Thread for posting tiny primes

[CRGreathouse]

Ding ding ding! kar_bon wins the prize. In this case I calculated it as N=(2^109+1)/3/104124649 and checked it with a quick GP script that finds the appropriate residue classes mod 8p. The running time was about 10 minutes on a slow computer.

My current project, 7984559573504259856359124657, is similar.

[CRGreathouse]

Originally Posted by kar_bon

And that's why this type is ridiculous!

Indeed, demonstrating this was my purpose.

Originally Posted by kar_bon

You can't spot a number 'general' or random or special!

Honestly, even aside from what Pi calls "trickery" (and I call "using math"), I'd love to see a good definition of general here that works, um, in general.

[kar_bon]

Originally Posted by CRGreathouse

My current project, 7984559573504259856359124657, is similar.

Cofactor of 2^149+1.

[3.14159]

Originally Posted by kar_bon

So it has a special form (cofactor of a Mersenne number for example!) and you are not able to notice this, so you have to specify your 'general number' type!

Nope. General cofactor is general cofactor.

Arguably, if you tried this trick, every prime would be a special-form number. Next!

[kar_bon]

Originally Posted by 3.14159

Nope. General cofactor is general cofactor.

Arguably, if you tried this trick, every prime would be a special-form number. Next!

No!

CRG gave the test he done to determine and it was not pure trial devision (test all primes from 3 to sqrt(N))!

And this prime has a special form, too!

If you declare this as 'general' why excluding Mersennes then?

[science_man_88]

Originally Posted by 3.14159

Nope. General cofactor is general cofactor.

Arguably, if you tried this trick, every prime would be a special-form number. Next!

are you saying we have to give you numbers of the general form of the ones on the list ? = general number ? I'm too confused to use logic anymore.

[CRGreathouse]

There's no way either of my numbers should count, in this context, as general numbers. The first one is 16 times easier to test than numbers of a comparable size; the second one is 19 times easier.

[3.14159]

Originally Posted by CRGreathouse

There's no way either of my numbers should count, in this context, as general numbers. The first one is 16 times easier to test than numbers of a comparable size; the second one is 19 times easier.

Here is an example of a general prime number:

835287624561584641455555490282511.

Here are 15 more examples:

348487007766634158834636277
46560109657576346735092487
277045504717467997710674401
216353885495012554061838517
632417547715984582289542201
624143746064634996383204353
90337507053320000006494187
54641588316034625817275383
157930264101508085911914083
737009482404243882804250081
601816399408713215418216769
833980612206480789317355653
167460761731424310078485189
547615446859522251920656277
820438575567154351773751057

[CRGreathouse]

Originally Posted by 3.14159

Here is an example of a general prime number:

835287624561584641455555490282511.

Thanks, but that doesn't tell me anything useful. There are 9 * 10³² 33-digit numbers, and most of them aren't 835287624561584641455555490282511.

[CRGreathouse]

Originally Posted by 3.14159

Retract the subcategories entirely.

sm can make his own categories and run his own competition, even if some of his categories are proper subcategories of yours.

[3.14159]

See here. There is nothing special about 835287624561584641455555490282511.

Originally Posted by Charles

sm can make his own categories and run his own competition, even if some of his categories are proper subcategories of yours.

I never said he could not. Just don't base it on mine. End of story.

As I was saying: The only property I would consider "special" of 835287624561584641455555490282511 is that 835287624561584641455555490282510! + 1 is divisible by 835287624561584641455555490282511.