user
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.
assistant
```
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;

```

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
```