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Editing: bigprimes.pl
#!/usr/bin/perl -w use Test; BEGIN { plan tests => 17; } use lib '../lib'; # comment out to use old module #use lib '../../old/Math-BigInt-0.01/lib'; # for old version use strict; #use Math::BigInt; use Math::BigInt qw/:constant/; #use Math::BigInt qw/calc BitVect :constant/; print "# Using Math::BigInt v",$Math::BigInt::VERSION,"\n"; # calculate some sample prime numbers from # http://www.utm.edu/research/primes/largest.html # also: http://www-stud.enst.fr/~bellard/mersenne.html # (c takes 1 minute on 800 Mhz, so Perl will take..ages..) my ($x,$y,$z); my $two = Math::BigInt->new(2); # some new() are to make stop Perl from calculating things like 1234 ** 4321 # at compile time. (we want to see run-time behaviour) # Also there is len(), since the old BigInt has not got length() and we want # this script to be comparable between old and new version. ############################################################################## # Todo: these do not complete in reasonable time: # $x = $two ** 6972593; $x--; #ok (len($x),'2098960'); # $x = $two ** 3021377; $x--; #ok (len($x),'909526'); # $x = $two ** 756839; $x--; #ok (len($x),'227832'); # $x = 1041870 ** 32768; $x++; #ok (len($x),'197192'); ############################################################################## # but these do: # some twin primes (first in list at 03/2001) $x = ($two ** 80025) * 665551035; $x++; $y = $x-2; ok (len($x),'24099'); $x = ($two ** 66443) * 1693965; $x++; $y = $x-2; ok (len($x),'20008'); $x = ($two ** 64955) * 83475759; $x++; $y = $x-2; ok (len($x),'19562'); # ... $x = ($two ** 38880) * 242206083; $x++; $y = $x-2; ok (len($x),'11713'); ############################################################################## # Sophie Germain primes # todo: does not finish after 30 m on 800 Mhz # $x = Math::BigInt->new(72021)**223630; $x--; ok (len($x),'7119'); ############################################################################## # some quadruplet primes... # 3510160221387831655*(2^3363-2^1121)-6*2^1121-7 $x = '3510160221387831655' * (2 ** 3363 - 2**1121) - 6*(2**1121); my @q = ( $x-7,$x-5,$x-1,$x+1); ok (len($q[0]),'1031'); ok (len($q[1]),'1031'); ok (len($q[2]),'1031'); ok (len($q[3]),'1031'); ############################################################################## # some real weird primes: # (2^3833-1)/(14193959303*340789152474053904109001) $x = Math::BigInt->new('340789152474053904109001'); $x *= '14193959303'; $x = (2**3833-1) / $x; ok (len($x),'1121'); #(2^4751-1)/(268982617*3274778783*629530076753*81630665742097*1507074535068001) $x = Math::BigInt->new('268982617'); $x = $x * '3274778783' * '629530076753' * '81630665742097' * '1507074535068001'; $x = ((2**4751)-1) / $x; ok (len($x),'1372'); # 2^7039-1)/ (1252943*1057032553*8541573097*218216841131937276721 $x = Math::BigInt->new('1252943')*'1057032553'*'8541573097'; $x *= '218216841131937276721'; $x = ((2**7039)-1) / $x; ok (len($x),'2074'); # 5616^1153-1)/5615 $x = Math::BigInt->new(5616) ** 1153; $x--; $x /= 5616; ok (len($x),'4320'); # (7147^2161-1)/7146 $x = Math::BigInt->new(7147) ** 2161; $x--; $x /= 7146; ok (len($x),'8325'); # 16*R(5700)*(150093*10^8000+1)+1 # most ending 7's # gives error in BigInt $x = 16 * R(5700); $x *= (150093*(Math::BigInt->new(10)**8000))+1; $x++; ok (len($x),'13706'); # 2*11^13359+1 $x = 2*(Math::BigInt->new(11)**13359)+1; ok(len($x),'13913'); # 10^14800+5*(10^8880+10^5920)+7*10^7400+1 # palindrome $x = Math::BigInt->new(10) ** 14800; $x += 5*((Math::BigInt->new(10) ** 8800) + (Math::BigInt->new(10)**5920)); $x += 7*(Math::BigInt->new(10) ** 7400); ok(len($x),'14801'); $y = "$x"; $y =~ s/^\+//; my $left = substr("$y",7400); my $right = substr("$y",-7401); ok($left,$right); # EOF ############################################################################## # some helper functions sub R { my $x = shift; # These numbers have a decimal expansion of n '1's, # and are usually called "repunits". return ((Math::BigInt->new(10) ** $x) - 1)/9; } sub len { # old bigint has not got length, so use "" and strip it's sign my $x = shift; $x = "$x"; $x =~ s/^\+//; return length($x); }
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