Erdös-Selfridge categorization of primes
You are encouraged to solve this task according to the task description, using any language you may know.
A prime p is in category 1 if the prime factors of p+1 are 2 and or 3. p is in category 2 if all the prime factors of p+1 are in category 1. p is in category g if all the prime factors of p+1 are in categories 1 to g-1.
The task is first to display the first 200 primes allocated to their category, then assign the first million primes to their category, displaying the smallest prime, the largest prime, and the count of primes allocated to each category.
C++
<lang cpp>#include <algorithm>
- include <cassert>
- include <iomanip>
- include <iostream>
- include <map>
- include <vector>
- include <primesieve.hpp>
class erdos_selfridge { public:
explicit erdos_selfridge(int limit);
uint64_t get_prime(int index) const { return primes_[index].first; }
int get_category(int index);
private:
std::vector<std::pair<uint64_t, int>> primes_; size_t get_index(uint64_t prime) const;
};
erdos_selfridge::erdos_selfridge(int limit) {
primesieve::iterator iter;
for (int i = 0; i < limit; ++i)
primes_.emplace_back(iter.next_prime(), 0);
}
int erdos_selfridge::get_category(int index) {
auto& pair = primes_[index];
if (pair.second != 0)
return pair.second;
int max_category = 0;
uint64_t n = pair.first + 1;
for (int i = 0; n > 1; ++i) {
uint64_t p = primes_[i].first;
if (p * p > n)
break;
int count = 0;
for (; n % p == 0; ++count)
n /= p;
if (count != 0) {
int category = (p <= 3) ? 1 : 1 + get_category(i);
max_category = std::max(max_category, category);
}
}
if (n > 1) {
int category = (n <= 3) ? 1 : 1 + get_category(get_index(n));
max_category = std::max(max_category, category);
}
pair.second = max_category;
return max_category;
}
size_t erdos_selfridge::get_index(uint64_t prime) const {
auto it = std::lower_bound(primes_.begin(), primes_.end(), prime,
[](const std::pair<uint64_t, int>& p,
uint64_t n) { return p.first < n; });
assert(it != primes_.end());
assert(it->first == prime);
return std::distance(primes_.begin(), it);
}
auto get_primes_by_category(erdos_selfridge& es, int limit) {
std::map<int, std::vector<uint64_t>> primes_by_category;
for (int i = 0; i < limit; ++i) {
uint64_t prime = es.get_prime(i);
int category = es.get_category(i);
primes_by_category[category].push_back(prime);
}
return primes_by_category;
}
int main() {
const int limit1 = 200, limit2 = 1000000;
erdos_selfridge es(limit2);
std::cout << "First 200 primes:\n";
for (const auto& p : get_primes_by_category(es, limit1)) {
std::cout << "Category " << p.first << ":\n";
for (size_t i = 0, n = p.second.size(); i != n; ++i) {
std::cout << std::setw(4) << p.second[i]
<< ((i + 1) % 15 == 0 ? '\n' : ' ');
}
std::cout << "\n\n";
}
std::cout << "First 1,000,000 primes:\n";
for (const auto& p : get_primes_by_category(es, limit2)) {
const auto& v = p.second;
std::cout << "Category " << std::setw(2) << p.first << ": "
<< "first = " << std::setw(7) << v.front()
<< " last = " << std::setw(8) << v.back()
<< " count = " << v.size() << '\n';
}
}</lang>
- Output:
First 200 primes: Category 1: 2 3 5 7 11 17 23 31 47 53 71 107 127 191 383 431 647 863 971 1151 Category 2: 13 19 29 41 43 59 61 67 79 83 89 97 101 109 131 137 139 149 167 179 197 199 211 223 229 239 241 251 263 269 271 281 283 293 307 317 349 359 367 373 419 433 439 449 461 479 499 503 509 557 563 577 587 593 599 619 641 643 659 709 719 743 751 761 769 809 827 839 881 919 929 953 967 991 1019 1033 1049 1069 1087 1103 1187 1223 Category 3: 37 103 113 151 157 163 173 181 193 227 233 257 277 311 331 337 347 353 379 389 397 401 409 421 457 463 467 487 491 521 523 541 547 569 571 601 607 613 631 653 683 701 727 733 773 787 797 811 821 829 853 857 859 877 883 911 937 947 983 997 1009 1013 1031 1039 1051 1061 1063 1091 1097 1117 1123 1153 1163 1171 1181 1193 1217 Category 4: 73 313 443 617 661 673 677 691 739 757 823 887 907 941 977 1093 1109 1129 1201 1213 Category 5: 1021 First 1,000,000 primes: Category 1: first = 2 last = 10616831 count = 46 Category 2: first = 13 last = 15482669 count = 10497 Category 3: first = 37 last = 15485863 count = 201987 Category 4: first = 73 last = 15485849 count = 413891 Category 5: first = 1021 last = 15485837 count = 263109 Category 6: first = 2917 last = 15485857 count = 87560 Category 7: first = 15013 last = 15484631 count = 19389 Category 8: first = 49681 last = 15485621 count = 3129 Category 9: first = 532801 last = 15472811 count = 363 Category 10: first = 1065601 last = 15472321 count = 28 Category 11: first = 8524807 last = 8524807 count = 1
F#
This task uses Extensible Prime Generator (F#) <lang fsharp> // Erdös-Selfridge categorization of primes. Nigel Galloway: April 12th., 2022 let rec fG n g=match n,g with ((_,1),_)|(_,[])->n |((_,p),h::_) when h>p->n |((p,q),h::_) when q%h=0->fG (p,q/h) g |(_,_::g)->fG n g let fN g=Seq.unfold(fun(n,g)->let n,g=n|>List.map(fun n->fG n g)|>List.partition(fun(_,n)->n<>1) in let g=g|>List.map fst in if g=[] then None else Some(g,(n,g)))(primes32()|>Seq.take g|>Seq.map(fun n->(n,n+1))|>List.ofSeq,[2;3]) fN 200|>Seq.iteri(fun n g->printfn "Category %d: %A" (n+1) g) fN 1000000|>Seq.iteri(fun n g->printfn "Category %d: first->%d last->%d count->%d" (n+1) (List.head g) (List.last g) ( </lang>
- Output:
Category 1: [2; 3; 5; 7; 11; 17; 23; 31; 47; 53; 71; 107; 127; 191; 383; 431; 647; 863; 971; 1151] Category 2: [13; 19; 29; 41; 43; 59; 61; 67; 79; 83; 89; 97; 101; 109; 131; 137; 139; 149; 167; 179; 197; 199; 211; 223; 229; 239; 241; 251; 263; 269; 271; 281; 283; 293; 307; 317; 349; 359; 367; 373; 419; 433; 439; 449; 461; 479; 499; 503; 509; 557; 563; 577; 587; 593; 599; 619; 641; 643; 659; 709; 719; 743; 751; 761; 769; 809; 827; 839; 881; 919; 929; 953; 967; 991; 1019; 1033; 1049; 1069; 1087; 1103; 1187; 1223] Category 3: [37; 103; 113; 151; 157; 163; 173; 181; 193; 227; 233; 257; 277; 311; 331; 337; 347; 353; 379; 389; 397; 401; 409; 421; 457; 463; 467; 487; 491; 521; 523; 541; 547; 569; 571; 601; 607; 613; 631; 653; 683; 701; 727; 733; 773; 787; 797; 811; 821; 829; 853; 857; 859; 877; 883; 911; 937; 947; 983; 997; 1009; 1013; 1031; 1039; 1051; 1061; 1063; 1091; 1097; 1117; 1123; 1153; 1163; 1171; 1181; 1193; 1217] Category 4: [73; 313; 443; 617; 661; 673; 677; 691; 739; 757; 823; 887; 907; 941; 977; 1093; 1109; 1129; 1201; 1213] Category 5: [1021] Category 1: first->2 last->10616831 count->46 Category 2: first->13 last->15482669 count->10497 Category 3: first->37 last->15485863 count->201987 Category 4: first->73 last->15485849 count->413891 Category 5: first->1021 last->15485837 count->263109 Category 6: first->2917 last->15485857 count->87560 Category 7: first->15013 last->15484631 count->19389 Category 8: first->49681 last->15485621 count->3129 Category 9: first->532801 last->15472811 count->363 Category 10: first->1065601 last->15472321 count->28 Category 11: first->8524807 last->8524807 count->1
Factor
<lang factor>USING: assocs combinators formatting grouping grouping.extras io kernel math math.primes math.primes.factors math.statistics prettyprint sequences sequences.deep ;
PREDICATE: >3 < integer 3 > ;
GENERIC: depth ( seq -- n )
M: sequence depth
0 swap [ flatten1 [ 1 + ] dip ] to-fixed-point drop ;
M: integer depth drop 1 ;
MEMO: pfactors ( n -- seq ) 1 + factors ;
- category ( m -- n )
[ dup >3? [ pfactors ] when ] deep-map depth ;
- categories ( n -- assoc ) nprimes [ category ] collect-by ;
- table. ( seq n -- )
[ "" pad-groups ] keep group simple-table. ;
- categories... ( assoc -- )
[ [ "Category %d:\n" printf ] dip 15 table. ] assoc-each ;
- row. ( category first last count -- )
"Category %d: first->%d last->%d count->%d\n" printf ;
- categories. ( assoc -- )
[ [ minmax ] keep length row. ] assoc-each ;
200 categories categories... nl 1,000,000 categories categories.</lang>
- Output:
Category 1: 2 3 5 7 11 17 23 31 47 53 71 107 127 191 383 431 647 863 971 1151 Category 2: 13 19 29 41 43 59 61 67 79 83 89 97 101 109 131 137 139 149 167 179 197 199 211 223 229 239 241 251 263 269 271 281 283 293 307 317 349 359 367 373 419 433 439 449 461 479 499 503 509 557 563 577 587 593 599 619 641 643 659 709 719 743 751 761 769 809 827 839 881 919 929 953 967 991 1019 1033 1049 1069 1087 1103 1187 1223 Category 3: 37 103 113 151 157 163 173 181 193 227 233 257 277 311 331 337 347 353 379 389 397 401 409 421 457 463 467 487 491 521 523 541 547 569 571 601 607 613 631 653 683 701 727 733 773 787 797 811 821 829 853 857 859 877 883 911 937 947 983 997 1009 1013 1031 1039 1051 1061 1063 1091 1097 1117 1123 1153 1163 1171 1181 1193 1217 Category 4: 73 313 443 617 661 673 677 691 739 757 823 887 907 941 977 1093 1109 1129 1201 1213 Category 5: 1021 Category 1: first->2 last->10616831 count->46 Category 2: first->13 last->15482669 count->10497 Category 3: first->37 last->15485863 count->201987 Category 4: first->73 last->15485849 count->413891 Category 5: first->1021 last->15485837 count->263109 Category 6: first->2917 last->15485857 count->87560 Category 7: first->15013 last->15484631 count->19389 Category 8: first->49681 last->15485621 count->3129 Category 9: first->532801 last->15472811 count->363 Category 10: first->1065601 last->15472321 count->28 Category 11: first->8524807 last->8524807 count->1
Java
Uses the PrimeGenerator class from Extensible prime generator#Java. <lang java>import java.util.*;
public class ErdosSelfridge {
private int[] primes; private int[] category;
public static void main(String[] args) {
ErdosSelfridge es = new ErdosSelfridge(1000000);
System.out.println("First 200 primes:");
for (var e : es.getPrimesByCategory(200).entrySet()) {
int category = e.getKey();
List<Integer> primes = e.getValue();
System.out.printf("Category %d:\n", category);
for (int i = 0, n = primes.size(); i != n; ++i)
System.out.printf("%4d%c", primes.get(i), (i + 1) % 15 == 0 ? '\n' : ' ');
System.out.printf("\n\n");
}
System.out.println("First 1,000,000 primes:");
for (var e : es.getPrimesByCategory(1000000).entrySet()) {
int category = e.getKey();
List<Integer> primes = e.getValue();
System.out.printf("Category %2d: first = %7d last = %8d count = %d\n", category,
primes.get(0), primes.get(primes.size() - 1), primes.size());
}
}
private ErdosSelfridge(int limit) {
PrimeGenerator primeGen = new PrimeGenerator(100000, 200000);
List<Integer> primeList = new ArrayList<>();
for (int i = 0; i < limit; ++i)
primeList.add(primeGen.nextPrime());
primes = new int[primeList.size()];
for (int i = 0; i < primes.length; ++i)
primes[i] = primeList.get(i);
category = new int[primes.length];
}
private Map<Integer, List<Integer>> getPrimesByCategory(int limit) {
Map<Integer, List<Integer>> result = new TreeMap<>();
for (int i = 0; i < limit; ++i) {
var p = result.computeIfAbsent(getCategory(i), k -> new ArrayList<Integer>());
p.add(primes[i]);
}
return result;
}
private int getCategory(int index) {
if (category[index] != 0)
return category[index];
int maxCategory = 0;
int n = primes[index] + 1;
for (int i = 0; n > 1; ++i) {
int p = primes[i];
if (p * p > n)
break;
int count = 0;
for (; n % p == 0; ++count)
n /= p;
if (count != 0) {
int category = (p <= 3) ? 1 : 1 + getCategory(i);
maxCategory = Math.max(maxCategory, category);
}
}
if (n > 1) {
int category = (n <= 3) ? 1 : 1 + getCategory(getIndex(n));
maxCategory = Math.max(maxCategory, category);
}
category[index] = maxCategory;
return maxCategory;
}
private int getIndex(int prime) {
return Arrays.binarySearch(primes, prime);
}
}</lang>
- Output:
First 200 primes: Category 1: 2 3 5 7 11 17 23 31 47 53 71 107 127 191 383 431 647 863 971 1151 Category 2: 13 19 29 41 43 59 61 67 79 83 89 97 101 109 131 137 139 149 167 179 197 199 211 223 229 239 241 251 263 269 271 281 283 293 307 317 349 359 367 373 419 433 439 449 461 479 499 503 509 557 563 577 587 593 599 619 641 643 659 709 719 743 751 761 769 809 827 839 881 919 929 953 967 991 1019 1033 1049 1069 1087 1103 1187 1223 Category 3: 37 103 113 151 157 163 173 181 193 227 233 257 277 311 331 337 347 353 379 389 397 401 409 421 457 463 467 487 491 521 523 541 547 569 571 601 607 613 631 653 683 701 727 733 773 787 797 811 821 829 853 857 859 877 883 911 937 947 983 997 1009 1013 1031 1039 1051 1061 1063 1091 1097 1117 1123 1153 1163 1171 1181 1193 1217 Category 4: 73 313 443 617 661 673 677 691 739 757 823 887 907 941 977 1093 1109 1129 1201 1213 Category 5: 1021 First 1,000,000 primes: Category 1: first = 2 last = 10616831 count = 46 Category 2: first = 13 last = 15482669 count = 10497 Category 3: first = 37 last = 15485863 count = 201987 Category 4: first = 73 last = 15485849 count = 413891 Category 5: first = 1021 last = 15485837 count = 263109 Category 6: first = 2917 last = 15485857 count = 87560 Category 7: first = 15013 last = 15484631 count = 19389 Category 8: first = 49681 last = 15485621 count = 3129 Category 9: first = 532801 last = 15472811 count = 363 Category 10: first = 1065601 last = 15472321 count = 28 Category 11: first = 8524807 last = 8524807 count = 1
Julia
<lang julia>using Primes
primefactors(n) = collect(keys(factor(n)))
function ErdösSelfridge(n)
highfactors = filter(>(3), primefactors(n + 1))
category = 1
while !isempty(highfactors)
highfactors = unique(reduce(vcat, [filter(>(3), primefactors(a + 1)) for a in highfactors]))
category += 1
end
return category
end
function testES(numshowprimes, numtotalprimes)
println("First $numshowprimes primes by Erdös-Selfridge categories:")
dict = Dict{Int, Vector{Int}}(i => [] for i in 1:5)
for p in primes(prime(numshowprimes))
push!(dict[ErdösSelfridge(p)], p)
end
for cat in 1:5
println("$cat => ", dict[cat])
end
dict2 = Dict{Int, Tuple{Int, Int, Int}}(i => (0, 0, 0) for i in 1:11)
println("\nTotals for first $numtotalprimes primes by Erdös-Selfridge categories:")
for p in primes(prime(numtotalprimes))
cat = ErdösSelfridge(p)
fir, tot, las = dict2[cat]
fir == 0 && (fir = p)
dict2[cat] = (fir, tot + 1, p)
end
for cat in 1:11
first, total, last = dict2[cat]
println("Category", lpad(cat, 3), " => first:", lpad(first, 8), ", total:", lpad(total, 7), ", last:", last)
end
end
testES(200, 1_000_000)
</lang>
- Output:
First 200 primes by Erdös-Selfridge categories: 1 => [2, 3, 5, 7, 11, 17, 23, 31, 47, 53, 71, 107, 127, 191, 383, 431, 647, 863, 971, 1151] 2 => [13, 19, 29, 41, 43, 59, 61, 67, 79, 83, 89, 97, 101, 109, 131, 137, 139, 149, 167, 179, 197, 199, 211, 223, 229, 239, 241, 251, 263, 269, 271, 281, 283, 293, 307, 317, 349, 359, 367, 373, 419, 433, 439, 449, 461, 479, 499, 503, 509, 557, 563, 577, 587, 593, 599, 619, 641, 643, 659, 709, 719, 743, 751, 761, 769, 809, 827, 839, 881, 919, 929, 953, 967, 991, 1019, 1033, 1049, 1069, 1087, 1103, 1187, 1223] 3 => [37, 103, 113, 151, 157, 163, 173, 181, 193, 227, 233, 257, 277, 311, 331, 337, 347, 353, 379, 389, 397, 401, 409, 421, 457, 463, 467, 487, 491, 521, 523, 541, 547, 569, 571, 601, 607, 613, 631, 653, 683, 701, 727, 733, 773, 787, 797, 811, 821, 829, 853, 857, 859, 877, 883, 911, 937, 947, 983, 997, 1009, 1013, 1031, 1039, 1051, 1061, 1063, 1091, 1097, 1117, 1123, 1153, 1163, 1171, 1181, 1193, 1217] 4 => [73, 313, 443, 617, 661, 673, 677, 691, 739, 757, 823, 887, 907, 941, 977, 1093, 1109, 1129, 1201, 1213] 5 => [1021] Totals for first 1000000 primes by Erdös-Selfridge categories: Category 1 => first: 2, total: 46, last:10616831 Category 2 => first: 13, total: 10497, last:15482669 Category 3 => first: 37, total: 201987, last:15485863 Category 4 => first: 73, total: 413891, last:15485849 Category 5 => first: 1021, total: 263109, last:15485837 Category 6 => first: 2917, total: 87560, last:15485857 Category 7 => first: 15013, total: 19389, last:15484631 Category 8 => first: 49681, total: 3129, last:15485621 Category 9 => first: 532801, total: 363, last:15472811 Category 10 => first: 1065601, total: 28, last:15472321 Category 11 => first: 8524807, total: 1, last:8524807
Phix
You can run this online here (but expect a blank screen for about 20s)
with javascript_semantics sequence escache = {} function es_cat(integer p) if p>length(escache) and platform()!=JS then escache &= repeat(0,p-length(escache)) end if integer category = escache[p] if not category then sequence f = filter(prime_factors(p+1,false,-1),">",3) category = 1 if length(f) then category += max(apply(f,es_cat)) end if escache[p] = category end if return category end function procedure categorise(integer n) sequence p = get_primes(n) printf(1,"First %,d primes:\n",n) atom t1 = time() sequence es = {} for i=1 to n do if time()>t1 then progress("categorising %d/%d...",{i,n}) t1 = time()+1 end if integer category = es_cat(p[i]) while length(es)<category do es = append(es,{}) end while -- es[category] &= p[i] -- (sadly not p2js compatible...[yet]) sequence ec = es[category] es[category] = 0 ec &= p[i] es[category] = ec end for progress("") for c=1 to length(es) do sequence e = es[c] if n=200 then printf(1,"Category %d: %s\n",{c,join(shorten(e,"primes",5,"%d"),",")}) else printf(1,"Category %2d: %7d .. %-8d Count: %d\n",{c,e[1],e[$],length(e)}) end if end for printf(1,"\n") end procedure atom t0 = time() categorise(200) categorise(1e6) ?elapsed(time()-t0)
- Output:
First 200 primes: Category 1: 2,3,5,7,11,...,431,647,863,971,1151, (20 primes) Category 2: 13,19,29,41,43,...,1069,1087,1103,1187,1223, (82 primes) Category 3: 37,103,113,151,157,...,1163,1171,1181,1193,1217, (77 primes) Category 4: 73,313,443,617,661,...,1093,1109,1129,1201,1213, (20 primes) Category 5: 1021 First 1,000,000 primes: Category 1: 2 .. 10616831 Count: 46 Category 2: 13 .. 15482669 Count: 10497 Category 3: 37 .. 15485863 Count: 201987 Category 4: 73 .. 15485849 Count: 413891 Category 5: 1021 .. 15485837 Count: 263109 Category 6: 2917 .. 15485857 Count: 87560 Category 7: 15013 .. 15484631 Count: 19389 Category 8: 49681 .. 15485621 Count: 3129 Category 9: 532801 .. 15472811 Count: 363 Category 10: 1065601 .. 15472321 Count: 28 Category 11: 8524807 .. 8524807 Count: 1 "11.0s"
Takes about twice as long under pwa/p2js.
Raku
<lang perl6>use Prime::Factor; use Lingua::EN::Numbers; use Math::Primesieve; my $sieve = Math::Primesieve.new;
my %cat = 2 => 1, 3 => 1;
sub Erdös-Selfridge ($n) {
my @factors = prime-factors $n + 1;
my $category = max %cat{ @factors };
unless %cat{ @factors[*-1] } {
$category max= ( 1 + max %cat{ prime-factors 1 + @factors[*-1] } );
%cat{ @factors[*-1] } = $category;
}
$category
}
my $upto = 200;
say "First { cardinal $upto } primes; Erdös-Selfridge categorized:"; .say for sort $sieve.n-primes($upto).categorize: &Erdös-Selfridge;
$upto = 1_000_000;
say "\nSummary of first { cardinal $upto } primes; Erdös-Selfridge categorized:"; printf "Category %2d: first: %9s last: %10s count: %s\n", ++$, |(.[0], .[*-1], .elems).map: &comma for $sieve.n-primes($upto).categorize( &Erdös-Selfridge ).sort(+*.key)».value;</lang>
- Output:
First two hundred primes; Erdös-Selfridge categorized: 1 => [2 3 5 7 11 17 23 31 47 53 71 107 127 191 383 431 647 863 971 1151] 2 => [13 19 29 41 43 59 61 67 79 83 89 97 101 109 131 137 139 149 167 179 197 199 211 223 229 239 241 251 263 269 271 281 283 293 307 317 349 359 367 373 419 433 439 449 461 479 499 503 509 557 563 577 587 593 599 619 641 643 659 709 719 743 751 761 769 809 827 839 881 919 929 953 967 991 1019 1033 1049 1069 1087 1103 1187 1223] 3 => [37 103 113 151 157 163 173 181 193 227 233 257 277 311 331 337 347 353 379 389 397 401 409 421 457 463 467 487 491 521 523 541 547 569 571 601 607 613 631 653 683 701 727 733 773 787 797 811 821 829 853 857 859 877 883 911 937 947 983 997 1009 1013 1031 1039 1051 1061 1063 1091 1097 1117 1123 1153 1163 1171 1181 1193 1217] 4 => [73 313 443 617 661 673 677 691 739 757 823 887 907 941 977 1093 1109 1129 1201 1213] 5 => [1021] Summary of first one million primes; Erdös-Selfridge categorized: Category 1: first: 2 last: 10,616,831 count: 46 Category 2: first: 13 last: 15,482,669 count: 10,497 Category 3: first: 37 last: 15,485,863 count: 201,987 Category 4: first: 73 last: 15,485,849 count: 413,891 Category 5: first: 1,021 last: 15,485,837 count: 263,109 Category 6: first: 2,917 last: 15,485,857 count: 87,560 Category 7: first: 15,013 last: 15,484,631 count: 19,389 Category 8: first: 49,681 last: 15,485,621 count: 3,129 Category 9: first: 532,801 last: 15,472,811 count: 363 Category 10: first: 1,065,601 last: 15,472,321 count: 28 Category 11: first: 8,524,807 last: 8,524,807 count: 1
Wren
Runs in about 23.5 seconds. <lang ecmascript>import "./math" for Int import "./fmt" for Fmt
var limit = (1e6.log * 1e6 * 1.2).floor // should be more than enough var primes = Int.primeSieve(limit)
var prevCats = {}
var cat // recursive cat = Fn.new { |p|
if (prevCats.containsKey(p)) return prevCats[p]
var pf = Int.primeFactors(p+1)
if (pf.all { |f| f == 2 || f == 3 }) return 1
if (p > 2) {
for (i in pf.count-1..1) {
if (pf[i-1] == pf[i]) pf.removeAt(i)
}
}
for (c in 2..11) {
if (pf.all { |f| cat.call(f) < c }) {
prevCats[p] = c
return c
}
}
return 12
}
var es = List.filled(12, null) for (i in 0..11) es[i] = []
System.print("First 200 primes:\n ") for (p in primes[0..199]) {
var c = cat.call(p) es[c-1].add(p)
} for (c in 1..6) {
if (es[c-1].count > 0) {
System.print("Category %(c):")
System.print(es[c-1])
System.print()
}
}
System.print("First million primes:\n") for (p in primes[200...1e6]) {
var c = cat.call(p) es[c-1].add(p)
} for (c in 1..12) {
var e = es[c-1]
if (e.count > 0) {
Fmt.print("Category $-2d: First = $7d Last = $8d Count = $6d", c, e[0], e[-1], e.count)
}
}</lang>
- Output:
First 200 primes: Category 1: [2, 3, 5, 7, 11, 17, 23, 31, 47, 53, 71, 107, 127, 191, 383, 431, 647, 863, 971, 1151] Category 2: [13, 19, 29, 41, 43, 59, 61, 67, 79, 83, 89, 97, 101, 109, 131, 137, 139, 149, 167, 179, 197, 199, 211, 223, 229, 239, 241, 251, 263, 269, 271, 281, 283, 293, 307, 317, 349, 359, 367, 373, 419, 433, 439, 449, 461, 479, 499, 503, 509, 557, 563, 577, 587, 593, 599, 619, 641, 643, 659, 709, 719, 743, 751, 761, 769, 809, 827, 839, 881, 919, 929, 953, 967, 991, 1019, 1033, 1049, 1069, 1087, 1103, 1187, 1223] Category 3: [37, 103, 113, 151, 157, 163, 173, 181, 193, 227, 233, 257, 277, 311, 331, 337, 347, 353, 379, 389, 397, 401, 409, 421, 457, 463, 467, 487, 491, 521, 523, 541, 547, 569, 571, 601, 607, 613, 631, 653, 683, 701, 727, 733, 773, 787, 797, 811, 821, 829, 853, 857, 859, 877, 883, 911, 937, 947, 983, 997, 1009, 1013, 1031, 1039, 1051, 1061, 1063, 1091, 1097, 1117, 1123, 1153, 1163, 1171, 1181, 1193, 1217] Category 4: [73, 313, 443, 617, 661, 673, 677, 691, 739, 757, 823, 887, 907, 941, 977, 1093, 1109, 1129, 1201, 1213] Category 5: [1021] First million primes: Category 1 : First = 2 Last = 10616831 Count = 46 Category 2 : First = 13 Last = 15482669 Count = 10497 Category 3 : First = 37 Last = 15485863 Count = 201987 Category 4 : First = 73 Last = 15485849 Count = 413891 Category 5 : First = 1021 Last = 15485837 Count = 263109 Category 6 : First = 2917 Last = 15485857 Count = 87560 Category 7 : First = 15013 Last = 15484631 Count = 19389 Category 8 : First = 49681 Last = 15485621 Count = 3129 Category 9 : First = 532801 Last = 15472811 Count = 363 Category 10: First = 1065601 Last = 15472321 Count = 28 Category 11: First = 8524807 Last = 8524807 Count = 1