05.12.2017

The Advent of Void: Day 5: perl-Math-Prime-Util

Folks that enjoy playing with numbers and riddles probably know factor(1), a small tool of coreutils to factorize a number:

% factor {32077..32079}
32077: 32077
32078: 2 43 373
32079: 3 17 17 37

Likewise, we can compute random prime numbers with libressl:

% openssl prime -generate -bits 16
63719
% factor 63719
63719: 63719

This works pretty well for numbers up to a certain size, but trying to check a 160-bit prime already takes a few seconds.

Luckily, there is Math::Prime::Util, a Perl library consisting of “utilities related to prime numbers, including fast sieves and factoring”. And it also contains two command line tools primes.pl and factor.pl, which are far more powerful than above tools.

For example, we can find all the first siblings of the prime twins below 100:

% primes.pl --twin 100 | fmt
3 5 11 17 29 41 59 71

Or compute all primes between 2256 and 2256+1000:

% primes.pl '2**256' +1000
115792089237316195423570985008687907853269984665640564039457584007913129640233
115792089237316195423570985008687907853269984665640564039457584007913129640237
115792089237316195423570985008687907853269984665640564039457584007913129640293
115792089237316195423570985008687907853269984665640564039457584007913129640423
115792089237316195423570985008687907853269984665640564039457584007913129640519
115792089237316195423570985008687907853269984665640564039457584007913129640693
115792089237316195423570985008687907853269984665640564039457584007913129640731
115792089237316195423570985008687907853269984665640564039457584007913129640743
115792089237316195423570985008687907853269984665640564039457584007913129640783
115792089237316195423570985008687907853269984665640564039457584007913129640867

factor.pl uses quite fancy algorithms, and has no trouble factorizing this 3⨯64-bit number, with --verbose it even says what it is trying:

% dc <<<'16356729367488596873 17354808482073126563 18118954313623728623 * * p' |
    factor.pl --verbose
...
small ecm (40k,40) found factor 18118954313623728623
SIMPQS found factor 16356729367488596873
...
5143389612051975703439435217628486568888382710496544633877:
    16356729367488596873 17354808482073126563 18118954313623728623

Finally we can look at all palindromic primes with 12 digits:

% primes.pl --palindr '10**12' '10**13'
1000008000001
1000017100001
1000024200001
1000027200001
...
9999961699999
9999970799999
9999980899999
9999987899999


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