Thread for posting tiny primes - Page 37

CRGreathouse · 2010-09-07, 20:43

Quote:

Originally Posted by 3.14159

See here. There is nothing special about 835287624561584641455555490282511.

How does that tell me there's nothing special about it?

Quote:

Originally Posted by 3.14159

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

How do you propose to stop him?

3.14159 · 2010-09-07, 20:45

Quote:

Originally Posted by Charles

How does that tell me there's nothing special about it?

Not a Proth, Mersenne, or Fermat number, not a factorial/primorial/k-b-b number, nothing special about it. An odd prime number is all.

Quote:

Originally Posted by Charles

How do you propose to stop him?

Let's clear this up: sm88 never intended to make any list, he was making modifications to my list. Therefore, there is nothing to stop and this is irrelevant.

kar_bon · 2010-09-07, 20:46

Quote:

Originally Posted by 3.14159

See here. There is nothing special about 835287624561584641455555490282511.

So you only decide if the number is general or not?

CRG, you can post more such numbers, he even can't figure it out of his own (your number would be rank #1 if I/you have not mentioned it) and I will not do such search again!

3.14159 · 2010-09-07, 20:48

Quote:

Originally Posted by Karsten

So you only decide if the number is general or not?

If there are no remarkable/non-trivial properties about the number, it is a general number. Though I suppose I'm wrong there: I can easily set up where it is a factor of a Proth/Generalized Proth, etc.

It seems as if every integer has an interesting property or two.

3.14159 · 2010-09-07, 20:53

Using that number: 311200808643826446977257839095069700 * 2^540 + 1 is divisible by 835287624561584641455555490282511.

124491606493269288006783110814207807 * 150! + 1 is divisible by 835287624561584641455555490282511.

67992905416506165571512904391251448 * 7!⁶⁰ + 1 is divisible by 835287624561584641455555490282511.

Etc, etc..

kar_bon · 2010-09-07, 20:54

Quote:

Originally Posted by 3.14159

If there are no remarkable/non-trivial properties about the number, it is a general number.

Your number 835287624561584641455555490282511 = 52205476535099040090972218142657 * 2^4 - 1, so a special form, too!

3.14159 · 2010-09-07, 20:55

@Karsten: See posts 400 and 401.

CRGreathouse · 2010-09-07, 20:59

Quote:

Originally Posted by 3.14159

If there are no remarkable/non-trivial properties about the number, it is a general number.

That doesn't help, because we don't know what "remarkable" or "non-trivial" properties are. This is a standard fallacy of definition.

In particular, you haven't given a test that lets us determine, unambiguously, whether a number is general or not.

3.14159 · 2010-09-07, 21:00

Quote:

Originally Posted by Charles

In particular, you haven't given a test that lets us determine, unambiguously, whether a number is general or not.

If it's not a Proth/Generalized Proth/k-b-b/Fermat/Generalized Fermat/Cullen-Woodall/Generalized Cullen-Woodall/Mersenne/Fibonacci/Lucas/Generalized Fibonacci, it's a general number.

kar_bon · 2010-09-07, 21:02

Conclusion?

Every number can submit but you have to be sure, it was tested by trial division only!

So like a log-file with all N mod p or something like a test to verify.

CRGreathouse · 2010-09-07, 21:03

Quote:

Originally Posted by 3.14159

Ultimately, it seems that no definition would ever work.

So the category (and any other that uses the term "general") are ill-defined.

2010-09-07, 20:53	#401
3.14159 May 2010 Prime hunting commission. 3220₈ Posts	Using that number: 311200808643826446977257839095069700 * 2^540 + 1 is divisible by 835287624561584641455555490282511. 124491606493269288006783110814207807 * 150! + 1 is divisible by 835287624561584641455555490282511. 67992905416506165571512904391251448 * 7!⁶⁰ + 1 is divisible by 835287624561584641455555490282511. Etc, etc.. Last fiddled with by 3.14159 on 2010-09-07 at 20:53

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2010-09-07, 20:55	#403
3.14159 May 2010 Prime hunting commission. 2⁴×3×5×7 Posts	@Karsten: See posts 400 and 401.

2010-09-07, 21:02	#406
kar_bon Mar 2006 Germany 2908₁₀ Posts	Conclusion? Every number can submit but you have to be sure, it was tested by trial division only! So like a log-file with all N mod p or something like a test to verify.