raku}}==
All timings are purely informational. Will vary by system specs and load.
=== Pure Raku ===
<syntaxhighlight lang="raku" line>use Math::Primesieve;
use Lingua::EN::Numbers;
my $primes = Math::Primesieve.new;
my @mem;
sub ramanujan-prime (\n) {
1 + (1..(4×n × (4×n).log / 2.log).floor).first: :end, -> \x {
my \y = x div 2;
((@mem[x] //= $primes.count(x)) - (@mem[y] //= $primes.count(y))) < n
}
}
say 'First 100:';
say (1..100).map( &ramanujan-prime ).batch(10)».&comma».fmt("%6s").join: "\n";
say "\n 1,000th: { comma 1000.&ramanujan-prime }";
say "10,000th: { comma 10000.&ramanujan-prime }";
say (now - INIT now).fmt('%.3f') ~ ' seconds';</syntaxhighlight>
{{out}}
<pre>First 100:
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
1,000th: 19,403
10,000th: 242,057
18.405 seconds</pre>
=== ntheory library ===
{{libheader|ntheory}}
<syntaxhighlight lang="raku" line>use ntheory:from<Perl5> <ramanujan_primes nth_ramanujan_prime>;
use Lingua::EN::Numbers;
say 'First 100:';
say ramanujan_primes( nth_ramanujan_prime(100) ).batch(10)».&comma».fmt("%6s").join: "\n";
for (2..12).map: {exp $_, 10} -> $limit {
say "\n{tc ordinal $limit}: { comma nth_ramanujan_prime($limit) }";
}
say (now - INIT now).fmt('%.3f') ~ ' seconds';</syntaxhighlight>
{{out}}
<pre>First 100:
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
One hundredth: 1,439
One thousandth: 19,403
Ten thousandth: 242,057
One hundred thousandth: 2,916,539
One millionth: 34,072,993
Ten millionth: 389,433,437
One hundred millionth: 4,378,259,731
One billionth: 48,597,112,639
Ten billionth: 533,902,884,973
One hundred billionth: 5,816,713,968,619
One trillionth: 62,929,891,461,461
15.572 seconds</pre>
=={{header|Wren}}==
{{
{{libheader|Wren-
{{libheader|Wren-fmt}}
<br>
This takes about 1.1 seconds to find the 100,000th Ramanujan prime on my machine. The millionth takes 13.2 seconds.
<syntaxhighlight lang="wren">import "./
import "./fmt" for Fmt
var count
var
count = List.filled(limit, 1)
if (limit > 0) count[0] = 0
for (i in Stepped.new(4...limit, 2)) count[i] = 0
var p = 3
var
while (sq < limit) {
if (count[p] != 0) {
var q = sq
while (q < limit) {
count[q] = 0
q = q + p * 2
}
}
sq = sq + (p + 1) * 4
p = p + 2
}
var sum = 0
for (i in 0...limit) {
sum = sum + count[i]
count[i] = sum
}
}
var primeCount = Fn.new { |n| (n < 1) ? 0 : count[n] }
var ramanujanMax = Fn.new { |n| (4 * n * (4*n).log).ceil }
var ramanujanPrime = Fn.new { |n|
if (n == 1) return 2
for (i in ramanujanMax.call(n)..2*n) {
if (i % 2 == 1) continue
if (primeCount.call(i) - primeCount.call((i/2).floor) < n) return i + 1
}
return 0
}
primeCounter.call(1 + ramanujanMax.call(1e6))
System.print("The first 100 Ramanujan primes are:")
var rams = (1..100).map { |n|
Fmt.print("\nThe 1,000th Ramanujan prime is $,6d",
Fmt.print("\nThe 10,000th Ramanujan prime is $,7d",
Fmt.print("\nThe 100,000th Ramanujan prime is $,9d", ramanujanPrime.call(100000))
Fmt.print("\nThe 1,000,000th Ramanujan prime is $,10d", ramanujanPrime.call(1000000))</syntaxhighlight>
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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
The 10,000th Ramanujan prime is 242,057
The 100,000th Ramanujan prime is 2,916,539
The 1,000,000th Ramanujan prime is 34,072,993
</pre>
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