Thread for posting tiny primes - Page 35

science_man_88 · 2010-09-07, 18:50

well I never knew about general forms meaning anything different anyway if i retract my 5iii statement the above is what you have conveyed to me from what posts i can find still.

3.14159 · 2010-09-07, 18:52

Quote:

Originally Posted by science_man_88

well I never knew about general forms meaning anything different anyway if i retract my 5iii statement the above is what you have conveyed to me from what posts i can find still.

Retract the subcategories entirely. I already submitted top primes for every category.

The largest so far is 219561 digits, submitted by Batalov.

Second largest is 118995 digits, submitted by me, followed by Max's 109443-digit prime for the -1 analogues of the Generalized Proth numbers.

science_man_88 · 2010-09-07, 18:55

Quote:

Originally Posted by science_man_88

okay technically

Code:

if

I did my research proper all until 5iii can go under 1

please note all the highlighting of the important words.

3.14159 · 2010-09-07, 18:58

I remember the good old days, four or so months ago.. When I became excited about finding a now measly 4000-digit prime. Fun times?

I think I remember the sequence of records I have made (Length of prime found in decimal digits): ≤ 1000, 2986, 4457, 5423, 8608, 13050, 27507, 40078, 77285, 118995, etc..

Sadly, 25-50% of them were already well-known cases.

Only the last four are of my own discovery for sure.

Since I snapped personal records by about 40k digits for about 2x in a row, I will search for a 165k-digit prime.

Using b = 2; n = 552600;

I measured the odds as 1 in 7366 when I removed 25 out of 26 candidates, or 96.1% of the candidates. To be safe, and quick, the k-range is 20 times the odds.

... If the odds are 1 in 7366, and there are 3460 candidates left; Does that mean I have only a 47% chance of finding a prime? And the sieve actually decreased my odds of finding a prime?

In that case; I'm going to increase the range by a factor of 15.

kar_bon · 2010-09-07, 19:23

Quote:

Originally Posted by CRGreathouse

OK, proof is done!

2077756847362348863128179 is prime, and this was proven only with trial division.

Good job so but I have to say this:

PI, just be more specific what you call a 'General number'!

Is the number above of your declared type?

3.14159 · 2010-09-07, 19:26

Quote:

Originally Posted by Karsten

PI, just be more specific what you call a 'General number'!

I call any integer that is not a special-form number a general number.

science_man_88 · 2010-09-07, 19:29

sorry for upsetting you Pi I just don't understand most of what I read some days.

all I can think of is something like k*b^n+c form for "general number" that fits one of the ones on the list.

science_man_88 · 2010-09-07, 19:31

Quote:

Originally Posted by 3.14159

I call any integer that is not a special-form number a general number.

okay well I have you stating they are all special form primes hence no primes on your list. yet all primes with a certain length should fit your list.

kar_bon · 2010-09-07, 19:31

Sorry, but the above number 2077756847362348863128179 is a cofactor of these numbers:

(4^109-1)/3, 2^218-1, 2^109+1, 2*2^108+1, 2^110+2, 2*2^109+2, 2^111+4, 2^110+4,
2^2507+1, 2^5014-1, (4^2507-1)/3, 2^10028-1 and perhaps much more.

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!

CRGreathouse · 2010-09-07, 19:31

Quote:

Originally Posted by 3.14159

Using b = 2; n = 552600;

I measured the odds as 1 in 7366 when I removed 25 out of 26 candidates, or 96.1% of the candidates. To be safe, and quick, the k-range is 20 times the odds.

The chance of a random odd number around 2^552600 being prime is about 2/log(2^552600). If you sieve up to about 4 trillion you should remove about 25/26 of candidate odd numbers.

Quote:

Originally Posted by 3.14159

... If the odds are 1 in 7366, and there are 3460 candidates left; Does that mean I have only a 47% chance of finding a prime? And the sieve actually decreased my odds of finding a prime?

I don't know how you'd come to that conclusion. In rough terms: You're starting with C candidates with probability p of being prime. You sieve out a fraction (S-1)/S of the candidates, giving you C/S remaining candidates with probability pS of being prime. The expectations remain the same.

kar_bon · 2010-09-07, 19:36

And that's why this type is ridiculous!

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

Sorry and thanks CRG!

Sorry: You lost your 1# place!
Thanks: to show this!

2010-09-07, 18:58	#378
3.14159 May 2010 Prime hunting commission. 11010010000₂ Posts	I remember the good old days, four or so months ago.. When I became excited about finding a now measly 4000-digit prime. Fun times? I think I remember the sequence of records I have made (Length of prime found in decimal digits): ≤ 1000, 2986, 4457, 5423, 8608, 13050, 27507, 40078, 77285, 118995, etc.. Sadly, 25-50% of them were already well-known cases. Only the last four are of my own discovery for sure. Since I snapped personal records by about 40k digits for about 2x in a row, I will search for a 165k-digit prime. Using b = 2; n = 552600; I measured the odds as 1 in 7366 when I removed 25 out of 26 candidates, or 96.1% of the candidates. To be safe, and quick, the k-range is 20 times the odds. ... If the odds are 1 in 7366, and there are 3460 candidates left; Does that mean I have only a 47% chance of finding a prime? And the sieve actually decreased my odds of finding a prime? In that case; I'm going to increase the range by a factor of 15. Last fiddled with by 3.14159 on 2010-09-07 at 19:20

2010-09-07, 19:29	#381
science_man_88 "Forget I exist" Jul 2009 Dumbassville 2⁶·131 Posts	sorry for upsetting you Pi I just don't understand most of what I read some days. all I can think of is something like kb^n+c form for "general number" that fits one of the ones on the list. Last fiddled with by science_man_88 on 2010-09-07 at 19:33*

2010-09-07, 19:36	#385
kar_bon Mar 2006 Germany 2²·727 Posts	And that's why this type is ridiculous! You can't spot a number 'general' or random or special! Sorry and thanks CRG! Sorry: You lost your 1# place! Thanks: to show this! Last fiddled with by kar_bon on 2010-09-07 at 19:37

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2010-09-07, 18:50	#375
science_man_88 "Forget I exist" Jul 2009 Dumbassville 2⁶×131 Posts	well I never knew about general forms meaning anything different anyway if i retract my 5iii statement the above is what you have conveyed to me from what posts i can find still.

2010-09-07, 19:31	#383
kar_bon Mar 2006 Germany 2²×727 Posts	Sorry, but the above number 2077756847362348863128179 is a cofactor of these numbers: (4^109-1)/3, 2^218-1, 2^109+1, 22^108+1, 2^110+2, 22^109+2, 2^111+4, 2^110+4, 2^2507+1, 2^5014-1, (4^2507-1)/3, 2^10028-1 and perhaps much more. 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!