Q:About primes?
- From: Dan <30pack@xxxxxxxxxxxxx>
- Date: Thu, 05 Jan 2006 16:38:20 EST
Q:About primes?
Why does a certain large prime require much more
processing time to verify its primality than one that
is more than 60 times its size?
e.g.
This prime below with 749 digits required 17+ hours to
establish its primality.
30535097901345064310236174839489700080459663520096
69602323498345043501772521614789116618159734458191
33012276115769665116991385003007412849595725955497
82539025065316343685145506155812832930826308169991
03235521001534695731579798918213609701985238868299
05496367134467697182318980972065541838326121951538
51781656086684834199171972635458068998756131746296
31420187415749557187675872346102211430205807025283
26705059999206625008430333192533577908997722753658
00363494431851465001513590565074718403193054203954
12026385658659107627667163043534168346074818615904
03907488402966740762510012534574398079748765760746
92538684507407889491956489657862373272667461155274
58446365135106689722576148786264906866555969699021
2902628454402671432601097708301629332576840702301
Whereas this prime below with 751 digits that is more
than 60 times the size of the above prime took a little
more than 5 hours to establish its primality.
21050265664569505769747657916173104050801827994035
28900317501493517070407298733921181990193407231801
43779408314930824549947110712317894480745373003159
21609632251704831259629428482666756056164418464321
45924606837701476025109370522412427317600804201258
57752617867042568131395890575081564774449072424545
61562203237127127715927715805695165379004622744086
33824748961582141083837458534816036730734320316375
10015304390077652342973808023948567899720274885017
91725615628604900118526886951303916264715442921635
01827664696110096809557007351405735419350432680968
09849034558962642757629291379218668705620426295819
31347136109687471629580989255229645075893447269762
76271163934758185867446989768887541305780135020808
082967563934122807704444794896789338846027416989917
Both verified as primes under the APRT-CLE process.
Dan
.
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