Anaprimes: Difference between revisions
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For comparison, on the same (ten year old 16GB) box the Julia entry took 38s (2nd run) to complete to 9 digits.<br>
I simply don't have enough memory to attempt 10 digits, and in fact trying to run the Julia entry as-is forced a hard reboot.<br>
When transpiled to JavaScript and run
=={{header|Raku}}==
|
Revision as of 10:44, 2 February 2023
Anaprimes are prime numbers that are anagrams of each other, i.e. they use exactly the same digits with the same frequency but in a different order.
Anaprimes are very common. To illustrate this, we will investigate the sizes of the equivalence classes defined by the "is an anagram of" relation.
For example, the equivalence class of 149 has four anaprimes: {149, 419, 491, 941}. It turns out that there is no larger equivalence class of 3-digit anaprimes.
- Task
- Find prime numbers that are anagrams of each other.
- Find the largest anagram group of prime numbers and display the count, and minimum and maximum members for prime numbers:
- up to three digits long (before 1,000)
- up to four digits long (before 10,000)
- up to five digits long (before 100,000)
- up to six digits long (before 1,000,000)
- Stretch
- Find the largest anagram group and display the count, and smallest and largest members for prime numbers:
- up to seven digits long (before 10,000,000)
- up to eight digits long (before 100,000,000)
- up to nine digits long (before 1,000,000,000)
- ???!
- Related tasks
C++
This takes about 70 seconds on my system. Memory usage is 4G.
#include <algorithm>
#include <iomanip>
#include <iostream>
#include <map>
#include <vector>
#include <primesieve.hpp>
class digit_set {
public:
digit_set() {}
explicit digit_set(uint64_t n) {
for (; n > 0; n /= 10)
++count_[n % 10];
}
bool operator==(const digit_set& other) const {
return std::equal(count_, count_ + 10, other.count_);
}
bool operator<(const digit_set& other) const {
return std::lexicographical_compare(other.count_, other.count_ + 10,
count_, count_ + 10);
}
private:
int count_[10] = {};
};
int main() {
std::cout.imbue(std::locale(""));
primesieve::iterator pi;
using map_type = std::map<digit_set, std::vector<uint64_t>>;
map_type anaprimes;
for (uint64_t limit = 1000; limit <= 10000000000;) {
uint64_t prime = pi.next_prime();
if (prime > limit) {
size_t max_length = 0;
std::vector<map_type::iterator> groups;
for (auto i = anaprimes.begin(); i != anaprimes.end(); ++i) {
if (i->second.size() > max_length) {
groups.clear();
max_length = i->second.size();
}
if (max_length == i->second.size())
groups.push_back(i);
}
std::cout << "Largest group(s) of anaprimes before " << limit
<< ": " << max_length << " members:\n";
for (auto i : groups) {
std::cout << " First: " << i->second.front()
<< " Last: " << i->second.back() << '\n';
}
std::cout << '\n';
anaprimes.clear();
limit *= 10;
}
anaprimes[digit_set(prime)].push_back(prime);
}
}
- Output:
Largest group(s) of anaprimes before 1,000: 4 members: First: 149 Last: 941 First: 179 Last: 971 First: 379 Last: 937 Largest group(s) of anaprimes before 10,000: 11 members: First: 1,237 Last: 7,321 First: 1,279 Last: 9,721 Largest group(s) of anaprimes before 100,000: 39 members: First: 13,789 Last: 98,731 Largest group(s) of anaprimes before 1,000,000: 148 members: First: 123,479 Last: 974,213 Largest group(s) of anaprimes before 10,000,000: 731 members: First: 1,235,789 Last: 9,875,321 Largest group(s) of anaprimes before 100,000,000: 4,333 members: First: 12,345,769 Last: 97,654,321 Largest group(s) of anaprimes before 1,000,000,000: 26,519 members: First: 102,345,697 Last: 976,542,103 Largest group(s) of anaprimes before 10,000,000,000: 152,526 members: First: 1,123,465,789 Last: 9,876,543,211
Go
Getting up to 10 billion takes around 2 minutes 28 seconds on my Core i7 machine.
package main
import (
"fmt"
"rcu"
"sort"
)
func main() {
const limit = int(1e10)
const maxIndex = 9
primes := rcu.Primes(limit)
anaprimes := make(map[int][]int)
for _, p := range primes {
digs := rcu.Digits(p, 10)
key := 1
for _, dig := range digs {
key *= primes[dig]
}
if _, ok := anaprimes[key]; ok {
anaprimes[key] = append(anaprimes[key], p)
} else {
anaprimes[key] = []int{p}
}
}
largest := make([]int, maxIndex+1)
groups := make([][][]int, maxIndex+1)
for key := range anaprimes {
v := anaprimes[key]
nd := len(rcu.Digits(v[0], 10))
c := len(v)
if c > largest[nd-1] {
largest[nd-1] = c
groups[nd-1] = [][]int{v}
} else if c == largest[nd-1] {
groups[nd-1] = append(groups[nd-1], v)
}
}
j := 1000
for i := 2; i <= maxIndex; i++ {
js := rcu.Commatize(j)
ls := rcu.Commatize(largest[i])
fmt.Printf("Largest group(s) of anaprimes before %s: %s members:\n", js, ls)
sort.Slice(groups[i], func(k, l int) bool {
return groups[i][k][0] < groups[i][l][0]
})
for _, g := range groups[i] {
fmt.Printf(" First: %s Last: %s\n", rcu.Commatize(g[0]), rcu.Commatize(g[len(g)-1]))
}
j *= 10
fmt.Println()
}
}
- Output:
Largest group(s) of anaprimes before 1,000: 4 members: First: 149 Last: 941 First: 179 Last: 971 First: 379 Last: 937 Largest group(s) of anaprimes before 10,000: 11 members: First: 1,237 Last: 7,321 First: 1,279 Last: 9,721 Largest group(s) of anaprimes before 100,000: 39 members: First: 13,789 Last: 98,731 Largest group(s) of anaprimes before 1,000,000: 148 members: First: 123,479 Last: 974,213 Largest group(s) of anaprimes before 10,000,000: 731 members: First: 1,235,789 Last: 9,875,321 Largest group(s) of anaprimes before 100,000,000: 4,333 members: First: 12,345,769 Last: 97,654,321 Largest group(s) of anaprimes before 1,000,000,000: 26,519 members: First: 102,345,697 Last: 976,542,103 Largest group(s) of anaprimes before 10,000,000,000: 152,526 members: First: 1,123,465,789 Last: 9,876,543,211
jq
One point of interest here is the definition of `maximals_by/2` so that [size, min, max] details about all the maximally-sized groups in each category can be displayed.
General utilities
# return an array, $a, of length .+1 or .+2 such that
# $a[$i] is $i if $i is prime, and false otherwise.
def primeSieve:
# erase(i) sets .[i*j] to false for integral j > 1
def erase(i):
if .[i] then
reduce range(2; (1 + length) / i) as $j (.; .[i * $j] = false)
else .
end;
(. + 1) as $n
| (($n|sqrt) / 2) as $s
| [null, null, range(2; $n)]
| reduce (2, 1 + (2 * range(1; $s))) as $i (.; erase($i))
;
# Produce a stream of maximal elements in the stream s.
# To emit both the item and item|f, run: maximal_by( s | [., f]; .[1])
def maximals_by(s; f):
reduce s as $x ({v:null, a:[]};
($x|f) as $y
| if $y == .v then .a += [$x] elif $y > .v then .v = $y | .a = [$x] else . end)
| .a[];
# Input: the size of the sieve
def primes: primeSieve | map(select(.));
Anaprimes
# Input: null or a suitable array of primes
# Output: for each maximally sized group: [number, min, max]
def anaprimes($limit):
def stats:
maximals_by(.[]; length)
| [length, min, max];
def groupOf: tostring | explode | sort | implode;
(if . then . else $limit|primes end) as $primes
| reduce $primes[] as $p ({}; .[$p|groupOf] += [$p])
| stats;
def task($digits):
# Avoid recomputing the primes array:
(pow(10;$digits) | primes) as $primes
| range(3; $digits+1) as $i
| pow(10; $i) as $p
| "For \($i) digit numbers:",
($primes | map(select(.<$p)) | anaprimes($p)),
"";
task(7)
- Output:
For 3 digit numbers: [4,149,941] [4,179,971] [4,379,937] For 4 digit numbers: [11,1237,7321] [11,1279,9721] For 5 digit numbers: [39,13789,98731] For 6 digit numbers: [148,123479,974213] For 7 digit numbers: [731,1235789,9875321]
Julia
Takes a bit over 1.5 minutes on a 10-year-old Haswell i7 machine.
""" rosettacode.org task Anaprimes """
using Primes
@time for pow10 = 2:9
parr = primes(10^pow10, 10^(pow10 + 1))
anap = map(n -> evalpoly(10, sort!(digits(n))), parr)
anasorted = sort(anap)
longest, maxlen, maxstart, maxend = 0, 1, 1, 1
while maxstart < length(anasorted)
maxend = searchsortedfirst(anasorted, anasorted[maxstart] + 1)
if maxlen <= maxend - maxstart
maxlen = maxend - maxstart
longest = anasorted[maxend - 1]
end
maxstart = maxend
end
println(
"For $(pow10 + 1)-digit primes, a largest anagram group, [",
parr[findfirst(==(longest), anap)],
", ..",
parr[findlast(==(longest), anap)],
"], has a group size of $maxlen.",
)
end
- Output:
For 3-digit primes, a largest anagram group, [379, ..937], has a group size of 4. For 4-digit primes, a largest anagram group, [1279, ..9721], has a group size of 11. For 5-digit primes, a largest anagram group, [13789, ..98731], has a group size of 39. For 6-digit primes, a largest anagram group, [123479, ..974213], has a group size of 148. For 7-digit primes, a largest anagram group, [1235789, ..9875321], has a group size of 731. For 8-digit primes, a largest anagram group, [12345769, ..97654321], has a group size of 4333. For 9-digit primes, a largest anagram group, [102345697, ..976542103], has a group size of 26519. For 10-digit primes, a largest anagram group, [1123465789, ..9876543211], has a group size of 152526. 186.920326 seconds (455.94 M allocations: 72.961 GiB, 1.54% gc time, 0.02% compilation time)
Phix
with javascript_semantics atom t0 = time(), t1 = time()+1 function lastsame(sequence s, integer i) while i<length(s) and s[i+1]=s[i] do i += 1 end while return i end function integer start = length(get_primes_le(1e2))+1 printf(1,"Largest anagram groups:\n") for pow10=3 to iff(platform()=JS?8:9) do progress("getting_primes...\r") -- (~15s in total) sequence primes = get_primes_le(power(10,pow10)), anap = primes[start..$] for i,a in anap do -- (~4M/s, 16s in total) if time()>t1 then progress("converting %d/%d...\r",{i,length(anap)}) t1 = time()+1 end if integer sig = 0 while a do sig *= primes[remainder(a,10)+1] a = floor(a/10) end while anap[i] = sig end for progress("sorting...\r") -- (~16s in total) sequence anasorted = sort(deep_copy(anap)) progress("scanning...\r") -- (pretty fast) integer longest=0, maxlen = 1, maxstart = 1, maxend while maxstart <= length(anasorted) do maxend = lastsame(anasorted, maxstart)+1 if maxlen <= maxend-maxstart then maxlen = maxend-maxstart longest = anasorted[maxstart] end if maxstart = maxend end while progress("") integer lodx = find(longest,anap)+start-1, hidx = rfind(longest,anap)+start-1 string e = elapsed_short(time()-t0) printf(1,"%d-digits: [%d..%d], size %d (%s)\n",{pow10,primes[lodx],primes[hidx],maxlen,e}) start = length(primes)+1 end for
- Output:
Largest anagram groups: 3-digits: [101..997], size 143 (0s) 4-digits: [1009..9973], size 1061 (0s) 5-digits: [10007..99991], size 8363 (0s) 6-digits: [100003..999983], size 68906 (0s) 7-digits: [1000003..9999991], size 586081 (0s) 8-digits: [10000019..99999989], size 5096876 (4s) 9-digits: [100000007..999999937], size 45086079 (47s)
For comparison, on the same (ten year old 16GB) box the Julia entry took 38s (2nd run) to complete to 9 digits.
I simply don't have enough memory to attempt 10 digits, and in fact trying to run the Julia entry as-is forced a hard reboot.
When transpiled to JavaScript and run in a web browser, 8 digits took 18secs, so I capped it at that.
Raku
9 digit is slooow. I didn't have the patience for 10.
use Lingua::EN::Numbers;
use Math::Primesieve;
my $p = Math::Primesieve.new;
for 3 .. 9 {
my $largest = $p.primes(10**($_-1), 10**$_).classify(*.comb.sort.join).max(+*.value).value;
put "\nLargest group of anaprimes before {cardinal 10 ** $_}: {+$largest} members.";
put 'First: ', ' Last: ' Z~ $largest[0, *-1];
}
- Output:
Largest group of anaprimes before one thousand: 4 members. First: 179 Last: 971 Largest group of anaprimes before ten thousand: 11 members. First: 1237 Last: 7321 Largest group of anaprimes before one hundred thousand: 39 members. First: 13789 Last: 98731 Largest group of anaprimes before one million: 148 members. First: 123479 Last: 974213 Largest group of anaprimes before ten million: 731 members. First: 1235789 Last: 9875321 Largest group of anaprimes before one hundred million: 4,333 members. First: 12345769 Last: 97654321 Largest group of anaprimes before one billion: 26,519 members. First: 102345697 Last: 976542103
Wren
Getting up to 1 billion takes around 2 minutes 25 seconds on my Core i7 machine. I've left it at that.
import "./math" for Int
import "./fmt" for Fmt
var limit = 1e9
var maxIndex = 8
var primes = Int.primeSieve(limit)
var anaprimes = {}
for (p in primes) {
var digs = Int.digits(p)
var key = 1
for (dig in digs) key = key * primes[dig]
if (anaprimes.containsKey(key)) {
anaprimes[key].add(p)
} else {
anaprimes[key] = [p]
}
}
var largest = List.filled(maxIndex + 1, 0)
var groups = List.filled(maxIndex + 1, null)
for (key in anaprimes.keys) {
var v = anaprimes[key]
var nd = Int.digits(v[0]).count
var c = v.count
if (c > largest[nd-1]) {
largest[nd-1] = c
groups[nd-1] = [v]
} else if (c == largest[nd-1]) {
groups[nd-1].add(v)
}
}
var j = 1000
for (i in 2..maxIndex) {
Fmt.print("Largest group(s) of anaprimes before $,d: $,d members:", j, largest[i])
groups[i].sort { |a, b| a[0] < b[0] }
for (g in groups[i]) Fmt.print(" First: $,d Last: $,d", g[0], g[-1])
j = j * 10
System.print()
}
- Output:
Largest group(s) of anaprimes before 1,000: 4 members: First: 149 Last: 941 First: 179 Last: 971 First: 379 Last: 937 Largest group(s) of anaprimes before 10,000: 11 members: First: 1,237 Last: 7,321 First: 1,279 Last: 9,721 Largest group(s) of anaprimes before 100,000: 39 members: First: 13,789 Last: 98,731 Largest group(s) of anaprimes before 1,000,000: 148 members: First: 123,479 Last: 974,213 Largest group(s) of anaprimes before 10,000,000: 731 members: First: 1,235,789 Last: 9,875,321 Largest group(s) of anaprimes before 100,000,000: 4,333 members: First: 12,345,769 Last: 97,654,321 Largest group(s) of anaprimes before 1,000,000,000: 26,519 members: First: 102,345,697 Last: 976,542,103