Prime Numbers

Professor Curtis Cooper at the University of Central Missouri discovered the largest known prime number yet.  It has 17,425,170 digits.

The first prime number with more than 1000 digits was discovered in 1961.

There is a simple way of calculating numbers that are probably prime.  It is the java code BigInteger.probablePrime.  Using it, I "discovered" a prime number with 1000 bits (about 300 digits).  It is:

9963674221904846875004772742469716240732284806163235306913601541068702535788035 8378248279121641026337062302563348112132220511521684958059818512338166399380059 4983486852057091915348457165611833585904793747452915201707995380350741640019955 1120494915326023684727757570487388716610506004667245348348035339

It took me less than 1 second to discover it, but 2.5 minutes to verify.  So they are much easier to verify than to confirm.
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Here is my second one, with 1500 bits (452 digits).

25821946823221687522800424764255519248762418770863643515671235367728004958 43261339156595164772295234679488002729082955939137621881986803719731294045 85403471375481951013067766013678456489995577498445349621663202412034263558 21038104542039211091289904109996684240836306040789041229458170533339070257 41448572078455272772922999923855505972318320804848009087721107525013352919 54583237665867308649558396079879540422728192166051936072805882614239832132 46000179

Again, it took less than 1 second to calculate, but more than 17 minutes to verify.  So that is about the limit of what I am interested in.

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And one more, with 1600 bits and 482 digits.

3040700700214984479875619957483325563622095794966743260938998049255575 4995386466199958284474576857218213559757049761841725155157355055706282 2090906970039482518550080806618544945855248534043470119521303942938666 0599863811665338205935421825887348293033335335284598589012993429811234 2764605567198782802556435661163618605294783095296064381839243281355193 6727705550818897799868100353229755172386944276609945399486599939193802 82050193503823222185322023568758977555023827777796303357693187

This took 21:22 to verify.