Anaprimes

Anaprimes are prime numbers that are anagrams of each other; i.e. they use all of the same digits but in a different order.

Anaprimes are very common. There is an anagram group however, in each order of magnitude greater than two, that contains more members than any other.

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

Circular primes Ormiston pairs

Julia

""" rosettacode.org task Anagram primes """


using Primes

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.

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