Re: Pell's Equation



Bruce Stephens wrote:

These numbers (commonly 1024 bits for RSA public keys) are *not* "too
large to store in a computer".

It should be obvious to you that computers can easily process 1024 bit
(and larger) numbers in various ways,

Dude! 1024 bits?! That's like a vector of 32 32-bit numbers!

Most Lisps (including Schemes) have arbitrary precision integer and
rational arithmetic, for example. A more common example is Python:
type "2**1024" into a python interpreter and it'll tell you what 2 to
the power of 1024 is, exactly. Just about all languages have
libraries that provide the same functionality, for example
<http://portal.acm.org/citation.cfm?id=164394>.

Indeed.

$ time echo 2^4096 | bc
10443888814131525066917527107166243825799642490473837803842334832839\
53907971557456848826811934997558340890106714439262837987573438185793\
60726323608785136527794595697654370999834036159013438371831442807001\
18559462263763188393977127456723346843445866174968079087058037040712\
84048740118609114467977783598029006686938976881787785946905630190260\
94059957945343282346930302669644305902501597239986771421554169383555\
98852914863182379144344967340878118726394964751001890413490084170616\
75093668333850551032972088269550769983616369411933015213796825837188\
09183365675122131849284636812555022599830041234478486259567449219461\
70238065059132456108257318353800876086221028342701976982023131690176\
78006675195485079921636419370285375124784014907159135459982790513399\
61155179427110683113409058427288427979155484978295432353451706522326\
90613949059876930021229633956877828789484406160074129456749198230505\
71642377154816321380631045902916136926708342856440730447899971901781\
46576347322385026725305989979599609079946920177462481771844986745565\
92501783290704731194331655508075682218465717463732968849128195203174\
57002440926616910874148385078411929804522981857338977648103126085903\
00130241346718972667321649151113160292078173803343609024380470834040\
3154190336

real 0m0.046s
user 0m0.077s
sys 0m0.015s

Regards.
.